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<div class="Section1"> <h1 style='page-break-after:auto'><a name="node0" id= "node0"></a>Introduction</h1> <p class="MsoBodyText">Pictorial Image Processor© is a designed as a tool for development of image processing algorithms, testing the algorithms on plethora of images with a capability to store any intermediary image results. The goal of Pictorial Image Processor© project is to enable the developer of image analysis algorithms to perform a quick interactive prototyping, test algorithms on multiplicity of images, record test results and present the proposed algorithms to customers. End users of these algorithms would have means to identify the cases where the logic of the proposed algorithms is flawed and convey the images in question back to the developers. Thus Pictorial Image Processor© creates a common platform for image processing algorithm development and usage with fast feedback.</p> <p class="MsoBodyText">The application can also be useful for the students who are interested in image analysis and can get a hands-on experience with different techniques used in this area of information technology.</p> <span style= 'font-size:10.0pt;font-family:"Times New Roman"'><br clear="all" style='page-break-before:always'></span> <p class="MsoBodyText"> </p> <h2><a name="node1" id="node1"></a>Version Info</h2> <p class="MsoBodyText">This help describes Pictorial Image Processor version 2.1</p> <span style= 'font-size:10.0pt;font-family:"Times New Roman"'><br clear="all" style='page-break-before:always'></span> <p class="MsoBodyText"> </p> <h1><a name="node2" id="node2"></a>Using Pictorial Image Processor</h1> <p class="MsoBodyText"><img width="627" height="329" src= "PIPUserManualNoFootnotes_files/image001.jpg" alt= "image"><br clear="all"> Each image analysis algorithm developed by the user make a project, which can be stored in a form of a project file. The file has the extension pxp. The file contains information about the <a href= "start.htm#_Operations">operations</a> performed by the algorithm blocks, <a href="start.htm#_Operands">operands</a> and their position on the project canvas. Project files are text files compliant with XML standard and can be viewed and edited by any text editor. We don’t recommend editing *.pxp since it can lead to corruption of the project information.</p> <p class="MsoBodyText"> </p> <p class="MsoBodyText">By opening the project file in the Pictorial Image Processor© user can re-run the algorithm stored. During re-run the project window follows the last performed operation keeping it always within the viewport. Progress of the project recalculation is shown by the progress bar which appears in the status bar at the bottom of the main window. The bar shows approximately the position of the currently performed operation in the total list of the operations for the project. Some operations, like convolutions may take noticeable time to complete. As the operation is being performed, a small box with a running indicator appears on the control bar. User may chose to analyse images, results of already performed operations by double-clicking on them, while other long operations are performed. </p> <p class="MsoBodyText"><img border="0" width="600" height="29" src= "PIPUserManualNoFootnotes_files/image002.jpg" alt="image"></p> <p class="MsoBodyText"> </p> <p class="MsoBodyText">Drag and drop operation for the projects is supported. This mode can be used for processing multiple projects simultaneously creating a form of batch processing mode.</p> <span style= 'font-size:10.0pt;font-family:"Times New Roman"'><br clear="all" style='page-break-before:always'></span> <p class="MsoBodyText"> </p> <h2><a name="_Basic_steps"></a>Basic steps</h2> <p class="MsoBodyText">On starting Pictorial Image Processor© user sees a project canvas. By double-clicking on any point within the canvas user gets access to a pop-up menu of new operand creation. Currently 2 types of operands are supported: image and scalar operands.</p> <p class="MsoNormal" style='margin-right:-25.55pt'><img border="0" width="254" height="251" src= "PIPUserManualNoFootnotes_files/image003.jpg" alt="image"></p> <p class="MsoBodyText">By selecting an image operand user gets access to the Open File dialog. See <a href= "start.htm#_Open_Image">Open Image</a> for more detail. Upon selection of image operand into the project a thumbnail of the image appears on the canvas within the operand rectangle. In order to use the image area more efficiently first thumbnail of the project is placed not where the mouse was clicked but at the top left hand of the project window. All other thumbnails are snapped to an invisible grid to ensure their uniform spacing.</p> <p class="MsoBodyText"><img border="0" width="260" height="283" src="PIPUserManualNoFootnotes_files/image004.jpg" alt="image"></p> <p class="MsoBodyText">By selecting a scalar operand user gets access to a dialog string where user can enter an operand consisting of single number, e.g. a threshold value which will be later used in a threshold operation. Typing scalar value and pressing “Enter” creates a scalar operand represented on the project canvas by the rectangle with the value in it.</p> <p class="MsoBodyText"><img border="0" width="266" height="309" src="PIPUserManualNoFootnotes_files/image005.gif" alt="image"></p> <p class="MsoBodyText">After entering 2 operands user can apply a binary operation to them, for example grey level thresholding operation at the level set by the scalar operand. After this operation a new binary image is created where all pixels having the grey value higher than given threshold will become foreground (white), while those pixels</p> <p class="MsoNormal" style='margin-right:-25.55pt'><img border="0" width="557" height="438" src= "PIPUserManualNoFootnotes_files/image006.jpg" alt="image"></p> <p class="MsoNormal" style='margin-right:-25.55pt'> </p> <p class="MsoBodyText">with the grey level lower or equal to the threshold will become background (black ) pixels.</p> <p class="MsoBodyText"><img border="0" width="378" height="388" src="PIPUserManualNoFootnotes_files/image007.jpg" alt="image"></p> <p class="MsoBodyText">Upon selection of the operation the operation result appears as a new operand. This operand is preceded on the project canvas by an icon or icons representing the operation. The icons are listed in the <a href= "start.htm#_Operations">operation description section</a> of the manual. Icon is connected with the lines to the operands that participated in the operation to create the result. The number of icons depends on how ambiguous the relationships between the input operands could be with respect to the operation result. For example, in operations like sum of 2 operands there is no difference which operand is used as a source image and which is added to it, where as in operations like difference of 2 operands the result can be very different if the operands are swapped, especially taking into account that the majority of modern images are coded with unsigned integers. For such operations with ambiguity in role of the operands we introduced a special icon <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image008.jpg" alt= "image"> indicating the source operand.</p> <p class="MsoBodyText">To get a short description of the operation in a form of a tip window user needs to positions the cursor over the operation icon. Source operands sharing the same icon are described differently when associated with different operations. The tip tool indicates the role of the particular source operand in a particular operation.</p> <p class="MsoBodyText">User can associate a comment with the particular operand by selecting “Comment” menu option. Comment can be viewed by placing the cursor over the operand and waiting for a second. Comment can be edited by selecting “Comment” menu option for the operand that already has a comment associated with it. Maximum length of the comment string is 512 bytes.</p> <p class="MsoBodyText">As user builds the algorithm, the project window follows the last performed operation keeping it always within the viewport.</p> <span style= 'font-size:10.0pt;font-family:"Times New Roman"'><br clear="all" style='page-break-before:always'></span> <p class="MsoBodyText"> </p> <h2><a name="node3" id="node3"></a>Project window navigation</h2> <p class="MsoBodyText">Ease of creation of image operation sequences poses a task of navigation in the project window which can become quite big quickly. Use the following key combinations to navigate through the project:</p> <p class="MsoBodyText">“Home” moves the window to the beginning of the project. This is handy when you want to apply the algorithm stored in the project to another image by using “<a href= "start.htm#_Batch_processing_of">Replace operation batch file</a>” processing operation.</p> <p class="MsoBodyText">“End” moves the window to the end of the project.</p> <p class="MsoBodyText">Arrow keys move project window up, down, left, right by one operand thumbnail.</p> <p class="MsoBodyText">Ctrl-G is a “go to a particular operand id” command. Press Ctrl-G and type the operand number to change the viewport position to see the particular operand.</p> <span style= 'font-size:10.0pt;font-family:"Times New Roman"'><br clear="all" style='page-break-before:always'></span> <p class="MsoBodyText"> </p> <h2><a name="node4" id="node4"></a><span class= "MsoFootnoteReference"> </span>Project Edit functions</h2> <p class="MsoBodyText">Project is consists of a sequence of operations, which can have quite complex topology: the algorithm can split into branches, which may rejoin down the operation sequence. During design stage the algorithm developer can trial different methods of which only some lead to desirable outcome. This may result in build up of unused code in the algorithm tree. In order to facilitate pruning of unused code introduction of new branches into the existing algorithm Pictorial Image Processor© provides the following project edit functions:</p> <p class="MsoBodyText">Add Image provides access to image File Open dialog. This function is also available by double-click on the empty space within the project window as described in <a href= "start.htm#_Basic_steps">Basic Steps</a> section.</p> <p class="MsoBodyText">Add Scalar provides access to scalar value input dialog. This function is also available by double-click on the empty space within the project window as described in Basic Steps section.</p> <p class="MsoBodyText">Add Operation provides access to operation context manu after selection of one source operand from the screen. This function is also available by right-click on one of the project operands as described in <a href= "start.htm#_Basic_steps">Basic Steps</a> section.</p> <p class="MsoBodyText">Last entered operation can be removed by pressing simultaneously Ctrl+Z (Undo). Each subsequent press of Ctrl+Z will delete last operation present in the remaining project until all operations are removed.</p> <p class="MsoBodyText">The last removed in such way operation can be restored by simultaneously pressing Ctrl+Y (Redo). Each subsequent pressing of Ctrl+Y will restore next operation until all operations previously entered are restored.</p> <p class="MsoBodyText">Undo and Redo operations are disabled when user placed a list of files in one of the input operands thus setting up batch processing. In order to get acces to those operations replace the list of image files with a single image.</p> <p class="MsoBodyText">Apart from simple edit functions, which allow only basic manipulation of the project operations Pictorial Image Processor© provides an arsenal of editing functions, which permit addition, removal and redirection of algorithm branches. Those are called here Extended Edit functions.</p> <p class="MsoBodyText"><b>Extended Edit functions include</b>:</p> <p class="MsoBodyText">Delete Operation Chain deletes all operations depending on the operand which user ia asked to pick within the project window. If operand has a Save File operation associated with it, operator is asked first whether one wants to delete the Save File operation prior to asking to confirm deletion of the whole operation chain. Note that this function is different from Undo Last Operation function described above because it removes whole sections of the algorithm depending on selected operand.</p> <p class="MsoBodyText">Insert Operation After inserts an image processing operation after a selected operand. If you perceive the algorithm topology as a tree, this operation creates a new brunch in the tree. This function inserts any operation available to user apart from input operations of creation of new image or scalar. Those operations are handled by Insert Operation Before function. During this editing action user can choose as a source operand for elected operation any operand with the operand number lower than the one after which the operation is inserted. This is indicated to the user by greying out inaccessible operands.</p> <p class="MsoBodyText"><img border="0" width="159" height="139" src="PIPUserManualNoFootnotes_files/image009.jpg" alt= "image"> <img border="0" width="176" height="140" src= "PIPUserManualNoFootnotes_files/image010.jpg" alt="image"></p> <p class="MsoBodyText">Insert Operation Before inserts an input (open image or enter value) operation before selected operand. The intended use of this function is to supply input parameters prior to inserting a new image processing operation. Since the insertion of image processing operations requires the operands to have lower numbers than the selected operand, this insertion function permits adding parameters before the operand of interest.</p> <p class="MsoBodyText"><img border="0" width="223" height="255" src="PIPUserManualNoFootnotes_files/image011.jpg" alt="image"></p> <p class="MsoBodyText">Replace Operation Input(s) is a function which is applied to an existing operation and permits change of the input operands to other operands which have operand numbers lower than the chosen operand. This allows switching of the branches of the algorithm tree.</p> <p class="MsoBodyText"><img border="0" width="219" height="246" src="PIPUserManualNoFootnotes_files/image012.jpg" alt="image"></p> <p class="MsoBodyText">Revert last Extended Edit action restores project to the state prior to application of the last Extended Edit action.</p> <p class="MsoBodyText">Insert Project After inserts contents of the whole project after a picked operation. The user is asked to select a project from the list of open project. This action is as close as in Pictorial Image Processor© got to introduction of functions called within the project. This edit action helps to develop modular algorithm then quickly integrate them into a larger combined algorithm using Replace Operation Input(s) action.</p> <p class="MsoBodyText">Together extended editing operations allow application of significant changes to the algorithm without rewriting already written parts of it as well as cleaning up the branches whose promise never eventualised.<br clear="all" style= 'page-break-before:always'></p> <h2><a name="node5" id="node5"></a>Project attributes</h2> <p class="MsoBodyText">A single algorithm is called in Pictorial Image Processor© a project. A project can have the following attributes: project header/comment and project specific spatial calibration. The attributes are accessible through the Attributes menu in the main window of the application.</p> <p class="MsoNormal"><img border="0" width="271" height="81" src= "PIPUserManualNoFootnotes_files/image013.jpg" alt="image"></p> <p class="MsoNormal"> </p> <p class="MsoBodyText">Project header or comment can be any text user wants to put to identify the project. It appears at the top in the project window above the first row of operands.</p> <p class="MsoBodyText">Project spatial calibration allows setting the image resolution in world coordinates. Spatial calibration menu opens the calibration dialog.</p> <p class="MsoNormal"><img border="0" width="285" height="192" src= "PIPUserManualNoFootnotes_files/image014.gif" alt= "image"> </p> <p class="MsoNormal"> </p> <p class="MsoBodyText">From this dialog the calibration parameters could be set either manually or number of pixels corresponding to particular length in the world units (meters) can be selected from a user specified image. In the later case pressing “Pixel count from image” button allows selection of the image file. The right-click on the mouse within the image starts drawing of a line. As the mouse is dragged across the image the number of pixels in the line is counted and appears in the pixel count box of the dialog. Releasing of the right mouse button finishes the line.</p> <p class="MsoBodyText">To remove spatial calibration set any of the selectable parameters to 0.</p> <p class="MsoBodyText">Internally the calibration is stored in the form 1 pixel =X meters. When the dialog is closed and open again the data will be presented in the form X meters per 1 pixel.</p> <p class="MsoBodyText">Calibrated and non-calibrated projects have different background colour of the project window.</p> <p class="MsoBodyText">Calibration is attributed to all images in the project. It is natural to assume that all images in the project have the same spatial scale. Some value operands, derived from the image operands and having the spatial meaning are also subject to calibration. That is they will change the value depending on spatial calibration.</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2 style='page-break-after:auto'><a name= "_Convolution_Kernel_Designer"></a>Convolution Kernel Designer</h2> <p class="MsoBodyText"> </p> <p class="MsoBodyText">Convolution operations in Pictorial Image Processor© define kernels as images of floating point types Double (64-bit) or Float (32-bit). Kernel image is usually defined by the type of the filter one wants to design. There are not many applications supporting images of floating point types to say nothing about editing them. Hence Pictorial Image Processor© offers a simple tool for creating this type of images. The tool, Convolution Kernel Designer allows creating, manually editing and saving images of types Double (64-bit) or Float (32-bit). The Convolution Kernel Designer is accessible through Tools menu</p> <p class="MsoBodyText"> </p> <p class="MsoBodyText"><img border="0" width="208" height="90" src= "PIPUserManualNoFootnotes_files/image015.jpg" alt= "image"> or <img border="0" width= "272" height="84" src="PIPUserManualNoFootnotes_files/image016.jpg" alt="image"> </p> <p class="MsoBodyText"> </p> <p class="MsoBodyText">This menu gives access to the main Designer dialog where user can select size of the kernel image its shape and <img border="0" width="342" height="388" src= "PIPUserManualNoFootnotes_files/image017.jpg" alt="image"></p> <p class="MsoBodyText">initial intensity distribution function. Elliptic/round kernel for flat distribution function will create a kernel where the pixels within the ellipse are set to intensity shown in “Intensity” text box while those outside the ellipse are set to 0. When Normalised tick box is selected the sum of intensity of all pixels in the flat kernel will be the intensity shown in “Intensity” text box, other wise each non-zero pixel is set to that value. For the Gaussian kernel normalisation will results in total sum of intensities being equal to the value set in Max text box.</p> <p class="MsoBodyText"><img width="237" height="97" src= "PIPUserManualNoFootnotes_files/image018.jpg" alt= "image"><br clear="all"> By pressing “Create” button user gets access to the initial image of the kernel in the Kernel Image window and editing tool of 5x5 pixel neighbourhood. The editing tool has a hint message on editing procedure.</p> <p class="MsoBodyText">Initially Neighbourhood View window is not ready for user input. This is indicated by the grey colouring of the boxes on the window. It can be used for precise positioning of the cursor in Kernel Image window since area under the cursor in in Kernel Image window is shown magnified in Neighbourhood View window. In order to edit a 5x5 block of pixels user has to position the cursor’s square over the block inside the Kernel Image window and click left mouse button. At this point Neighbourhood View window becomes active and user can edit part of the image falling within the neighbourhood. By pressing “Store” button the updated data is transferred into the Kernel image. At this point the image palette is recalculated to match the updated image. User can cancel the update by pressing ”Cancel“ button. This will deactivate Neighbourhood View window and position the cursor back into the Kernel Image window.</p> <p class="MsoBodyText"><img border="0" width="600" height="325" src="PIPUserManualNoFootnotes_files/image019.jpg" alt="image">Gamma menu in the Kernel Image window allows gamma correction of the image for better visualisation. The resulting image can be saved through File menu, which gives access to Save TIF menu where the kernel can be saved as a grey scale image of types Double (64-bit) or Float (32-bit).</p> <p class="MsoBodyText"><img border="0" width="234" height="103" src="PIPUserManualNoFootnotes_files/image020.jpg" alt="image"></p> <p class="MsoBodyText">The designer can build the kernels of both odd and even dimensions. In the later ones the centre falls between the pixels.</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2><a name="node6" id="node6"></a>Logging execution time for project operations</h2> <p class="MsoBodyText">Pictorial Image Processor provides means for algorithm profiling allowing user to monitor execution speed of the operations and develop the algorithms according to the speed-of-execution requirements. </p> <p class="MsoBodyText">User can enable logging execution time on a per-project basis by selecting “Log Execution Time” in the “Tools” menu of the main application window. One has to close all projects in order to see this menu.</p> <p class="MsoBodyText"><img border="0" width="208" height="93" src= "PIPUserManualNoFootnotes_files/image021.jpg" alt= "image"> </p> <p class="MsoBodyText">This functionality is designed to measure the speed of execution for full algorithm cycle. Hence it only records the data when the <i>whole algorithm is loaded</i> into the Pictorial Image Processor or in a batch processing mode, not in the design mode when user creates individual operations.</p> <p class="MsoBodyText">The execution time is saved into the log file at the end of each algorithm execution cycle. The name of the log file consists of the name of the project followed by the “.ExecTime.log” prefix. The path is the same as the project path. The file consists of the records of the execution times and corresponding destination or source operand numbers from the project. Input operands containing path for the source images are also tagged with the path to the source file. This helps to identify the execution times for different images during batch processing. The log file can be loaded into Excel as a comma delimited CSV file. For this purpose the execution time and the source operand number text are delimited by a comma. Multiple executions of the project with the same name will have multiple logged appended to the same file. </p> <p class="MsoBodyText"> </p> <p class="MsoBodyText"> </p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2 style='page-break-after:auto'><a name= "_Viewing_full_size"></a>Viewing full size image</h2> <p class="MsoBodyText">In the project window image <a href= "start.htm#_Operands">operands</a> are presented as thumbnails. In order to view the image in full size user double-clicks on the thumbnail. This brings a Full Size Image window. The window’s caption is the path where the images is stored or will be stored should user elect to store it. The file extension is omitted because user can select the file format for the image storage.</p> <p class="MsoNormal"><img border="0" width="600" height="242" src= "PIPUserManualNoFootnotes_files/image022.jpg" alt="image"></p> <p class="MsoBodyText">Narrow bar at the top of the image displays screen coordinates and intensity values for the point indicated by the cursor. For RGB images it displays all 3 components, for complex images real and imaginary components. </p> <p class="MsoBodyText">File menu gives access to Print, Image Info and Image Intensity Histogram functions. For 24-bit images this menu provides access to 2D Histograms of RG, GB and BR channel pairs. The image printed from here will fit <img border="0" width= "172" height="157" src= "PIPUserManualNoFootnotes_files/image023.jpg" alt="image"></p> <p class="MsoBodyText">into the full page of the system’s default printer. For 8-bit grey scale images and components of the RGB images this menu allows to access <a href= "start.htm#_Spatial_Statistics_Histogram_Window">histograms of spatial statistics</a> obtained from the image </p> <h3><a name="node7" id="node7"></a>Image Information</h3> <p class="MsoBodyText">Image info displays image size, image depth (number of bits per pixel) and image dynamic range. The information displayed depends on type of image. Here is an example of the info screen for a 24-bit image.</p> <p class="MsoBodyText"><img border="0" width="173" height="220" src="PIPUserManualNoFootnotes_files/image024.jpg" alt="image"></p> <p class="MsoBodyText">For binary images the info dialog contains information about blobs of foreground (white). Here user also has a choice of selecting the connectivity of the blobs for calculation of the blob statistics. This information is handy for identifying the <a href="start.htm#_Threshold_by_Blob">area threshold</a> for the largest blob.</p> <p class="MsoBodyText"><img border="0" width="189" height="241" src="PIPUserManualNoFootnotes_files/image025.jpg" alt= "image"> </p> <p class="MsoBodyText">Intensity Histogram menu option opens <a href="start.htm#_Intensity_Histogram_Window">intensity histogram window</a>.</p> <h3><a name="node8" id="node8"></a>Viewing Zoomed Image</h3> <p class="MsoBodyText">Zoom menu allows 2 types of image resolution change:</p> <p class="MsoBodyText"><b>windows style</b> pixel doubling or halving. Hint: when image size is small it could be more efficient to use the <a href= "start.htm#Neighbours_menu">Neighbours</a><span style= 'display:none'>!ALink(NeighboursMenuOption)</span> feature instead of multiple application of the Zoom feature.</p> <p class="MsoBodyText"><b>smooth zoom</b> with new pixels introduced between the original ones are interpolated using separable optimal non-recursive convolution mask of radius 3 pix from Bernd Jahne “Image Processing for Scientific Applications” p. 279.</p> <p class="MsoFootnoteText"><img border="0" width="128" height="124" src="PIPUserManualNoFootnotes_files/image026.jpg" alt="image"></p> <p class="MsoFootnoteText"> </p> <h3><a name="node9" id="node9"></a>Copying Image to Clipboard</h3> <p class="MsoNormal"> </p> <p class="MsoBodyText">By selecting ”Copy” menu option user can place the image displayed in Full Size Image Screen to the Windows Clipboard. This feature is particularly useful when the user is interested in the interpolated image of higher resolution after applying “x2 Smooth” zoom.</p> <h3><a name="node10" id="node10"></a>Viewing Palette Selection</h3> <p class="MsoNormal"><a name="Palette_menu" id= "Palette_menu">Palette menu</a> allows to chose a palette for a grey scale image, that is any type but 24-bit</p> <p class="MsoNormal"><img border="0" width="290" height="238" src= "PIPUserManualNoFootnotes_files/image027.jpg" alt="image"></p> <p class="MsoNormal"> </p> <p class="MsoBodyText">Currently selectable palettes are:</p> <p class="MsoNormal">Geyscale, image is mapped into the grey scale range from 0 to 255</p> <p class="MsoNormal">Geyscale with 5% of saturated pixels, the bulk, 95% of the image pixels of low intensity is mapped into the grey scale range from 0 to 255. This palette is convenient for viewing noisy images where few pixels can determine the dynamic range of the image but can make the bulk of the pixels mapped into indistinguishable range of intensities.</p> <p class="MsoNormal">Circular, is designed for Hue images that have a range of [0, 2<span style='font-family:Symbol'>p</span>). The mapping goes from red at 0 with decreasing red and increasing green till full green at 2<span style='font-family:Symbol'>p</span>/3, then decreasing green and increasing blue till full blue at 2<span style='font-family:Symbol'>p</span>*2/3, then decreasing blue and increasing red till full red at 2<span style= 'font-family: Symbol'>p</span>. This 768-level palette permits detailed and natural presentation of hue images. </p> <p class="MsoBodyText">Distinct, all different levels in the image are shown with a distinct colour. Number of different levels cannot be more than 2<sup>24</sup>. Palette is selected in such a way that close intensity values have contrasting RGB display values.</p> <p class="MsoBodyText">Random, all different levels in the image are shown with a distinct colour. Number of different levels cannot be more than 2<sup>24</sup>. Palette colours are obtained by random selection.</p> <p class="MsoBodyText">Custom, the palette which was stored in the source file, if available.</p> <p class="MsoBodyText">Elevation, the pseudo-colour palette spaning up to 513 levels from blue for lower levels through blue-green to green then trough green-red to red for higher levels. Level 0 if present is set to black.</p> <p class="MsoBodyText">Other available palettes are generated automatically by certain operations hence only available for the images which are the results of such operations:</p> <p class="MsoNormal">Label, the palette generated during operation of labelling of disjoint blobs</p> <p class="MsoBodyText">Fuzzy c-means, the palette consisting of grey or RGB values corresponding to the mean value of each cluster identified by the fuzzy c-means algorithm.</p> <p class="MsoBodyText">Setting Greyscale and Elevation palette may fail for floating point images if there are pixels resulting from division by zero. It is impossible to viewing these images in linear scale with those palettes.</p> <p class="MsoBodyText">Palette display is not available for images of 128-bit complex type.</p> <h3><a name="node11" id="node11"></a>Mapping Image into Viewing Range</h3> <p class="MsoBodyText">Lookup method menu shows available options for mapping image component intensity ranges into the display intensity range. The availability of four possible options depends on type of image on the screen. Two options Linear and Gamma are available for all image types. For high bit count images apart from complex type additional option Range allows to map part of the dynamic range into distinct visible intensities. User selects the range mapped into 256 colours from the following dialog</p> <p class="MsoBodyText"><img border="0" width="253" height="151" src="PIPUserManualNoFootnotes_files/image028.jpg" alt="image"></p> <p class="MsoBodyText">All levels below selected range are mapped into black; all levels above the selected range are mapped into white.</p> <p class="MsoBodyText">For images of complex type additional option is available: the Uniform. This option allows visualisation of FFT images where the dynamic range is so vast that even logarithmic scale of Gamma mapping is not sufficient. The histogram of a FFT image looks like a histogram of white noise with each level met once or twice. Uniform method allocates each display level to equal number of pixel intensities according to the intensity order thus making possible visualisation of the FFT images. This is a default method for visualisation of the thumbnails of the FFT images in the project. Without it all FFT images would look the same.</p> <p class="MsoBodyText">Gamma menu item gives access to gamma dialog. Gamma dialog shows the graph of the power function applied to the image pixels prior to display. In fact the curve shows the function in the power 1/<span style='font-family:Symbol'>g</span>, where <span style='font-family:Symbol'>g</span> is the value in the edit box. Supported gamma values are ranging from 0.0001 to 10000. Image pixels are not modified, only the display bitmap.</p> <p class="MsoNormal"><img border="0" width="547" height="453" src= "PIPUserManualNoFootnotes_files/image029.jpg" alt="image"></p> <p class="MsoBodyText">Gamma is supported for 24-bit RGB images and for two palettes grey scale and elevation. Gamma correction is applied to the 8 and 24-bit images in a traditional way: power function is applied to pixel values, which are clamped at 255. For the other image type another mapping method has been chosen, which preserves dynamic range of the original image. For 16, 32 and 64 bit images full dynamic range is mapped to the range [0,1], then power function is applied to the pixels, which then is mapped into the palette display range.</p> <h3><a name="node12" id="node12"></a>Viewing Neighbourhood of Pixel under Cursor</h3> <p class="MsoBodyText"><a name="Neighbours_menu" id= "Neighbours_menu">Neighbours menu</a> option opens the dialog showing the 5x5 neighbourhood of a given pixel. The dialog shows the horizontal and vertical pixel addresses on top and left. It also shows magnified bitmap of the neighbourhood.</p> <p class="MsoNormal"><img border="0" width="516" height="340" src= "PIPUserManualNoFootnotes_files/image030.jpg" alt="image"></p> <p class="MsoBodyText">If zoom is applied to the image in the Full Size window, the view in the neighbourhood dialog will depend on type of zoom applied. If smooth zoom is applied, the neigh neighbourhood dialog shows interpolated pixels. In case of windows, pixel doubling zoom the neighbourhood dialog always shows neighbours of the central pixel in original image disregarding of zoom value. This action was elected because no image data is changed in windows zoom. If gamma correction is applied to the image, gamma corrected pixels are shown in the 5x5 pixel window in the dialog. The numeric values though correspond to the true pixel values.</p> <h3><a name="node13" id="node13"></a>Cross-section Line profiles</h3> <p class="MsoBodyText">User can obtain a line profile across the image by pressing the right mouse button and dragging the line across the image. When user releases the mouse button <a href= "start.htm#_Intensity_Profile_Window">line profile window</a> appears.</p> <h3><a name="node14" id="node14"></a>Component view</h3> <p class="MsoNormal">For multi-component images user can view individual components by choosing View components menu. Pictorial Image Processor supports the following multi-component images:</p> <p class="MsoNormal">RGB</p> <p class="MsoNormal"><img border="0" width="386" height="137" src= "PIPUserManualNoFootnotes_files/image031.jpg" alt="image"></p> <p class="MsoNormal">FFT</p> <p class="MsoNormal"><img border="0" width="386" height="116" src= "PIPUserManualNoFootnotes_files/image032.jpg" alt="image"></p> <p class="MsoNormal">The components are presented as grey scale images of corresponding types: 8-bit for RGB and 64-bit floating point for FFT images</p> <p class="MsoNormal"> </p> <p class="MsoNormal">User has access to all tools like histogram, cross section, etc when viewing the component images </p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2 style='margin-left:0cm;text-indent:0cm;page-break-after:auto'> <a name="_Intensity_Histogram_Window"></a>Intensity Histogram Window</h2> <p class="MsoFootnoteText">Intensity histogram widow displays the image histogram in a fixed size of 512 pixels wide and 256 pixels high.</p> <p class="MsoFootnoteText"><img border="0" width="562" height="664" src="PIPUserManualNoFootnotes_files/image033.jpg" alt="image"></p> <p class="MsoFootnoteText">Horizontal lines indicate 4 quarters of the pixel count for the most frequently met grey level. X coordinate describes grey levels and Y coordinate pixel counts for the particular level.</p> <p class="MsoFootnoteText">As user moves the cursor across the histogram window 2 windows on the status bar at the bottom display corresponding grey level and pixel count, grey line on the histogram indicates the position. As user moves cursor across histogram window, pixels having average intensity equal to the level shown under the cursor on the histogram window are highlighted in a distinct tone. The tone is bright for the dark pixels and dark for the bright pixels. For 8-bit and 24-bit images the number of pixels shown in the image window is equal to the number shown in the histogram window for the current level. For other image types the number of displayed pixels is usually higher than the number shown in the histogram. This limitation of the feature is caused by the disparity between the mapping of the pixels of high bit count into 24-bit bitmap and display threshold based on average intensity of the RGB value.</p> <p class="MsoFootnoteText">For 24-bit images the histogram is an intensity histogram, where intensity is an average of RGB values.</p> <p class="MsoFootnoteText"> </p> <p class="MsoFootnoteText">User can chose to highlight style of the threshold through Display threshold type menu</p> <p class="MsoFootnoteText"><img border="0" width="144" height="77" src="PIPUserManualNoFootnotes_files/image034.gif" alt="image"></p> <p class="MsoFootnoteText">Threshold at selected level is described above. Display below selected level highlights all pixels below selected level on the image and shows corresponding levels the histogram. Display above selected level highlights all pixels above intensity selected on the histogram.</p> <p class="MsoFootnoteText"> </p> <p class="MsoFootnoteText">For images of large dynamic range (16, 32, 64 and 128-bit), where number of histogram levels exceeds the size of the view window Pictorial Image Processor© offers three view options, the options for the mapping of the dynamic range of the image into the 512 levels displayable in the histogram window “Sampling”, “Binning into bins of equal length” (default), and “Binning into bins with equal number of levels in a bin”</p> <p class="MsoFootnoteText"> The “Sampled” option uniformly samples the “grey” levels present in the image. In other words if the level has a pixel count 0, it is not shown in the histogram window. For these images the fixed size histogram window covers the whole grey scale range of the image when the histogram is requested from the Full Size Image view via menu. This means that some of the levels are not displayed. Moving the pointer across the window user can see which grey levels are displayed. A particular range of grey levels is accessible through “Select Range” menu.</p> <p class="MsoFootnoteText"> </p> <p class="MsoFootnoteText">The “Binning into bins of equal length” method gives a “natural” look to the histogram by preserving distances between clusters of “grey” levels in the image but some bins can have pixel count of 0.</p> <p class="MsoFootnoteText"> </p> <p class="MsoFootnoteText">The “Binning into bins with equal number of levels in a bin” option groups levels only present in the image hence each bin contains always some number of pixels.</p> <p class="MsoFootnoteText"> </p> <p class="MsoFootnoteText">For the binned options the status bar “x” displays the range of intensity levels covered by the bin under the cursor and status bar “y” the total number of levels in the bin.</p> <p class="MsoFootnoteText"> </p> <p class="MsoFootnoteText"> “Select Range” menu opens grey level range selection dialog. The dialog initial values show the full dynamic range of the image</p> <p class="MsoFootnoteText"><img width="287" height="158" src= "PIPUserManualNoFootnotes_files/image035.jpg" alt= "image"><br clear="all"></p> <p class="MsoFootnoteText">Copy menu option copies histogram onto the Clipboard. The histogram can be pasted into another application either as a picture or as a text with 2 columns representing grey levels and pixel counts.</p> <p class="MsoFootnoteText"> </p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2 style='margin-left:0cm;text-indent:0cm;page-break-after:auto'> <a name="node15" id="node15"></a>2D Histogram Window</h2> <p class="MsoBodyText">For 24-bit images there are three 2d histograms: Red-Green, Green-Blue and Blue-Red. These are presented in one window. Three coloured sectors starting at the centr</p> <table cellpadding="0" cellspacing="0"> <tr> <td width="26" height="0"></td> </tr> <tr> <td></td> <td><img width="522" height="568" src= "PIPUserManualNoFootnotes_files/image036.jpg" alt="image"></td> </tr> </table> <br clear="all"> e of the window represent the range of possible levels of particular colour pair. The red axis goes from the centre to right top, the green axis from the centre down to the bottom, the blue axis from the centre horizontally to the left. Each point in a sector represents a colour pair coded in the window with the corresponding colour. The components of the colour are shown in 3 lower windows in the top grey section of 2d histogram window. The position of the windows follows the axes pattern. As cursor hovers over the coloured pattern, the position of the cursor defines (usually) 2 components of the 2d histogram. The values of these components are shown in corresponding windows with red, green or blue font. If the component is equal 0, then the window stays clear. If 2 windows are clear, the cursor is over the axis. <p class="MsoBodyText">The pixel count of a particular bi-component element is coded with a grey level. This level is displayed in the top window on the top grey patch marked “count=…”. If the level is absent for a particular pair one, can see the underlying bi-component colour on that spot. Hence the coloured areas correspond to the pixel-less bi-component elements of the image and grey (from black to white) to the filled ones. The intensity of the grey corresponds to the number of pixels for the bi-component element up to level 255. After that display intensity saturates and is not representative of the true pixel count at given level. The true level can be viewed in the level window.</p> <p class="MsoBodyText">2D histograms give additional insight into the properties of the image not obvious from intensity diagram. For example, the 2D above belongs to the image that appears to have reasonable smoothness of colour tones.</p> <p class="MsoBodyText"><img border="0" width="600" height="649" src="PIPUserManualNoFootnotes_files/image037.jpg" alt="image"></p> <p class="MsoBodyText">Meanwhile a 2D histogram (above) shows that the source image has missing levels in red, green and blue. In fact nearly every second level is missing. This indicates that useful dynamic range of the image is about half of the range in the original image. The contrast of the source image was increased in each channel with multiplication of each pixel RGB levels by a fixed number.</p> <p class="MsoBodyText"></p> <table cellpadding="0" cellspacing="0"> <tr> <td width="24" height="0"></td> </tr> <tr> <td></td> <td><img width="522" height="568" src= "PIPUserManualNoFootnotes_files/image038.jpg" alt="image"></td> </tr> </table> <br clear="all"> The 2D histograms are available in 2 colour spaces RGB and Hue-Intensity-Saturation (HIS). The HIS histogram for the same image is shown below. The orthogonal part of the histogram set is the Intensity-Saturation histogram with the maximum at the centre of the image. Hue-Intensity histogram is at the top-left side of the widow, Hue-Saturation is on the right of the window. The pixel count for each histogram is coded in shades of grey from black to white. <p class="MsoBodyText">More on this method of the 2D histogram presentation can be found in <i>“Alexander A. Gutenev, Method of Visualization of Two-Dimensional Histogram Set of a Color Image, Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering 2012, WCE 2012, 4-6 July, 2012, London, U.K., pp1214-1218.”</i></p> <i><span style= 'font-size:10.0pt;font-family:"Times New Roman"'><br clear="all" style='page-break-before:always'></span></i> <p class="MsoBodyText"> </p> <h2 style='margin-left:0cm;text-indent:0cm'><a name= "_Intensity_Profile_Window"></a><a name= "_Spatial_Statistics_Histogram_Window"></a>Spatial Statistics Histogram Window</h2> <p class="MsoNormal">Unlike an intensity histogram, that shows distribution of intensity levels in the image, a spatial statistics histogram describes spatial relationships between the blobs of the same intensity. In order to calculate such histogram the image is thresholded at each grey level and statistics on distances between the blobs are calculated. Currently such histograms are implemented only for 8-bit images. The spatial statistics histogram window appears similarly to intensity histogram window but instead of pixel counts the ordinate displays some spatial statistic for the image.</p> <p class="MsoNormal"><img border="0" width="600" height="281" src= "PIPUserManualNoFootnotes_files/image039.jpg" alt="image"></p> <p class="MsoNormal">User can select the type of the spatial statistic to display from Statistics menu. Currently four statistics are supported: average internal distance within the blobs, maximum internal distance within the blobs, average (external) distance between the blobs, maximum (external) distance between the blobs. Like in the case of an intensity histogram, user can select the range of level within the window, effectively zooming into particular parts of the histogram. User can also copy the viewed histogram to a clipboard.</p> <p class="MsoNormal">Moving cursor across the histogram window will highlight the pixels of the corresponding grey level in the image window.</p> <p class="MsoNormal">For large images the statistics calculation can be relatively time consuming.</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2 style='margin-left:0cm;text-indent:0cm'><a name="node16" id= "node16"></a>Intensity Profile Window</h2> <p class="MsoBodyText">Line profile window shows the cross-section of the image along the line shown on the full size image window</p> <p class="MsoNormal"><img border="0" width="600" height="453" src= "PIPUserManualNoFootnotes_files/image040.jpg" alt="image"></p> <p class="MsoBodyText">As user moves the mouse pointer across the profile window sections of the status bar show horizontal and vertical position of the point on the profile within the full size image window and intensity at this point. For RGB images all 3 values are shown. The last section of the status bar shows the length of the line drawn of the screen. If the project is not spatially calibrated, the length is shown in pixels otherwise the length is in world coordinates. Similarly the coordinates of the point within the profile window are presented in world coordinates, if the project is calibrated. The origin of the coordinate system is the top left corner.</p> <p class="MsoBodyText">Copy menu option copies profile on Clipboard. The profile can be retrieved by other applications as either picture or table of values.</p> <p class="MsoBodyText">User can adjust the position of the cross-section line by clicking Adjust line. This gives the dialog to set start and end positions of the line.</p> <p class="MsoBodyText"><img border="0" width="205" height="109" src="PIPUserManualNoFootnotes_files/image041.jpg" alt="image"></p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2><a name="_Batch_processing_of"></a>Batch processing of file lists</h2> <p class="MsoNormal"> </p> <p class="MsoNormal">Development of algorithms usually requires fine-tuning of the algorithm parameters. The optimal set of the parameters is usually identified during testing of the algorithms on a range of images or with a range of different parameters (e.g. convolution masks). The task could be quite tedious if the test set of images or possible parameters are large. In order to automate processing of large image sets, Pictorial Image Processor© offers the functionality of batch file processing. The workflow for the batch processing is as follows:</p> <p class="MsoNormal"> </p> <p class="MsoNormal">When user develops an algorithm, the algorithm usually includes <a href="start.htm#_Open_Image">Open Image</a> <span style='display:none'>IDH_OPEN_IMAGE</span> operations for supplying processed images or processing operations kernels. File batch menu item in the I/O menu allows replacing the file <img width="274" height="169" src= "PIPUserManualNoFootnotes_files/image042.jpg" alt= "image"><br clear="all"> with the list of files which can be processed one after another. When user selects the “File batch” option the dialog appears, which allows selecting the images for processing. Use 4 buttons in the middle to select/deselect <img width="600" height="240" src= "PIPUserManualNoFootnotes_files/image043.jpg" alt= "image"><br clear="all"> image files from the left window of the source file list to the right window of the batch file list. “Clear processing list button” removes all images from the destination batch list. The right part of the dialog facilitates navigation of the mapped drives of the computer.</p> <p class="MsoNormal"> </p> <p class="MsoNormal">When user sets the batch list, the Open Image operation is replaced with the Image List operation. The batch</p> <p class="MsoNormal"><img border="0" width="326" height="79" src= "PIPUserManualNoFootnotes_files/image044.jpg" alt= "image"> </p> <p class="MsoNormal"></p> <table cellpadding="0" cellspacing="0"> <tr> <td width="12" height="0"></td> </tr> <tr> <td></td> <td><img width="73" height="24" src= "PIPUserManualNoFootnotes_files/image045.jpg" alt="image"></td> </tr> </table> <br clear="all"> processing toolbar becomes available to the user. The buttons mean “Reset”, or point the batch processing to the first file in the list, “Run whole batch” – execute the algorithm for all lists in the algorithm project, “Run one cycle and stop” execute algorithm for one, next set of files in the lists set for the project. User can set up to 4 lists within the project which will be calculated nesting the loops for the operands with higher operand numbers<span style='display:none'>IDH_OPERAND_ID</span> inside the loops for the operands with the lower numbers. For example, if the file list for operand 1 contains 4 files and file list for the operand 5 contains 3 files, the total batch will be 12 cycles where first 3 cycles are performed for the first file in the list for operand 1 and all 3 files from the list for operand 5. If output operation is part of the project, the names of the image results will automatically include the names of the images from the lists participating in the current cycle of batch processing. <p class="MsoNormal"> </p> <p class="MsoNormal">In this method of batch processing one project is executed multiple times processing the lists consequentially. If user wants to process multiple projects then use of drag-and-drop operation on a set of projects initiates their “simultaneous” processing. In this case the progress bar cannot be trusted in representing the status of the processing for the cycle because multiple projects being processed simultaneously will try to use the bar for displaying their progress.</p> <p class="MsoNormal"> </p> <p class="MsoNormal">WORKFLOW CONSIDERATIONS</p> <p class="MsoNormal">Batch processing is designed to help users to test algorithms on large data sets. It is recommended to design algorithms on individual images and apply image lists after the user settled on the algorithm design. With this workflow in mind UNDO and REDO operations are disabled when user selects image lists as inputs.</p> <b><span style='font-size:14.0pt;font-family:Arial'><br clear="all" style='page-break-before:always'></span></b> <h1 style='page-break-after:auto'><a name= "_Operands"></a>Operands</h1> <p class="MsoBodyText">Operands are the objects, which make input or output of an image processing operation. Currently supported are 2 types of operands: scalar and image. Operands are represented on PIP project by rectangles of a fixed size. For a scalar operand the value is shown in the rectangle, for an image operand an image thumbnail preserving the image aspect ratio is shown. Each operand in the project is given a sequential number, an operand ID in the project. Each operand has an invisible “name” associated with it. The name is generated automatically from the file name of the first operand in the operation sequence with first letter of the operation and operand number added. When user opts to save the operand this hidden name is given to the output file. When saving image operand user is prompted for the image file format. The scalar operands are saved in text format. Name of the saved file is generated automatically. The directory where the files are saved is the same directory where the first image of the project is stored.</p> <h2><a name="node17" id="node17"></a>Scalar Operand</h2> <p class="MsoBodyText">Scalar operand is either a real number, an RGB triple or a real/imaginary pair depending on type of the scalar.</p> <p class="MsoNormal"> </p> <table cellpadding="0" cellspacing="0"> <tr> <td width="24" height="0"></td> </tr> <tr> <td></td> <td><img width="126" height="94" src= "PIPUserManualNoFootnotes_files/image046.jpg" alt="image"></td> </tr> </table> <br clear="all"> <h2><a name="node18" id="node18"></a>Image Operand</h2> <p class="MsoBodyText">Image operands are images of one of the following types: binary (1-bit), 8-bit greyscale, 16-bit greyscale, 24-bit RGB, 32-bit greyscale, 32-bit single precision floating point, 64-bit double precision floating point,128-bit complex. 36 and 48-bit RGB images are only partially supported, application attempts to read image of this type then converts it into 24-bit RGB image mapping whole dynamic range of the source image into 8 bit per channel. The application can read palletized 8-bit images and during the operations conserving the image format it will attempt to preserve the palette of the image. Normally the resulting operand palette is a copy of the first operand’s palette.</p> <p class="MsoBodyText"><img border="0" width="121" height="90" src= "PIPUserManualNoFootnotes_files/image047.jpg" alt="image"></p> <p class="MsoBodyText">In Windows operating system there are no means to display 16, 32 or 64-bit images correctly. In PIP these images are coded for display as 24-bitRGB images, in other words palettised. A range of <a href= "start.htm#Palette_menu">palettes</a> is available for 16, 32 and 64-bit grey scale images. If user wants to see all distinct levels in the image, there is a limitation on display of 32 and 64-bit images. The number of distinct grey levels in those images cannot exceed 2<sup>24</sup>, that is around 16 million levels. The default palette for their display was selected to be greyscale. That palette can be changed and recorded for future viewing within the project via Palette menu of the Full Size View of the operand.</p> <p class="MsoNormal"> </p> <b><span style='font-size:14.0pt;font-family:Arial'><br clear="all" style='page-break-before:always'></span></b> <h1 style='page-break-after:auto'><a name= "_Operations"></a>Operations</h1> <p class="MsoBodyText">Operations are the actions performed on the operands<span style='display:none'>OPERANDSOPERANDS</span> to obtain a result.</p> <p class="MsoBodyText">Operation are represented in the PIP project canvas by an operation icon and a set of lines linking the input operands with the output operands. Some operations like for example “Save to a file” operation may not have the result operand. These operations are represented by icons only.</p> <p class="MsoBodyText">Normally operations are specified explicitly by the designer of the algorithm by right-clicking on one of the operation source operands. There is one operation “Copy Operand”, which is presented on the canvas but cannot be selected explicitly. This operation is invoked automatically when one of the input operands of the operation is too far on the resulting operand. In this case a copy of the far operand is placed close to the output on the project canvas.</p> <p class="MsoBodyText">Most of operations are accessed by right click on one of the operation’s input operands. Operations, which don’t have input operands, are accessed by double-click of left mouse button on the project canvas.</p> <p class="MsoFootnoteText">Supported operations can be classified by the following types: <a href= "start.htm#_Input/Output">Input/Output</a> , <a href= "start.htm#_Type_Conversion_Operations">Type Conversion</a>, <a href="start.htm#_Function_Operations">Functions</a>, <a href= "start.htm#_Unary_Operations">Unary</a>, <a href= "start.htm#_Binary_Arithmetic_Operations">Binary</a> and <a href= "start.htm#_Ternary_Filter_Operations">Ternary</a> depending on number of input operators. There are subgroups in each of those operations. In the <a href="start.htm#_Viewing_full_size">Full Size View</a> window for binary images there is a special operation for <a href="start.htm#_Determining_Average_Grain">Calculation of Grain Size in Metallographic Images</a></p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2 style='page-break-after:auto'><a name= "_Input/Output"></a>Input/Output</h2> <p class="MsoNormal">This group of operations is responsible for image and scalar input and output. The first image of the project sets project-wide path for the results of the project. This project-wide path is used as a stem name for the output results of the processing. Whenever Save operation is requested the operand number is added to the project wide path and is used as the name of the saved result.</p> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="_Open_Image"></a>Open Image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image048.jpg" alt= "image">. Operation is accessed by double click of left button on the canvas. This opens an “Open File” dialog. Currently the following image file types are supported:</p> <p class="MsoBodyText">Microsoft Bitmaps(*.bmp)</p> <p class="MsoBodyText">Tagged Image File Format (*.tif)</p> <p class="MsoBodyText">JPEG (*.jpg).</p> <p class="MsoBodyText">Text images (*.txt) . Those are compatible with LabView and ImageJ.</p> <p class="MsoBodyText">MS Bitmap files of 1, 8 and 24 bits are supported. Supported TIFs are 1, 8, 16, 32, 64, 128 bits per pixel grey scale and 24-bit colour. Two floating point types 32-bit and 64-bit are compatible with tiff version 3.8.2. . Complex images are stored as 2-component 64-bit floating point images. The library was obtained from <a href= "http://www.libtiff.org/">http://www.libtiff.org</a> and is copyright of Sam Leffler. Reading multi-page TIFs is supported. Opening a multi-page TIF file is equivalent to opening multiple image files. It results in multiple images. Note that multi-page input can only be replaced with another multi-page image in order not to break the project that uses those images.</p> <p class="MsoBodyText">JPEG library <span lang="EN-US" style= 'layout-grid-mode: line'>6b 27-Mar-1998</span> supports only 8-bit grey scale and 24-bit colour images. The library was obtained from <span lang="EN-US" style='layout-grid-mode: line'><a href= "ftp://ftp.uu.net/graphics/jpeg/">ftp://ftp.uu.net/graphics/jpeg/</a></span> and is a copyright of <span lang="EN-US" style= 'layout-grid-mode:line'>Thomas G. Lane</span><span lang="EN-US" style='font-family:"Courier New";layout-grid-mode: line'>.</span> Pixel format for integral file types is assumed unsigned. Drag and drop operation for the images is supported. The text images are the images without header, where pixels are separated by a tab character (\t or 0x09) and scan-lines are separated by new line characters (\n or \r, or both). If any of the scan-lines in the supplied image has a length different from the first scan-line an error is reported. Text images are detected based purely on file extension because they do not contain a header.</p> <h3 style='page-break-after:auto'><a name="node19" id= "node19"></a>Image List</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image049.jpg" alt= "image">. Sets/shows file list of images for batch processing. Supported images are the same as in Open Image operation. When operation is loaded from the project file this operation shows that a list rather than a single file is set as an input. This operation is an extension of Replace Image operation. The images which can be replaced by the lists are subject to the same conditions as the Replace Image operation</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node20" id= "node20"></a>Save Operand</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image050.jpg" alt= "image">. For image operand user has to select one of the supported image types, BMP, TIFF or JPEG. <b>It is</b> <b>not advisable to use JPEG format for any images that are intended to be analysed</b> later because of the lossy compression. The format is only handy for presentation purposes. Scalar operands are saved in text format. Palette is saved in BMP and TIFF images of 8-bit depth. For higher bit depth images it would be impractical to save the palette. Hence if you prefer a particular palette for an image, save it in a project because project tracks the palettes of the images, while other image display applications will not be aware of the preferred palette. </p> <p class="MsoBodyText">Name of the saved file is generated automatically. It is produced from the name of the first image in the project followed by _ and the first character of the name of operation before the operand the id of the operand which is being saved. The directory where the files are saved is the same directory where the first image of the project is stored. For example, if user opens file c:\temp\foo.tif inverts the image and saves it as a TIFF in the PIP project, the save file will have the name c:\temp\foo_i2.tif. The side effect of this behaviour is of cause overwriting of the original file, if “save” operation is used immediately after “open”. If the first operand is not an image than after first image is entered this operand, if saved will have in its prefix the name of first image entered later.</p> <h3 style='page-break-after:auto'><a name="node21" id= "node21"></a>Save Image Histogram</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image051.jpg" alt= "image">. This operation stores the single-dimensional histogram of the source image in a comma delimited text file with the extension “.histo.csv” preceded by the common to the whole project file name stemming from the first image of the project. The file contains 2 columns of numbers the first column is the intensities present in the image; the second column is the pixel counts for those intensities. The levels with counts 0 are not recorded in the file. For RGB images intensity histogram is saved.</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node22" id= "node22"></a>Replace Image</h3> <p class="MsoBodyText">This operation does not have an icon and is not shown on the PIP project. It is designed to facilitate application of the algorithms to images it was not developed on. This property of the “Replace” allows to use it for selection of the most (or least) illustrative example of the project algorithm performance. The operation can only be applied to 2 types of images:</p> <p class="MsoList" style='margin-left:0cm;text-indent:0cm'> a) images which are starting nodes of the algorithm graphs</p> <p class="MsoList" style='margin-left:0cm;text-indent:0cm'> b) images which are results of the manual selection of sub-images of other images. Here replacement means re-selection of another subregion.</p> <p class="MsoBodyText">The operation is not logged separately in the project file. It affects a memory stored project operations log but if the PIP project is saved after a “Replace” operation, the replacement image name is saved in the project file. Replacement is not considered an algorithm change and does not trigger “Save changes in …?” message on closure of the project. Operation “Replace” is a test mode operation.</p> <p class="MsoNormal">In some cases the nature of the algorithm would not allow replacement of a single image, that is, replacement of one input image requires replacement of another as well. The reason for such “synchronised” replacement is easy understood in a context of operations on images. Many operations can only be applied to the images of the same size, hence if 2 input images in the algorithm are involved in such operations, the images replacing them have to have the same size as well. Such synchronised replacement is facilitated by the “Replace Operands” dialog. In order to change the input file or value double-click on the item in ”New image” or “New value”</p> <p class="MsoNormal"><img border="0" width="563" height="419" src= "PIPUserManualNoFootnotes_files/image052.jpg" alt="image"></p> <p class="MsoNormal">columns. Icons on the left indicate which images or values were modified in this replacement operation. Old entries can be checked in the “Old image” and “Old value” columns.</p> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="node23" id= "node23"></a>Enter Scalar</h3> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image053.jpg" alt= "image">. Operation is accessed by double click of left button on the canvas. This opens a text box where user can type an operand value. Enter will close the box and put operand on the canvas.</p> <p class="MsoBodyText"><img border="0" width="118" height="77" src= "PIPUserManualNoFootnotes_files/image054.jpg" alt="image"> or</p> <p class="MsoBodyText"> <img border="0" width="275" height= "77" src="PIPUserManualNoFootnotes_files/image055.jpg" alt= "image"> or</p> <p class="MsoBodyText"> <img border="0" width="186" height= "77" src="PIPUserManualNoFootnotes_files/image056.jpg" alt= "image"></p> <h3 style='page-break-after:auto'><a name="node24" id= "node24"></a>Edit Scalar</h3> <p class="MsoNormal">This operation does not have an icon. This is a scalar analog of Replace Image operation. Replacement of multiple values are facilitated by the replacement facilitated by the “Replace Operands” dialog.</p> <p class="MsoNormal"><img border="0" width="118" height="77" src= "PIPUserManualNoFootnotes_files/image057.jpg" alt="image"></p> <p class="MsoNormal">This dialog does not allow you to change the type of the scalar operand</p> <h3 style='page-break-after:auto'><a name="node25" id= "node25"></a>Select Subimage</h3> <p class="MsoFootnoteText">Operation icon <img border="0" width= "31" height="31" src="PIPUserManualNoFootnotes_files/image058.jpg" alt="image"> . User interface command allows the user interactively select rectangular region of interest within the image.</p> <p class="MsoFootnoteText"> </p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2 style='page-break-after:auto'><a name= "_Type_Conversion_Operations"></a>Type Conversion Operations</h2> <p class="MsoBodyText">This group of operations is designed to homogenise operands for the operations, which demand operands of the same bit-per-pixel format. For some operations the type of the image produced is only known at the run time. An example of such operation is binary image <a href= "start.htm#_Label_4-connected_Blobs">labelling</a>. In order to prevent problems with type conversions the implementation of the conversions is input type independent.</p> <h3 style='page-break-after:auto'><a name="node26" id= "node26"></a>1-bit to 8-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image059.jpg" alt= "image">. The operation converts a 1-bit image to 8-bit image (0/1). For the display purposes image palette is set to 2 entries 0/255.</p> <h3 style='page-break-after:auto'><a name="node27" id= "node27"></a>1-bit to 16-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image060.jpg" alt= "image">. The operation converts a 1-bit image to 16-bit, 2-byte image (0/1).</p> <h3 style='page-break-after:auto'><a name="node28" id= "node28"></a>1-bit to 24-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image061.jpg" alt= "image">. The operation converts a 1-bit image to 24-bit RGB image ({0,0,0}/{255,255,255}).</p> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="node29" id= "node29"></a>1-bit to 32-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image062.jpg" alt= "image">. The operation converts 1-bit image to 32-bit, 4 byte integral type image (0/1).</p> <h3 style='page-break-after:auto'><a name="node30" id= "node30"></a>1-bit to Float, 32-bit single precision floating point</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image063.jpg" alt= "image">. The operation converts 1-bit image to 32-bit, floating point image (0/1).</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node31" id= "node31"></a>1-bit to 64-bit double precision floating point</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image064.jpg" alt= "image">. The operation converts 1-bit per pixel image to 64-bit per pixel double precision floating point type image (0/1.0)..</p> <h3 style='page-break-after:auto'><a name="node32" id= "node32"></a>1-bit to 128-bit complex</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image065.jpg" alt= "image">. The operation converts a 1-bit per pixel image to 128-bit per pixel complex type image ((0,0)/(1.0,0.0)).</p> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="node33" id= "node33"></a>8-bit to 16-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image060.jpg" alt= "image">. The operation converts 8-bit image to 16-bit, 2-byte image. All grey level values preserved.</p> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="node34" id= "node34"></a>8-bit to 24-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image066.jpg" alt= "image">. The operation converts 8-bit image to 24-bit, RGB image. All grey level values preserved.</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node35" id= "node35"></a>8-bit to 32-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image062.jpg" alt= "image">. The operation converts 8-bit image to 32-bit, 4 byte integral type image. All grey level values preserved.</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node36" id= "node36"></a>8-bit to Float, 32-bit single precision floating point</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image063.jpg" alt= "image">. The operation converts 8-bit image to 32-bit, single precision floating point type image. All grey level values preserved.</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node37" id= "node37"></a>8-bit to 64-bit double precision floating point</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image064.jpg" alt= "image">. The operation converts 8-bit per pixel image to 64-bit per pixel double precision floating point type image. All grey level values are preserved.</p> <h3 style='page-break-after:auto'><a name="node38" id= "node38"></a>8-bit to 128-bit complex</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image065.jpg" alt= "image">. The operation converts 8-bit per pixel image to 128-bit per pixel complex type image. All grey level values are preserved in the real part of the output image, the imaginary part is set to 0.</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node39" id= "node39"></a>16-bit to 8-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image059.jpg" alt= "image"> The operation converts 16-bit image to 8-bit image . The values are truncated into the range 0 to 255 without any re-scaling. Negative values assigned value 0. Values exceeding 255 assigned the value 255. If re-scaling is required, use arithmetic operations with scalar operands.</p> <h3 style='page-break-after:auto'><a name="node40" id= "node40"></a>16-bit to 32-bit</h3> <p class="MsoNormal">Operation icon <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image062.jpg" alt="image">. The operation converts 16-bit image to 32-bit, 4 byte integral type image. All grey level values preserved.</p> <h3 style='page-break-after:auto'><a name="node41" id= "node41"></a>16-bit to Float, 32-bit single precision floating point</h3> <p class="MsoNormal">Operation icon <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image063.jpg" alt="image">. The operation converts 16-bit image to 32-bit, single precision floating point type image. All grey level values preserved.</p> <h3 style='page-break-after:auto'><a name="node42" id= "node42"></a>16-bit to 64-bit double precision floating point</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image064.jpg" alt= "image">. The operation converts 16-bit per pixel image to 64-bit per pixel double precision floating point type image. All grey level values preserved.</p> <h3><a name="node43" id="node43"></a>16-bit to 128-bit complex</h3> <p class="MsoNormal">Operation icon <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image065.jpg" alt="image">. The operation converts 16-bit per pixel image to 128-bit per pixel complex type image. All grey level values are preserved in the real part of the output image, the imaginary part is set to 0.</p> <h3 style='page-break-after:auto'><a name="node44" id= "node44"></a>24-bit to 8-bitt</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image059.jpg" alt= "image">. The operation converts 24-bit RGB image to 8-bit grey scale image. Grey level of the output pixel is equal to the brightness component of the input pixel, (R+G+B)/3.</p> <h3 style='page-break-after:auto'><a name="node45" id= "node45"></a>24-bit to 16-bit</h3> <p class="MsoBodyText">Operation icon<img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image067.jpg" alt= "image">. The operation converts 24-bit RGB image to 16-bit grey scale image derived from the first principal component. Principal component or Hotelling transform of the image is calculated. Only the component, which has the largest variance, is used. This component is shifted so that the minimum luminance value for the image is 0. This operation allows to display the image which is used for watershed calculations for the corresponding RGB image.</p> <h3 style='page-break-after:auto'><a name="node46" id= "node46"></a>24-bit to 32-bit</h3> <p class="MsoBodyText">Operation icon<img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image068.jpg" alt= "image">. The operation converts 24-bit RGB image to packed 32-bit grey scale image. This operation is handy for alternative presentation of RGB images and consecutive processing using greyscale methods. LSB of 32-bit pixel value is red component of the pixel, second byte of 32-bit pixel is green, and third byte is blue, 4<sup>th</sup> byte is zero.</p> <h3 style='page-break-after:auto'><a name="node47" id= "node47"></a>Extract 1<sup>st</sup> principal component from 24-bit image</h3> <p class="MsoBodyText">Operation icon<img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image069.jpg" alt= "image">. Directly extracts 1<sup>st</sup> principal component, the component of the largest variance from 24-bit RGB image. The result is a 32-bit, single precision floating point grey scale image. Unlike in 24bit to 16-bit operation the result can have pixels with negative intensity.</p> <h3 style='page-break-after:auto'><a name="node48" id= "node48"></a>Extract red component of 24-bit image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image070.jpg" alt= "image">. The operation extracts 8-bit grey scale red component image out of 24-bit RGB.</p> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="node49" id= "node49"></a>Extract green component of 24-bit image</h3> <p class="MsoNormal"> </p> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image071.jpg" alt= "image">. The operation extracts 8-bit grey scale green component image out of 24-bit RGB.</p> <h3 style='page-break-after:auto'><a name="node50" id= "node50"></a>Extract blue component of 24-bit image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image072.jpg" alt= "image">. The operation extracts 8-bit grey scale blue component image out of 24-bit RGB.</p> <h3 style='page-break-after:auto'><a name="node51" id= "node51"></a>Combine 3 grey components into 24-bit image</h3> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image073.jpg" alt="image"> <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image074.jpg" alt= "image"> <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image075.jpg" alt= "image"> indicating red, green and blue components. Operation combines three 8-bit grey scale images into a 24-bit RGB image. User initiates the operation selecting the red component then prompted by the shape of the cursor to select other components. Technically it is a ternary operation, the one which takes 3 input parameters</p> <h3 style='page-break-after:auto'><a name="node52" id= "node52"></a>Extract hue component of 24-bit image</h3> <p class="MsoNormal"> </p> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image076.jpg" alt= "image">. Operation extracts the 32-bit, single precision floating point image of hue component out of 24-bit RGB image. The component is defined as an angle in the range of [0, 2<span style= 'font-family:Symbol'>p</span>). Value 0=2<span style= 'font-family:Symbol'>p</span> corresponds to colour red, value 2<span style='font-family:Symbol'>p</span>/3 corresponds to colour green, value 4<span style='font-family:Symbol'>p</span>/3 corresponds to colour blue. The default palette for the hue images is Circular. It permits display of the perceptually smooth transition between hue of 2<span style= 'font-family:Symbol'>p</span> and 0. This presentation is more natural than traditional mapping into grey scale from 0 to 255 that shows high contrast between the values close in hue on both sides of 2<span style='font-family: Symbol'>p</span>.</p> <h3 style='page-break-after:auto'><a name="node53" id= "node53"></a>Extract saturation component of 24-bit image</h3> <p class="MsoNormal"> </p> <p class="MsoBodyText">Operation icon<img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image077.jpg" alt= "image">. Operation extracts the 32-bit, single precision floating point image of saturation component out of 24-bit RGB image. The component is defined in the range of [0,1]. Saturation 0 describes grey-scale pixels.</p> <h3 style='page-break-after:auto'><a name="node54" id= "node54"></a>Extract intensity component of 24-bit image</h3> <p class="MsoNormal"> </p> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image078.jpg" alt= "image">. Operation extracts the 32-bit, single precision floating point image of intensity component out of 24-bit RGB image. The component is defined in the range of [0,255] as the original 8-bit RGB image.</p> <h3 style='page-break-after:auto'><a name="node55" id= "node55"></a>Combine 3 HSI components into 24-bit image</h3> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image079.jpg" alt="image"> <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image080.jpg" alt= "image"> <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image081.jpg" alt= "image"> indicating hue, saturation and intensity components. Operation combines 3 32-bit, single precision floating point image into a 24-bit RGB image. The assumptions about the components are as follows:</p> <p class="MsoList">1) Hue is an angle, where value 0 corresponds to red hue,</p> <p class="MsoList">2) Saturation belongs to the interval [0,1]. If saturation is outside this interval error is generated.</p> <p class="MsoList">3) Intensity is belongs to the interval [0,255]. For the pixels whose intensity exceeds this value will have their conversion from HSI to RGB calculated and result truncated to 255. This may cause some distortion of colour which can be avoided by proper scaling of the intensity component.</p> <p class="MsoNormal">User initiates the operation selecting the hue component then prompted by the shape of the cursor to select other components.</p> <h3 style='page-break-after:auto'><a name="node56" id= "node56"></a>32-bit integral to 8-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image059.jpg" alt= "image">. The operation converts a 32-bit image to 8-bit image. The values are truncated into the range 0 to 255 without any re-scaling. Negative values assigned value 0. Values exceeding 255 assigned the value 255. If re-scaling is required, use arithmetic operations with scalar operands.</p> <h3 style='page-break-after:auto'><a name="node57" id= "node57"></a>32-bit integral to 16-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image060.jpg" alt= "image">. The operation converts a 32-bit image to 16-bit, 2-byte image. The values are truncated into the range 0 to 65535 without any re-scaling. Negative values assigned value 0. Values exceeding 65535 assigned the value 65535. If re-scaling is required, use arithmetic operations with scalar operands.</p> <h3 style='page-break-after:auto'><a name="node58" id= "node58"></a>32-bit integral to 32-bit single precision floating point</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image063.jpg" alt= "image">. The operation converts a 32-bit per pixel integral type image to 32-bit per pixel single precision floating point type image. Since mantissa of the floating point image has a smaller than 32 bit count some of the grey levels in the original image are lost.</p> <h3 style='page-break-after:auto'><a name="node59" id= "node59"></a>32-bit integral to 64-bit double precision floating point</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image064.jpg" alt= "image">. The operation converts a 32-bit per pixel image to 64-bit per pixel double precision floating point type image. All grey level values preserved.</p> <h3><a name="node60" id="node60"></a>32-bit integral to 128-bit complex</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image065.jpg" alt= "image">. The operation converts a 32-bit per pixel integral image to 128-bit per pixel complex type image. All grey level values are preserved in the real part of the output image; the imaginary part is set to 0.</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node61" id= "node61"></a>32-bit single precision floating point to 8-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image059.jpg" alt= "image">. The operation converts a 32-bit per pixel, single precision floating point type image to 8-bit per pixel image. The values are truncated into the range 0 to 255 without any re-scaling. Negative values assigned value 0. Values exceeding 255 assigned the value 255. If re-scaling is required, use arithmetic operations with scalar operands.</p> <h3 style='page-break-after:auto'><a name="node62" id= "node62"></a>32-bit single precision floating point to 16-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image060.jpg" alt= "image">. The operation converts a 32-bit per pixel, single precision floating point type image to 16-bit per pixel image. The values are truncated into the range 0 to 65535 without any re-scaling. Negative values assigned value 0. Values exceeding 65535 assigned the value 65535. If re-scaling is required, use arithmetic operations with scalar operands.</p> <h3 style='page-break-after:auto'><a name="node63" id= "node63"></a>32-bit single precision floating point to 32-bit integral</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image062.jpg" alt= "image">. The operation converts a 32-bit per pixel, single precision floating point image to 32-bit per pixel image. The values are truncated into the range 0 to 4294967295 without any re-scaling. Negative values assigned value 0. If re-scaling is required, use arithmetic operations with scalar operands.</p> <h3 style='page-break-after:auto'><a name="node64" id= "node64"></a>32-bit single precision floating point to 64-bit double precision floating point</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image064.jpg" alt= "image">. The operation converts a 32-bit per pixel, single precision floating point image to 64-bit per pixel double precision floating point type image. All grey level values preserved.</p> <h3><a name="node65" id="node65"></a>32-bit single precision floating point to 128-bit complex</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image065.jpg" alt= "image">. The operation converts 32-bit per pixel floating point image to 128-bit per pixel complex type image. All grey level values are preserved in the real part of the output image, the imaginary part is set to 0.</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node66" id= "node66"></a>64-bit double precision floating point to 8-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image059.jpg" alt= "image">. The operation converts 64-bit per pixel, double precision floating point type image to 8-bit per pixel image. The values are truncated into the range 0 to 255 without any re-scaling. Negative values assigned value 0. Values exceeding 255 assigned the value 255. If re-scaling is required, use arithmetic operations with scalar operands.</p> <h3 style='page-break-after:auto'><a name="node67" id= "node67"></a>64-bit double precision floating point to 16-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image060.jpg" alt= "image">. The operation converts 64-bit per pixel, double precision floating point type image to 16-bit per pixel image. The values are truncated into the range 0 to 65535 without any re-scaling. Negative values assigned value 0. Values exceeding 65535 assigned the value 65535. If re-scaling is required, use arithmetic operations with scalar operands.</p> <h3 style='page-break-after:auto'><a name="node68" id= "node68"></a>64-bit double precision floating point to 32-bit integral</h3> <p class="MsoBodyText">Operation icon<img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image062.jpg" alt= "image">. The operation converts 64-bit per pixel, double precision floating point image to 32-bit per pixel image. The values are truncated into the range 0 to 4294967295 without any re-scaling. Negative values assigned value 0. Values exceeding 4294967295 assigned the value 4294967295. If re-scaling is required, use arithmetic operations with scalar operands.</p> <h3 style='page-break-after:auto'><a name="node69" id= "node69"></a>64-bit double precision floating point to 32-bit single precision floating point</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image063.jpg" alt= "image">. The operation converts 64-bit per pixel, double precision floating point image to 32-bit per pixel single precision floating point image. Some of the grey levels of the original image may be lost in this conversion.</p> <h3><a name="node70" id="node70"></a>64-bit double precision floating point to 128-bit complex</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image065.jpg" alt= "image">. The operation converts 64-bit per pixel, double precision floating point image to 128-bit per pixel complex type image. All grey level values are preserved in the real part of the output image, the imaginary part is set to 0.</p> <h3 style='page-break-after:auto'><a name="node71" id= "node71"></a>128-bit complex to 8-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image059.jpg" alt="image">. The operation converts 128-bit per pixel, complex type image to 8-bit per pixel image. For each pixel the absolute value of the complex pixel value is truncated into the range 0 to 255 without any re-scaling. Negative values assigned value 0. Values exceeding 255 assigned the value 255. If re-scaling is required, use arithmetic operations with scalar operands.</p> <h3 style='page-break-after:auto'><a name="node72" id= "node72"></a>128-bit complex to 16-bit</h3> <p class="MsoBodyText">Operation icon <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image060.jpg" alt="image">. The operation converts 128-bit per pixel, complex type image to 16-bit per pixel image. For each pixel the absolute value of the complex pixel value is truncated into the range 0 to 65535 without any re-scaling. Negative values assigned value 0. Values exceeding 65535 assigned the value 65535. If re-scaling is required, use arithmetic operations with scalar operands.</p> <h3 style='page-break-after:auto'><a name="node73" id= "node73"></a>128-bit complex to 32-bit integral</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image062.jpg" alt= "image">. The operation converts 128-bit per pixel, complex type image to 32-bit per pixel image. For each pixel the absolute value of the complex pixel value is truncated into the range 0 to 4294967295 without any re-scaling. Negative values assigned value 0. Values exceeding 4294967295 assigned the value 4294967295. If re-scaling is required, use arithmetic operations with scalar operands.</p> <h3 style='page-break-after:auto'><a name="node74" id= "node74"></a>128-bit complex to 32-bit single precision floating point</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image063.jpg" alt= "image">. The operation converts 128-bit per pixel, complex type image to 32-bit per pixel single precision floating point image. . For each pixel the absolute value of the complex pixel value is converted. Some of the grey levels of the original image may be lost in this conversion.</p> <h3 style='page-break-after:auto'><a name="node75" id= "node75"></a>128-bit complex to 64-bit double precision floating point</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image064.jpg" alt= "image">. The operation converts 128-bit per pixel, complex type image to 64-bit per pixel double precision floating point image. . For each pixel the absolute value of the complex pixel value is converted</p> <h3 style='page-break-after:auto'><a name="node76" id= "node76"></a>Extract real component of 128-bit complex image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image082.jpg" alt= "image">. The operation extracts 64-bit floating point real component image out of 128-bit complex image.</p> <h3 style='page-break-after:auto'><a name="node77" id= "node77"></a>Extract imaginary component of 128-bit complex image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image083.jpg" alt= "image">. The operation extracts 64-bit floating point imaginary component image out of 128-bit complex image.</p> <h3 style='page-break-after:auto'><a name="node78" id= "node78"></a>Extract magnitude component of 128-bit complex image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image084.jpg" alt= "image">. The operation extracts 64-bit floating point magnitude component image out of 128-bit complex image.</p> <h3 style='page-break-after:auto'><a name="node79" id= "node79"></a>Extract argument component of 128-bit complex image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image085.jpg" alt= "image">. The operation extracts 64-bit floating point argument component image out of 128-bit complex image.</p> <h3 style='page-break-after:auto'><a name="node80" id= "node80"></a>Combine 2 images of the same size into 128-bit complex image</h3> <p class="MsoBodyText">Operation icons are: <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image086.jpg" alt="image"> for real component of the resulting image and <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image087.jpg" alt="image"> for imaginary component of the resultion image. This operation offers an explicit way of creation of a complex 128-bit image. Another, implicit way is the FFT.</p> <h3 style='page-break-after:auto'><a name="node81" id= "node81"></a>Extract red component interpolating Bayer mosaic image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image088.jpg" alt= "image">. The operation extracts red component image after interpolating input Bayer mosaic image. The mosaic is assumed to have the structure as shown on the left of the icon. Operation currently is implemented only for 16 bit images. Resulting image has the same bit count.</p> <h3 style='page-break-after:auto'><a name="node82" id= "node82"></a>Extract green component interpolating Bayer mosaic image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image089.jpg" alt= "image">. The operation extracts green component image after interpolating Bayer mosaic image. The mosaic is assumed to have the structure as shown on the left of the icon. Operation currently is implemented only for 16 bit images. Resulting image has the same bit count.</p> <h3 style='page-break-after:auto'><a name="node83" id= "node83"></a>Extract blue component interpolating Bayer mosaic image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image090.jpg" alt= "image">. The operation extracts blue component image after interpolating Bayer mosaic image. The mosaic is assumed to have the structure as shown on the left of the icon. Operation currently is implemented only for 16 bit images. Resulting image has the same bit count.</p> <p class="MsoBodyText"> </p> <p class="MsoNormal"> </p> <p class="MsoBodyText"> </p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2 style='page-break-after:auto'><a name= "_Function_Operations"></a>Function Operations</h2> <p class="MsoNormal">Different functions applied to images and values belong to the operation of this class. The operations here are Unary or Binary and their separation in a distinct class is probably artificial. The intention is to include here elementary algebraic functions.</p> <h3 style='page-break-after:auto'><a name="node84" id= "node84"></a>Histogram Equalisation</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image091.jpg" alt= "image">. Non-interactive contrast enhancement method resulting in distribution of the image pixel grey levels “uniformly” across the whole dynamic range permissible by the image bits per pixel count. Uniformity is described in terms of cumulative histogram. Note that for RGB images this operation is performed not as separate RGB equalisations. It takes into account human perception of colour by converting the image into Hue-Lightness-Saturation colour space and performing equalisation on lightness component only leaving hue and saturation components unchanged. For 32-bit single precision and 64-bit double precision floating point images this operation does not stretch the histogram over the whole range of corresponding precision floating point numbers but only within a limited range 0 to 1. This is done purely to reduce the complexity of implementation.</p> <h3 style='page-break-after:auto'><a name="node85" id= "node85"></a>Absolute value</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image092.jpg" alt= "image">. This operation calculates absolute value of all pixels in the image or of the value operand. In reality it is only useful for value operands and for images of signed, floating point types</p> <h3 style='page-break-after:auto'><a name="node86" id= "node86"></a>Power function</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image093.jpg" alt= "image">. This is a binary operation. It calculates power function of all pixels in the image or power of the value operand. The exponent is supplied as the operand connected to this icon. This is a binary operation. The first operand is the source image or value</p> <h3 style='page-break-after:auto'><a name="node87" id= "node87"></a>Reassign dark outliers</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image094.jpg" alt= "image">. This binary operation takes source image and the fraction as the inputs. It calculates the histogram of the input image; starting from the darkest part calculates all levels whose cumulative histogram makes the given fraction of the original histogram; then re-maps all those found histogram levels into the closest above. For 24-bit RGB image all 3 channels are processed individually.</p> <h3 style='page-break-after:auto'><a name="node88" id= "node88"></a>Reassign bright outliers</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image095.jpg" alt= "image">. This binary operation takes source image and the fraction as the inputs. It calculates the histogram of the input image; starting from the brightest part calculates all levels whose cumulative histogram makes the given fraction of the original histogram, then re-maps all those found histogram levels into the closest below. For 24-bit RGB image all 3 channels are processed individually.</p> <h3 style='page-break-after:auto'><a name="node89" id= "node89"></a>Reassign dark and bright outliers</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image096.jpg" alt= "image">. This binary operation takes source image and the fraction as the inputs. It splits fraction into 2 and processes dark and bright parts of the histogram using the half of the original fraction. It calculates the histogram of the input image; starting from the brightest part calculates all levels whose cumulative histogram makes the given fraction of the original histogram, then re-maps all those found histogram levels into the closest below. In a similar fashion starting from the darkest part it calculates all levels whose cumulative histogram makes the given fraction of the original histogram; then re-maps all those found histogram levels into the closest above. For 24-bit RGB image all 3 channels are processed individually.</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2><a name="_Unary_Operations"></a>Unary Operations</h2> <p class="MsoBodyText">Operations in this group require a single input operand. Some of the operations in this group can only be performed on images of a particular type. For example, Image Labelling is defined on binary images only. Pop-up menu of available operations lists all operations, which could be performed with the selected operand.</p> <h3 style='page-break-after:auto'><a name="node90" id= "node90"></a>Invert Image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image097.jpg" alt= "image">. This operation belongs to the class of Unary operations which can be be loosely described as arithmetic. It inverts the value of each pixel. Image type is preserved. For integral unsigned image types inversion of a pixel value <b><i><span style='font-size: 12.0pt'>a</span></i></b> means subtraction <b><i><span style= 'font-size:12.0pt'>TypeMAX–a</span></i></b>. where <b><i><span style='font-size:12.0pt'>TypeMAX</span></i></b> is the maximum value for the type. For signed, floating point image types the inversion means change of sign.</p> <h3 style='page-break-after:auto'><a name="node91" id= "node91"></a>Add Image to Itself</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image098.jpg" alt= "image">. This is an arithmetic operation of doubling each pixel value in the image. The result is clipped at maximum grey level permissible for source image type. Image type is preserved.</p> <h3 style='page-break-after:auto'><a name="node92" id= "node92"></a>Exclusive OR on Image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image099.jpg" alt= "image">. This is an arithmetic operation is equivalent to subtracting image by itself. The result is an image of the same size as the source image with all pixels set to 0. Image type is preserved.</p> <h3 style='page-break-after:auto'><a name="node93" id= "node93"></a>Multiply Image by Itself</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image100.jpg" alt= "image">. This is an arithmetic operation of squaring each pixel value in the image. The result is not clipped at maximum grey level permissible for source image type, it rolls over. Image type is preserved.</p> <h3 style='page-break-after:auto'><a name="node94" id= "node94"></a>Automatic Thresholding Using Simple Image Statistic</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image101.jpg" alt= "image">. This is one of the thresholding operations that is those classifying image pixels as belonging to one of 2 classes foreground or background. The result of the operation is a binary image. For grey scale images this technique classifies pixels based on their grey level. For RGB images individual red, green and blue channels are thresholded independently then the result is a union (in a bitwise sense) of those 3 binary maps. The thresholding method itself is an unattended method which does not require calculation of the image histogram and is described in J. Kittler, J. Illingworth, and J. Forglein, “Threshold selection based on a simple image statistic” <i>Computer Vision, Graphics, and Image Processing,</i> vol 30 ,pp. 125-147,1985</p> <h3 style='page-break-after:auto'><a name="node95" id= "node95"></a>Automatic Segmentation Using Simple Image Statistic</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image102.jpg" alt= "image">. This segmentation technique is inspired by the method described in J. Kittler, J. Illingworth, and J. Forglein, “Threshold selection based on a simple image statistic” <i>Computer Vision, Graphics, and Image Processing,</i> vol 30 ,pp. 125-147,1985. It extends the original method by grouping image intensities around the histogram maxima. Detailed description will be given in a pending publication.</p> <h3 style='page-break-after:auto'><a name="node96" id= "node96"></a>Automatic Thresholding using Maximum between Class Variance</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image103.jpg" alt= "image">. This is one of unattended thresholding operations. Segments image into 2 classes, foreground and background selecting the threshold so that between the class variance is minimal. The method is described in detail in Gerhard X. Ritter, Joseph N. Wilson “Computer vision algorithm in Image Algebra” CRC Press, 1996, p131.</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node97" id= "node97"></a>Automatic Thresholding using Isodata algorithm</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image104.jpg" alt= "image">. This unattended thresholding operation is introduced in order to perform thresholding similar to default method used in popular ImageJ package. It implements the algorithm described in T.W. Ridler, S. Calvard, Picture thresholding using an iterative selection method, IEEE Trans. System, Man and Cybernetics, SMC-8 (1978) pp.630-632. By design it is supposed to be faster than between class variance algorithm but its implementation in ImageJ is very inefficient and was rewritten in Pictorial Image Processor in order to make it usable for images of any supported bit count.</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node98" id= "node98"></a>Modified Roberts Cross Filter</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image105.jpg" alt= "image">. This is one of the first digital edge detectors as well as one of the simplest. Despite its simplicity most of image analysis applications include it into their toolbox possibly because of its high speed. In its original implementation due to application of an even size 2x2 mask the resulting edge image ends up on a grid shifted half-pixel down and right. Everyone is aware of this discrepancy but for some reason ignores it. In Pictorial Image Processor© we decided to correct at least this fault of the filter. After application of the convolution mask pair to the original image resulting in an image on shifted grid, the pixels on the original grid are linearly interpolated and the result of the interpolation is presented as the output of the modified filter. More on original Roberts filter can be found in B. Jahne, “Digital ImageProcessing” Springer-Verlag 2002, p.331.</p> <h3 style='page-break-after:auto'><a name="node99" id= "node99"></a>Sobel Filter</h3> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image106.gif" alt= "image">. This is a standard edge detection operator described in many books on image processing, for example in Gerhard X. Ritter, Joseph N. Wilson “Computer vision algorithm in Image Algebra” CRC Press, 1996, p187. For RGB images the operator is applied to each component.</p> <h3 style='page-break-after:auto'><a name="node100" id= "node100"></a>Elementary Dilation with 8-connected kernel </h3> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image107.jpg" alt= "image">. Morphological image dilation on binary image with 3x3 flat kernel. All 8-neighbours are participating in the operation. The diagonal pixels reach to radius <span style= 'font-family:Symbol'>Ö</span>2 while others reach only 1 pixel distance. This may create “blockyness” artefact in the operation result</p> <h3 style='page-break-after:auto'><a name="node101" id= "node101"></a>Elementary Dilation with 4-connected kernel </h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image108.jpg" alt= "image">. Morphological image dilation on binary image with 3x3 flat kernel where only 4-neighbours, 4 pixels at the distance of 1 pixel exactly plus the central pixel are participating in the operation.</p> <h3 style='page-break-after:auto'><a name="node102" id= "node102"></a>Elementary Erosion with 8-connected kernel</h3> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image109.jpg" alt= "image">. Morphological image erosion on binary image with 3x3 flat kernel. All 8-neighbours are participating in the operation.</p> <h3 style='page-break-after:auto'><a name="node103" id= "node103"></a>Elementary Erosion with 4-connected kernel</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image110.jpg" alt= "image">. Morphological image erosion on binary image with 3x3 flat kernel where only 4-neighbours, 4 pixels at the distance of 1 pixel exactly plus the central pixel are participating in the operation.</p> <h3 style='page-break-after:auto'><a name="node104" id= "node104"></a>Elementary Opening with 8-connected kernel</h3> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image111.jpg" alt= "image">. Morphological image opening on binary image with 3x3 flat kernel. All 8-neighbours are participating in the operation.</p> <h3 style='page-break-after:auto'><a name="node105" id= "node105"></a>Elementary Opening with 4-connected kernel</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image112.jpg" alt= "image">. Morphological image opening on binary image with 3x3 flat kernel where only 4-neighbours, 4 pixels at the distance of 1 pixel exactly plus the central pixel are participating in the operation.</p> <h3 style='page-break-after:auto'><a name="node106" id= "node106"></a>Elementary Closing with 8-connected kernel</h3> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image113.jpg" alt= "image">. Morphological image closing on binary image with 3x3 flat kernel. All 8-neighbours are participating in the operation.</p> <h3 style='page-break-after:auto'><a name="node107" id= "node107"></a>Elementary Closing with 4-connected kernel</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image114.jpg" alt= "image">. Morphological image closing on binary image with 3x3 flat kernel kernel where only 4-neighbours, 4 pixels at the distance of 1 pixel plus the central pixel exactly are participating in the operation.</p> <h3 style='page-break-after:auto'><a name="node108" id= "node108"></a>Watershed</h3> <p class="MsoFootnoteText">Operation icon <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image115.jpg" alt="image">. Image segmentation technique based on the notion of skeleton of influence zones (SKIZ). Operation segments image into set of labeled regions corresponding to catchment basins of the image “grey” level, where lower levels correspond to valleys and higher levels correspond to ridges. Thin, one pixel wide watershed lines make the SKIZ. Region labels start from “grey level” 1, SKIZ itself is labeled with level 0. The algorithm for the segmentation is described in L Vincent and P Soille IEEE Transactions PAMI v13, No 6 June 1991.</p> <p class="MsoFootnoteText">In case of RGB images only one component derived from RGB image is used. This component is obtained on a per-image basis as a first principal component of the image, i.e. the principal component associated with the highest eigenvalue.</p> <h3 style='page-break-after:auto'><a name="node109" id= "node109"></a>Label Disjoint Histogram Blobs</h3> <p class="MsoFootnoteText">Operation icon <img border="0" width= "30" height="31" src="PIPUserManualNoFootnotes_files/image116.gif" alt="image">. Operation segments the image into the areas corresponding to different levels of grey or RGB colour. For grey scale images two image areas get different label, if there is an “empty” grey level separating grey levels making the areas. For RGB images 2 areas get different label, if there is no contiguous path in 3d histogram of the image connecting the RGB values of the pixels making the areas.</p> <p class="MsoFootnoteText"> </p> <h3 style='page-break-after:auto'><a name="node110" id= "node110"></a>Direction of gradient</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image117.jpg" alt= "image">.This operation transforms image into a map of the direction of image intensity gradient at each pixel. The gradient is calculated using Sobel mask. For floating point images the gradient is defined within the interval [-<span style= 'font-family:Symbol'>p</span>/2,<span style= 'font-family:Symbol'>p</span>/2]. For the images of the integral type the gradient is mapped into the whole dynamic range of the image. For example, [0,255] for 8-bit images, where -<span style= 'font-family:Symbol'>p</span>/2 is mapped into 0 and <span style= 'font-family:Symbol'>p</span>/2 into 255. The For RGB images the operator is applied to each component. In order to obtain the orientation of the gradient use <i>abs</i> function with floating point images.</p> <h3 style='page-break-after:auto'><a name="node111" id= "node111"></a>Create circular 1-bit per pixel kernel</h3> <p class="MsoFootnoteText">Operation icon <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image118.jpg" alt="image">. This is a supplementary operation which takes a value operand, the diameter of the kernel as an input and creates a binary 1 bit per pixel image of a circular kernel. Kernels of this type are frequently used in morphological operations on binary images. Since the input is a scalar, the operation is available on value operand menu.</p> <h3 style='page-break-after:auto'><a name="node112" id= "node112"></a>Create vertical 1-bit per pixel line</h3> <p class="MsoFootnoteText">Operation icon <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image119.jpg" alt="image">. This is a supplementary operation which takes a value operand, the length of the line as an input and creates a binary 1 bit per pixel 1pixel wide image of a vertical line. Available on value operand menu.</p> <h3 style='page-break-after:auto'><a name="node113" id= "node113"></a>Create horizontal 1-bit per pixel line</h3> <p class="MsoFootnoteText">Operation icon <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image120.jpg" alt="image">. This is a supplementary operation which takes a value operand, the length of the line as an input and creates a binary 1 bit per pixel 1 pixel high image of a horizontal line. Available on value operand menu.</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2><a name="node114" id="node114"></a>Unary Operations Applicable Only To Binary Images</h2> <h3 style='page-break-after:auto'><a name="node115" id= "node115"></a>Fill Closed Contours</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image121.jpg" alt= "image">. This operation is applicable to binary images only. It fills areas of background (0) situated within a closed contour line of foreground (1). It will fill the area no matter how thin the contour line is (8-connectivity). Image edge is considered as a background, hence any background blob touching the edge will not be filled.</p> <h3 style='page-break-after:auto'><a name="node116" id= "node116"></a>Fill Small Holes</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image122.jpg" alt= "image">. This operation is applicable to binary images only. It fills areas of background (0) situated within a closed contour line of foreground (1). It will fill the area only if the contour line is thick (4-connectivity). Image edge is considered as a background, hence any background blob touching the edge will not be filled.</p> <h3 style='page-break-after:auto'><a name="node117" id= "node117"></a>Outline Foreground Blobs</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image123.jpg" alt= "image">. This operation is applicable to binary images only. Foreground pixels in the original image, which have 4-connected background neighbours are unchanged. All other pixels change to background. This produces an 8-connected foreground boundary.</p> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="node118" id= "node118"></a>Skeletonise</h3> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image124.jpg" alt= "image">. Binary image skeletonisation procedure preserving homotopy. Procedure described in G X Ritter Handbook of computer vision algorithms in Image Algebra CRC Press 1996, pp153-157.</p> <h3 style='page-break-after:auto'><a name="node119" id= "node119"></a>Prune</h3> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image125.jpg" alt= "image">. Binary image pruning procedure similar to described in G X Ritter Handbook of computer vision algorithms in Image Algebra CRC Press 1996, p.170 but for 8-connected blobs rather than 4-connected. Before removal pixel is checked for 8-connected neighbours and removed if it only has one.</p> <h3 style='page-break-after:auto'><a name="node120" id= "node120"></a>Prune Not Closed Lines</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image126.jpg" alt= "image">. This binary image pruning is stronger than the previous one. It removes all strenuous branches from the skeleton leaving only those branches that have close contours. As parts of their branches. The goal of this function is to leave only closed lines</p> <h3 style='page-break-after:auto'><a name= "_Label_4-connected_Blobs"></a>Label 4-connected Blobs in the Binary Image</h3> <p class="MsoBodyText">Operation icon<img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image127.jpg" alt= "image">. Identifies all disjoined blobs of the foreground (grey level 1) of the binary image and assigns each of them individual grey level. Two blobs are considered disjoint if neither pixel of one blob has pixels of the other blob in its 4-neighbourhood. This operation will mark as separate the areas separated by one- pixel-wide lines. Use this operation to label blobs obtained by inversion of a skeleton image. Image type of the operation result depends on number of blobs in the original B&W image. If number blobs below 256 the result is an 8-bit greyscale image otherwise it is 16-bit or even 32 bit integer type image.</p> <h3 style='page-break-after:auto'><a name="node121" id= "node121"></a>Label 8-connected Blobs in the Binary Image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image128.jpg" alt= "image">. Identifies all disjoined blobs of the foreground (grey level 1) of the binary image and assigns each of them individual grey level. Two blobs are considered disjoint if neither pixel of one blob has pixels of the other blob in its 4-neighbourhood. According to this definition one-pixel-thin separation line is not enough to make blobs separated by this line disjoint. When skeletonisation or watershed are employed to segment the image they produce 1 pixel wide lines. In order to perform labelling apply elementary erosion prior to labelling. On the other hand this operation will label thin line of 8-connected pixels as a single line while the 4-connected labelling will label each pixel as separate blob. Use this operation to label thin lines. Image type of the operation result depends on number of blobs in the original B&W image. If number blobs below 256 the result is an 8-bit greyscale image otherwise it is 16-bit or even 32 bit integer type image.</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node122" id= "node122"></a>Label 4-connected Blobs in the Binary Image by the Blob Area</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image129.jpg" alt= "image">. Identifies all disjoined blobs of the foreground (grey level 1) of the binary image and assigns each of them individual grey level. This grey level is the equal to the area of the blob in pixels. Two blobs are considered disjoint if neither pixel of one blob has pixels of the other blob in its 4-neighbourhood. If maximum blob size is below 256 the result is an 8-bit greyscale image otherwise it is 16-bit or even 32 bit integer type image. This operation provides capability to differentiate the blobs by their size or, if the blobs are skeletons, by their lengths. It encodes the size of the blob into its intensity and exposes it to the intensity-base processing techniques.</p> <h3 style='page-break-after:auto'><a name="node123" id= "node123"></a>Label 8-connected Blobs in the Binary Image by the Blob Area</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image130.jpg" alt= "image">. Identifies all disjoined blobs of the foreground (grey level 1) of the binary image and assigns each of them individual grey level. This grey level is the equal to the area of the blob in pixels. Two blobs are considered disjoint if neither pixel of one blob has pixels of the other blob in its 8-neighbourhood. If maximum blob size is below 256 the result is an 8-bit greyscale image otherwise it is 16-bit or even 32 bit integer type image. This operation provides capability to differentiate the blobs by their size or, if the blobs are skeletons, by their lengths. It encodes the size of the blob into its intensity and exposes it to the intensity-base processing techniques. </p> <h3 style='page-break-after:auto'><a name="node124" id= "node124"></a>Distance Transform with Outside Assumed Background</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image131.jpg" alt= "image">. This operation is applicable to binary images only. For each foreground pixel in the source image the grey level of the corresponding pixel in the operation output is proportional to its distance from the nearest background pixel. Pixels corresponding to background pixels in the source image have the value of distance set to zero in the output image. Image type of the operation result depends on maximum distance calculated for the source B&W image. If the distance is below 256 the result is an 8-bit greyscale image otherwise it is 16-bit or even 32 bit integer type image. For calculation efficiency Euclidean distance is approximated with chamfer 5-7-11 distance. The pixel grey levels obtained as the result of the operation should be divided by 5 to get the Euclidean distance in pixels. Since the pixel outside the boundary assumed to be background, the distance is measured either from background pixels or boundary.</p> <h3 style='page-break-after:auto'><a name="node125" id= "node125"></a>Distance Transform with Outside Assumed Foreground</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image132.jpg" alt= "image">. Same as previous chamfer 5-7-11 distance transform with exception of assumption of the area outside the boundary. Since it is considered foreground, the distance is measured only between the pixels within the image.</p> <span style= 'font-size:10.0pt;font-family:"Times New Roman"'><br clear="all" style='page-break-before:always'></span> <p class="MsoBodyText"> </p> <h2><a name="node126" id="node126"></a>Unary Operations Applicable Only To 24-bit Images</h2> <h3 style='page-break-after:auto'><a name="node127" id= "node127"></a>Extract Red-Green Histogram Image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image133.jpg" alt= "image">. This operation creates a 256x256 8-bit per pixel image of a two-dimensional histogram of the source image. The histogram describes red and green channels of the image with red intensities of the source image mapped into X axis and green intensities of the source image mapped into Y axis.</p> <h3 style='page-break-after:auto'><a name="node128" id= "node128"></a>Extract Red-Blue Histogram Image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image134.jpg" alt= "image">. This operation creates a 256x256 8-bit per pixel image of a two-dimensional histogram of the source image. The histogram describes red and blue channels of the image with red intensities of the source image mapped into X axis and blue intensities of the source image mapped into Y axis.</p> <h3 style='page-break-after:auto'><a name="node129" id= "node129"></a>Extract Blue-Green Histogram Image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image133.jpg" alt= "image">. This operation creates a 256x256 8-bit per pixel image of a two-dimensional histogram of the source image. The histogram describes blue and green channels of the image with blue intensities of the source image mapped into X axis and green intensities of the source image mapped into Y axis.</p> <h3 style='page-break-after:auto'><a name="node130" id= "node130"></a>Extract Hue-Intensity Histogram Image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image135.jpg" alt= "image">. This operation creates a 256x256 8-bit per pixel image of a two-dimensional histogram of the source image. The histogram describes hue and intensity channels of the image with hue intensities of the source image mapped into X axis and intensity channel intensities of the source image mapped into Y axis.</p> <h3 style='page-break-after:auto'><a name="node131" id= "node131"></a>Extract Hue-Saturation Histogram Image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image136.jpg" alt= "image">. This operation creates a 256x256 8-bit per pixel image of a two-dimensional histogram of the source image. The histogram describes hue and saturation channels of the image with hue intensities of the source image mapped into X axis and saturation intensities of the source image mapped into Y axis.</p> <h3 style='page-break-after:auto'><a name="node132" id= "node132"></a>Extract Intensity-Saturation Histogram Image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image137.jpg" alt= "image">. This operation creates a 256x256 8-bit per pixel image of a two-dimensional histogram of the source image. The histogram describes intensity and saturation channels of the image with intensity channel intensities of the source image mapped into X axis and green intensities of the source image mapped into Y axis.</p> <span style= 'font-size:10.0pt;font-family:"Times New Roman"'><br clear="all" style='page-break-before:always'></span> <p class="MsoBodyText"> </p> <h2><a name="node133" id="node133"></a>Unary Transforms</h2> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node134" id= "node134"></a>Forward Fast Fourier Transform</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image138.jpg" alt= "image">. Forward fast Fourier transform produces an image of type Complex. For the RGB images the transform is performed on the intensity component. Prior to transform the image is augmented in size to the closest power of 2 and fading is applied to the padded parts of the image in order to reduce any ringing in processed and converted back to space domain images. FFT images hold the information about their original size.</p> <h3 style='page-break-after:auto'><a name="node135" id= "node135"></a>Reverse Fast Fourier Transform</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image139.jpg" alt= "image">. Reverse fast Fourier transform converts a FFT image of type Complex to an image of type double by applying the reverse FFT.</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2 style= 'margin-left:36.0pt;text-indent:0cm;page-break-after:auto'><a name= "node136" id="node136"></a>Unary Geometric Operations</h2> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="node137" id= "node137"></a>Crop image removing dark border</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image140.jpg" alt= "image"> . This operation attempts to remove a dark border around the central part of the image. The central part is assumed the image and the dark border a worthless background. It is assumed that the sensible part of the picture is rectangular with the sides aligned with the frame sides. The operation attempts to find this rectangle and crop the image to it. Resulting image is smaller</p> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="node138" id= "node138"></a>Get Crop Mask</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image141.jpg" alt= "image">. This operation generates a binary image where the area of the dark border around perimeter is set to background 0 and the central area of higher than background intensity is set to 1. Output binary image has the same size as the input image.</p> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="node139" id= "node139"></a>Rotate image by 90<sup>o</sup></h3> <p class="MsoNormal">Operation icon. <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image142.jpg" alt= "image"> This operation rotates image counterclockwise by 90 degrees. Height and width of the image swap.</p> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="node140" id= "node140"></a>Rotate image by -90<sup>o</sup></h3> <p class="MsoNormal">Operation icon. <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image142.jpg" alt= "image"> This operation rotates image clockwise by 90 degrees. . Height and width of the image swap.</p> <h3 style='page-break-after:auto'><a name="node141" id= "node141"></a>Get Top Border Mask for the Image</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image143.jpg" alt= "image">. This operation generates a binary image where the line of pixels at the top of the image is set to 1. Output binary image has the same size as the input image. This mask can work as a probe to test objects touching the top border of the image.</p> <h3 style='page-break-after:auto'><a name="node142" id= "node142"></a>Get Bottom Border Mask for the Image</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image144.jpg" alt= "image">. This operation generates a binary image where the line of pixels at the bottom of the image is set to 1. Output binary image has the same size as the input image. This mask can work as a probe to test objects touching the bottom border of the image.</p> <h3 style='page-break-after:auto'><a name="node143" id= "node143"></a>Get Top Border Mask for the Image</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image145.jpg" alt= "image">. This operation generates a binary image where the line of pixels on the left edge of the image is set to 1. Output binary image has the same size as the input image. This mask can work as a probe to test objects touching the left border of the image.</p> <h3 style='page-break-after:auto'><a name="node144" id= "node144"></a>Get Right Border Mask for the Image</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image146.jpg" alt= "image">. This operation generates a binary image where the line of pixels on the right edge of the image is set to 1. Output binary image has the same size as the input image. This mask can work as a probe to test objects touching the right border of the image.</p> <h3 style='page-break-after:auto'><a name="node145" id= "node145"></a>Expand Image Half Size in Each Direction</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image147.jpg" alt= "image">. This operation is design to help the user to overcome the edge effects caused by mirroring of the border of the image, which is default border action in many operations in Pictorial Image Processor, and replace it with repeat of the border row/column of pixels in the image. This operation expands the image half image size in each direction by repeating corresponding border. Then user can apply the desired operation ensuring that the border action is “repeat last pixel” rather than “mirror last pixel”.</p> <h3 style='page-break-after:auto'><a name="node146" id= "node146"></a>Contract Image Quarter Size in Each Direction</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image148.jpg" alt= "image">. This operation inverts the action of the previous operation, setting the image back to the original after it was processed with “repeat last pixel” border action.</p> <h3 style='page-break-after:auto'><a name="node147" id= "node147"></a>Circular Shift of Origin by Half-Image</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image149.jpg" alt= "image">. This is a supportive operation for frequency domain processing. It is intended for different ways of presenting the FFT image: origin in the centre of the image (default) or origin in the top left corner, like any other image. Traditionally FFT images have the origin in the centre. This operation will toggle the position.</p> <h3 style='page-break-after:auto'><a name="node148" id= "node148"></a>Upsample Image by Linear Interpolation</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image150.jpg" alt= "image">. This operation doubles the image resolution by linearly interpolating the values between the pixels. The operation is designed to be the inverse of the Downsample by Linear Interpolation operation.</p> <h3 style='page-break-after:auto'><a name="node149" id= "node149"></a>Downsample Image by Linear Interpolation</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image151.jpg" alt= "image">. This operation halves the image resolution by linearly interpolating the values between every second row of the pixels. The operation is designed to be the inverse of the Upsample by Linear Interpolation operation.</p> <h3 style='page-break-after:auto'><a name="node150" id= "node150"></a>Upsample Image by Duplicating Each Pixel</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image152.jpg" alt= "image">. This operation doubles the image resolution by duplicating each pixel in both directions.</p> <h3 style='page-break-after:auto'><a name="node151" id= "node151"></a>Downsample Image by Removing Each Second Pixel</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image153.jpg" alt= "image">. This operation halves the image resolution by removing each second pixel in each direction.</p> <p class="MsoNormal"> </p> <p class="MsoNormal"> </p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2 style='margin-left:0cm;text-indent:0cm'><a name="node152" id= "node152"></a>Unary Statistical Operations</h2> <p class="MsoBodyText">This class of operations is designed to obtain measurements from the images. Their input operands are images and outputs are scalars</p> <h3 style='page-break-after:auto'><a name="node153" id= "node153"></a>Mean</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image154.jpg" alt= "image">. Calculates mean of the image pixel grey values. For RGB images calculates mean of the brightness component of the image.</p> <h3 style='page-break-after:auto'><a name="node154" id= "node154"></a>Standard Deviation</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image155.jpg" alt= "image">. Calculates standard deviation of the image pixel grey values. For RGB images calculates standard deviation of the brightness component of the image.</p> <h3 style='page-break-after:auto'><a name="node155" id= "node155"></a>Width</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image156.jpg" alt= "image">. Retrieves image width.</p> <h3 style='page-break-after:auto'><a name="node156" id= "node156"></a>Height</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image157.jpg" alt= "image">. Retrieves image height.</p> <h3 style='page-break-after:auto'><a name="node157" id= "node157"></a>Histogram Maximum</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image158.jpg" alt= "image">. Calculates the number of pixels corresponding to the most frequently met grey level in the image. Level 0, normally reserved for background, is ignored in the calculations. For RGB images calculates the number of pixels corresponding to the most frequently met RGB level in the image.</p> <h3 style='page-break-after:auto'><a name="node158" id= "node158"></a>Peak Grey Level</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image159.jpg" alt= "image">. Calculates the grey level corresponding to the image histogram maximum. Level 0, normally reserved for background, is ignored in the calculations. Currently this operation is not available for RGB images because it requires vector operands.</p> <h3 style='page-break-after:auto'><a name="node159" id= "node159"></a>Maximum Grey Level of the Image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image160.jpg" alt= "image">. Calculates maximum intensity, maximum grey level met in the image. For RGB images it calculates maximum intensity.</p> <h3 style='page-break-after:auto'><a name="node160" id= "node160"></a>Median Grey Level of the Image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image161.jpg" alt= "image">. Calculates median intensity, median grey level met in the image. For RGB images it calculates median intensity.</p> <h3 style='page-break-after:auto'><a name="node161" id= "node161"></a>Minimum Grey Level of the Image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image162.jpg" alt= "image">. Calculates minimum intensity, maximum grey level met in the image. For RGB images it calculates minimum intensity.</p> <h3 style='page-break-after:auto'><a name="node162" id= "node162"></a>Total sum of intensities</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image163.jpg" alt= "image">. Calculates total sum of the image pixel grey values. For RGB images calculates total sum of the intensities of the image pixels. This operation is handy when user needs to calculate weighting for kernels produced by <a href= "start.htm#_Convolution_Kernel_Designer">Kernel Designer</a></p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2 style='page-break-after:auto'><a name="node163" id= "node163"></a>Unary Statistical Operations Applicable Only To Binary Images</h2> <p class="MsoBodyText">This class of operations is designed to obtain measurements from binary, 1 bit per pixel images. Their input operands are binary images and outputs are scalars</p> <h3 style='page-break-after:auto'><a name="node164" id= "node164"></a>Blob count</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image164.jpg" alt= "image">. Operation calculates number of foreground blobs, connected areas in the binary, 1 bit per pixel image. Blobs are identified through image <a href= "start.htm#_Label_4-connected_Blobs">label</a> operation. According to its definition blobs are disjoint if no pixel of one blob has a pixel of another blob in its 8-neighbourhood.</p> <h3 style='page-break-after:auto'><a name="node165" id= "node165"></a>Mean blob area</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image165.jpg" alt= "image">. Operation calculates average area of foreground blobs across the whole image.</p> <h3 style='page-break-after:auto'><a name="node166" id= "node166"></a>Mean diagonal of minimum enclosing rectangle (MER)</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image166.jpg" alt= "image">. Operation calculates average across the whole binary image length of minimal enclosing rectangle (MER) for the foreground blobs. MER is illustrated in the picture below</p> <p class="MsoNormal"> </p> <p class="MsoNormal"><img border="0" width="537" height="285" src= "PIPUserManualNoFootnotes_files/image167.gif" alt="image"></p> <h3 style='page-break-after:auto'><a name="node167" id= "node167"></a>Total foreground area</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image163.jpg" alt= "image">. Calculates total area in pixels making the foreground. This operation is a binary equivalent of total sum of the image pixel grey values for gray scale images.</p> <h3 style='page-break-after:auto'><a name="node168" id= "node168"></a>Minimum distance of foreground blobs to the image right border</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image168.jpg" alt= "image">. This operation calculates horizontal distance from the right border of the image for a foreground pixel closest to that border.</p> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="node169" id= "node169"></a>Minimum distance of foreground blobs to the image left border</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image169.jpg" alt= "image">. This operation calculates horizontal distance from the left border of the image for a foreground pixel closest to that border.</p> <h3 style='page-break-after:auto'><a name="node170" id= "node170"></a>Minimum distance of foreground blobs to the image top border</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image170.jpg" alt= "image">. This operation calculates horizontal distance from the top border of the image for a foreground pixel closest to that border.</p> <h3 style='page-break-after:auto'><a name="node171" id= "node171"></a>Minimum distance of foreground blobs to the image bottom border</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image171.jpg" alt= "image">. This operation calculates horizontal distance from the bottom border of the image for a foreground pixel closest to that border.</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2><a name="_Binary_Arithmetic_Operations"></a>Binary Arithmetic Operations</h2> <h3 style='page-break-after:auto'><a name="node172" id= "node172"></a>Add</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image172.jpg" alt= "image">. This arithmetic operation takes either two image operands, or one image and one scalar operand, or two scalar operands. If both operands are images they have to have the same size. Images can be of different types, have different bit-per-pixel counts. .If the source operand is an image, he output image has the same type as the first operand. The result is clipped at maximum grey level permissible for source image type.</p> <p class="MsoBodyText"><b>Table of operation results for the operation A + b, where A is image and b is scalar</b></p> <table class="MsoNormalTable" border="1" cellspacing="0" cellpadding="0" style='border-collapse:collapse;border:none'> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText">Operand</p> <p class="MsoBodyText">Type</p> </td> <td width="95" valign="top" style= 'width:71.1pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b scalar</span></p> </td> <td width="87" valign="top" style= 'width:64.9pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float scalar</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>double scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex scalar</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A+b,255)</span></p> </td> <td width="87" valign="top" style= 'width:64.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ b mod 256, 255)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ |b|, 255)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ b mod 256, 255)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ floor(b) mod 256, 255)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ floor( Re(b)), 255)</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A+b,65535)</span></p> </td> <td width="87" valign="top" style= 'width:64.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A+b,65535)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ |b|, 65535)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ [b mod 65536], 65535)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ floor(b) mod 65536, 65535)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ floor( Re(b)), 65535)</span></p> </td> </tr> <tr style='height:17.55pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+b,256) for each channel R,G,B</span></p> </td> <td width="87" valign="top" style= 'width:64.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ b mod 256, 255) ) for each channel R,G,B</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>R =min(A+ b<sub>R</sub>, 255) ) , G=min(A+ b<sub>G</sub>, 255) ) B=min(A+ b<sub>B</sub>, 255) )</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ b mod 256, 255) ) for each channel R,G,B</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ floor(b) mod 256, 255) ) for each channel R,G,B</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ floor( Re(b)), 255) ) for each channel R,G,B</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A+b,</span> <span style= 'font-size:8.0pt'>4294967295)</span></p> </td> <td width="87" valign="top" style= 'width:64.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A+b,</span> <span style= 'font-size:8.0pt'>4294967295)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ |b|, 4294967295)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A+b,</span> <span style= 'font-size:8.0pt'>4294967295)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ floor(b) , 4294967295)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A+ floor( Re(b)), 4294967295)</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A+b</span></p> </td> <td width="87" valign="top" style= 'width:64.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A+b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A+ |b|</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A+b truncated to float</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A+b truncated to float</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A+Re(b) truncated to float</span></p> </td> </tr> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A+b</span></p> </td> <td width="87" valign="top" style= 'width:64.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A+b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A+ |b|</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A+b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A+b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A+Re(b)</span></p> </td> </tr> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(A)+b</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>Im = Im(A)</span></p> </td> <td width="87" valign="top" style= 'width:64.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(A)+b</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>Im = Im(A)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(A)+|b|</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>Im = Im(A)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(A)+b</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>Im = Im(A)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(A)+b</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>Im = Im(A)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(A)+Re(b)</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>Im = Im(A)+Im(b)</span></p> </td> </tr> </table> <p class="MsoBodyText">A+b denotes an image where each pixel C <sub>i,j</sub> =A<sub>i,j</sub>+ b</p> <p class="MsoBodyText">|b| denotes a norm of multi-component scalar. For the rgb image it is (R+G+B)/3,</p> <p class="MsoBodyText">b<sub>R ,</sub> b<sub>G</sub>, b<sub>B</sub> denotes R, G, B components of b</p> <p class="MsoBodyText">floor(b) is the largest integer smaller than b </p> <p class="MsoBodyText">Re(b) denotes the real component of the complex number b</p> <p class="MsoBodyText"> <b>a</b> mod <b>b</b> is a modulus <b>b</b> operation on <b>a</b></p> <p class="MsoBodyText"><b>Table of operation results for each element in the operation A + B, where A and B are images</b></p> <table class="MsoNormalTable" border="1" cellspacing="0" cellpadding="0" style='border-collapse:collapse;border:none'> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText">Operand</p> <p class="MsoBodyText">Type</p> </td> <td width="97" valign="top" style= 'width:72.55pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a+b,256)</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+ b mod 256, 255)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+ |b|, 255)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+ b mod 256, 255)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+ floor(b) mod 256, 255)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min (a+ floor( Re(b)), 255)</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a+b,65535)</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+ b mod 65536, 65535)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+ |b|, 65535)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+ b mod 65536, 65535)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+ floor(b) mod 65536, 65535)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min (a+ floor( Re(b)), 65535)</span></p> </td> </tr> <tr style='height:17.0pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+b,256) for each channel R,G,B</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+ b mod 256, 255) ) for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>R=min(a<sub>R</sub>+ b<sub>R</sub>, 255) ) , G=min(a<sub>G</sub>+ b<sub>G</sub>, 255) ) B=min(a<sub>B</sub>+ b<sub>B</sub>, 255) )</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+ b mod 256, 255) ) for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+ floor(b) mod 256, 255) ) for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+ floor( Re(b)), 255) ) for each channel R,G,B</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a+b,</span> <span style= 'font-size:8.0pt'>4294967295)</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a+b,</span> <span style= 'font-size:8.0pt'>4294967295)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+ |b|, 4294967295)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a+b,</span> <span style= 'font-size:8.0pt'>4294967295)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+ floor(b) , 4294967295)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a+ floor( Re(b)), 4294967295)</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a+b</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a+b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a+ |b|</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a+b truncated to float</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a+b truncated to float</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a+Re(b) truncated to float</span></p> </td> </tr> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a+b</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a+b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a+ |b|</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a+b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a+b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a+Re(b)</span></p> </td> </tr> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(a)+b</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>Im = Im(a)</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(a)+b</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>Im = Im(a)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(a)+|b|</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>Im = Im(a)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(a)+b</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>Im = Im(a)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(a)+b</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>Im = Im(a)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(a)+Re(b)</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>Im = Im(a)+Im(b)</span></p> </td> </tr> </table> <p class="MsoBodyText">a and b denote pixel values of matching pixels A<sub>i,j</sub> and B<sub>i,j</sub> of images A and B</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node173" id= "node173"></a>Subtract</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image173.jpg" alt= "image">. This arithmetic operation takes either two image operands, or one image and one scalar operand, or two scalar operands. If both operands are images they have to have the same size. Images can be of different types, have different bit-per-pixel counts. In case of image operand present the output image has the same type as the image operand. The output image has the same type as the first operand. . If the source operand is an image, the result is clipped to minimum grey level permissible for the source image type.</p> <p class="MsoBodyText"><b>Table of operation results for the operation A - b, where A is image and b is scalar</b></p> <table class="MsoNormalTable" border="1" cellspacing="0" cellpadding="0" style='border-collapse:collapse;border:none'> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText">Operand</p> <p class="MsoBodyText">Type</p> </td> <td width="95" valign="top" style= 'width:71.1pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b scalar</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float scalar</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>double scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex scalar</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A-b,0)</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A- b mod 256, 0)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A- |b|, 0)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A- b mod 256, 0)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A- floor(b) mod 256, 0)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A- floor( Re(b)), 0)</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A-b,0)</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A- b mod 65536, 0)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A- |b|, 0)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A- b mod 65536, 0)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A- floor(b) mod 65536, 0)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A- floor( Re(b)), 0)</span></p> </td> </tr> <tr style='height:17.55pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A-b,0) for each channel R,G,B</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A-b,0) for each channel R,G,B</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>R=max(A<sub>R</sub>-b<sub>R</sub>,0) G=max(A<sub>G</sub>-b<sub>G</sub>,0) B= max(A<sub>B</sub>-b<sub>B</sub>,0)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A-b,0) for each channel R,G,B</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A- floor(b) mod 256, 0) for each channel R,G,B</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A- floor( Re(b)), 0) for each channel R,G,B</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A-b,0)</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A-b,0)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A- |b|, 0)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A-b,0)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A-floor(b),0)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A- floor( Re(b)), 0)</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A-b</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A-b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A-|b|</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A-b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A-b truncated to float</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A-Re(b) truncated to float</span></p> </td> </tr> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A-b</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A-b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A-|b|</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A-b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A-b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A-Re(b)</span></p> </td> </tr> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(A)-b Im =0 </span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(A)-b </span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'> Im =0 </span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(A)-|b| Im =0 </span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(A)-b Im =0 </span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(A)-b Im =0 </span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(A)-Re(b) Im = Im(A)-Im(b)</span></p> </td> </tr> </table> <p class="MsoBodyText">A-b denotes an image where each pixel C <sub>i,j</sub> =A<sub>i,j</sub>- b</p> <p class="MsoBodyText">|b| denotes a norm of multi-component scalar. For the rgb image it is (R+G+B)/3,</p> <p class="MsoBodyText">floor(b) is the largest integer smaller than b</p> <p class="MsoBodyText">Re(b) denotes the real component of the complex number b</p> <p class="MsoBodyText"> <b>a</b> mod <b>b</b> is a modulus <b>b</b> operation on <b>a</b></p> <p class="MsoBodyText"><b>Table of operation results for each element in the operation A - B, where A and B are images</b></p> <table class="MsoNormalTable" border="1" cellspacing="0" cellpadding="0" style='border-collapse:collapse;border:none'> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText">Operand</p> <p class="MsoBodyText">Type</p> </td> <td width="97" valign="top" style= 'width:72.55pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a-b,0)</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a- b mod 256, 0)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a- |b|, 0)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a- b mod 256, 0)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a- floor(b) mod 256, 0)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a-floor( Re(b)) mod 256, 0)</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a-b,0)</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a- b mod 65536, 0)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a- |b|, 0)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a- b mod 65536, 0)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a- floor(b) mod 65536, 0)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a-floor( Re(b)) mod 65536, 0)</span></p> </td> </tr> <tr style='height:17.0pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a-b,0) for each channel R,G,B</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a-b,0) for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>R=max(a<sub>R</sub>-b<sub>R</sub>,0) G=max(a<sub>G</sub>-b<sub>G</sub>,0) B= max(a<sub>B</sub>-b<sub>B</sub>,0)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a-b,0) for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a- floor(b) mod 256, 0) for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a- floor( Re(b)), 0) for each channel R,G,B</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a-b,0)</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a-b,0)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a- |b|, 0)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a-b,0)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a-floor(b),0)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a- floor( Re(b)), 0)</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a-b</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a-b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a-|b|</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a-b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a-b truncated to float</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a-Re(b) truncated to float</span></p> </td> </tr> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a-b</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a-b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a-|b|</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a-b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a-b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a-Re(b)</span></p> </td> </tr> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(a)-b Im =0 </span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(a)-b </span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'> Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(a)-|b| Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(a)-b Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(a)-b Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re = Re(a)-Re(b) Im = Im(a)-Im(b)</span></p> </td> </tr> </table> <p class="MsoBodyText">a and b denote pixel values of matching pixels A<sub>i,j</sub> and B<sub>i,j</sub> of images A and B</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node174" id= "node174"></a>Multiply</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image174.jpg" alt= "image">. This arithmetic operation takes either two image operands, or one image and one scalar operand, or two scalar operands. If both operands are images they have to have the same size. Images can be of different types, have different bit-per-pixel counts. In case of image operand present the output image has the same type as the image operand. .If the source operand is an image, he result is not clipped at maximum grey level permissible for source image type, it rolls over.</p> <p class="MsoBodyText"><b>Table of operation results for the operation A</b> <b><span style='font-family:Symbol'>´</span> b, where A is image and b is scalar</b></p> <table class="MsoNormalTable" border="1" cellspacing="0" cellpadding="0" style='border-collapse:collapse;border:none'> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText">Operand</p> <p class="MsoBodyText">Type</p> </td> <td width="95" valign="top" style= 'width:71.1pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b scalar</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float scalar</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>double scalar</span></p> </td> <td width="89" valign="top" style= 'width:66.8pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex scalar</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b mod 256</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mod 256</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>|b|) mod 256</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b ) mod 256</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mode 256</span></p> </td> <td width="89" valign="top" style= 'width:66.8pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>[A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span> <span style= 'font-size: 8.0pt'>Re(b)] mod 256</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mod 65536</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mod 65536</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>|b|) mod 65536</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b ) mod 65536</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mode 65536</span></p> </td> <td width="89" valign="top" style= 'width:66.8pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>[A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span> <span style= 'font-size: 8.0pt'>Re(b)] mod 65536</span></p> </td> </tr> <tr style='height:17.55pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b mod 256 for each channel R,G,B</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mod 256 for each channel R,G,B</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>R =(A<sub>R</sub></span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b<sub>R</sub>) mod 256 G =(A<sub>G</sub></span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b<sub>G</sub>) mod 256 B =(A<sub>B</sub></span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b<sub>B</sub>) mod 256</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b ) mod 256 for each channel R,G,B</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mode 256 for each channel R,G,B</span></p> </td> <td width="89" valign="top" style= 'width:66.8pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>[A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span> <span style= 'font-size: 8.0pt'>Re(b)] mod 256 for each channel R,G,B</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mod 4294967296</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mod 4294967296</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>|b|) mod 4294967296</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b ) mod 4294967296</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mode 4294967296</span></p> </td> <td width="89" valign="top" style= 'width:66.8pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>[A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span> <span style= 'font-size: 8.0pt'>Re(b)] mod 4294967296</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>|b|</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b truncated to float</span></p> </td> <td width="89" valign="top" style= 'width:66.8pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>Re(b)</span></p> </td> </tr> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>|b|</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b</span></p> </td> <td width="89" valign="top" style= 'width:66.8pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>Re(b)</span></p> </td> </tr> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(A)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b Im =0 </span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(A)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b Im =0 </span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(A)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>|b| Im =0 </span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(A)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b Im =0 </span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(A)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b Im =0 </span></p> </td> <td width="89" valign="top" style= 'width:66.8pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(A)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>Re(b) –Im(A)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size:8.0pt'>Im(b) Im =Im(A)</span> <span style= 'font-size:8.0pt; font-family:Symbol'>´</span><span style= 'font-size:8.0pt'>Re(b) + Re(A)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>Im(b) </span></p> </td> </tr> </table> <p class="MsoBodyText">A<span style= 'font-size:8.0pt;font-family:Symbol'>´</span>b denotes an image where each pixel C <sub>i,j</sub> =A<sub>i,j</sub><span style= 'font-size:8.0pt;font-family:Symbol'>´</span>b</p> <p class="MsoBodyText">|b| denotes a norm of multi-component scalar. For the rgb image it is (R+G+B)/3,</p> <p class="MsoBodyText">floor(b) is the largest integer smaller than b</p> <p class="MsoBodyText">Re(b) denotes the real component of the complex number b</p> <p class="MsoBodyText"> <b>a</b> mod <b>b</b> is a modulus <b>b</b> operation on <b>a</b></p> <p class="MsoBodyText"><b>Table of operation results for each element in the operation A</b> <b><span style= 'font-family:Symbol'>´</span> B, where A and B are images</b></p> <table class="MsoNormalTable" border="1" cellspacing="0" cellpadding="0" style='border-collapse:collapse;border:none'> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText">Operand</p> <p class="MsoBodyText">Type</p> </td> <td width="97" valign="top" style= 'width:72.55pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mod 256</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span> <span style= 'font-size: 8.0pt'>b )mod 256</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>|b|) mod 256</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span> <span style= 'font-size: 8.0pt'>b) mod 256</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span> <span style= 'font-size: 8.0pt'>b) mode 256 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>[a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span> <span style= 'font-size: 8.0pt'>Re(b)] mod 256</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mod 65536</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span> <span style= 'font-size: 8.0pt'>b )mod 65536</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>|b|) mod 65536</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span> <span style= 'font-size: 8.0pt'>b) mod 65536</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span> <span style= 'font-size: 8.0pt'>b) mode 65536</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>[a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>Re(b)] mod 65536</span></p> </td> </tr> <tr style='height:17.0pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b mod 256 for each channel R,G,B</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mod 256 for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>R =(a<sub>R</sub></span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b<sub>R</sub>) mod 256 G =(a<sub>G</sub></span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b<sub>G</sub>) mod 256 B =(a<sub>B</sub></span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b<sub>B</sub>) mod 256</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b ) mod 256 for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mode 256 for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>[a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span> <span style= 'font-size: 8.0pt'>Re(b)] mod 256 for each channel R,G,B</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mod 4294967296</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mod 4294967296</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>|b|) mod 4294967296</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b ) mod 4294967296</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>(a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b) mode 4294967296</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>[a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span> <span style= 'font-size: 8.0pt'>Re(b)] mod 4294967296</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>|b|</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b truncated to float</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>Re(b)</span></p> </td> </tr> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>|b|</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>Re(b)</span></p> </td> </tr> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(a)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b Im =0 </span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(a)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(a)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>|b| Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(a)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(a)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>b Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(a)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>Re(b) –Im(a)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size:8.0pt'>Im(b) Im =Im(a)</span> <span style= 'font-size:8.0pt; font-family:Symbol'>´</span><span style= 'font-size:8.0pt'>Re(b) + Re(a)</span><span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>Im(b) </span></p> </td> </tr> </table> <p class="MsoBodyText">a and b denote pixel values of matching pixels A<sub>i,j</sub> and B<sub>i,j</sub> of images A and B</p> <p class="MsoBodyText"> If value of the product exceeds the largest 32-bit number the result of the product is 0. This is the default behaviour of runtime library when converting floating types to unsigned integer types</p> <h3 style='page-break-after:auto'><a name="node175" id= "node175"></a>Divide</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image175.jpg" alt= "image">. This arithmetic operation takes either two image operands, or one image and one scalar operand, or two scalar operands. If both operands are images they have to have the same same size. Images can be of different types, have different bit-per-pixel counts. In case of image operand present the output image has the same type as the image operand. If first selected operand is value operand but the second is an image the value operand is used as a divisor. In case of 2 value operands second operand divides the first. If the source operand is an image, he result is not clipped at maximum grey level permissible for source image type, it rolls over.</p> <p class="MsoBodyText"><b>Table of operation results for the operation A ÷ b, where A is image and b is scalar</b></p> <table class="MsoNormalTable" border="1" cellspacing="0" cellpadding="0" style='border-collapse:collapse;border:none'> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText">Operand</p> <p class="MsoBodyText">Type</p> </td> <td width="95" valign="top" style= 'width:71.1pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b scalar</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float scalar</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>double scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex scalar</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A÷b mod 256</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A÷ (b mod 256) mod 256</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A÷|b| mod 256</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A÷ (b mod 256) mod 256</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(A÷b) mode 256</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>[A÷ Re(b)] mod 256</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(A÷ b) mod 65536</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(A÷ b )mod 65536</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(A÷|b|) mod 65536</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(A÷ b) mod 65536</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(A÷ b) mode 65536</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>[A÷Re(b)] mod 65536</span></p> </td> </tr> <tr style='height:17.55pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A÷b mod 256 for each channel R,G,B</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(A÷b) mod 256 for each channel R,G,B</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>R =(A<sub>R</sub>÷b<sub>R</sub>) mod 256 G =(A<sub>G</sub>÷b<sub>G</sub>) mod 256 B =(A<sub>B</sub>÷b<sub>B</sub>) mod 256</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(A÷b ) mod 256 for each channel R,G,B</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(A÷b) mode 256 for each channel R,G,B</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>[A÷ Re(b)] mod 256 for each channel R,G,B</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(A÷b) mod 4294967296</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(A÷b) mod 4294967296</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(A÷|b|) mod 4294967296</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(A÷b ) mod 4294967296</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(A÷b) mode 4294967296</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>[A÷ Re(b)] mod 4294967296</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A÷b</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A÷b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A÷|b|</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A÷b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A÷b truncated to float</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A÷Re(b)</span></p> </td> </tr> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A÷b</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A÷b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A÷|b|</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A÷b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>A÷b</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>A÷Re(b)</span></p> </td> </tr> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(A)÷b Im =0 </span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(A)÷b Im =0 </span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(A)÷|b| Im =0 </span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(A)÷b Im =0 </span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(A)÷b Im =0 </span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(A)</span> <span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>Re(b) +Im(A)</span> <span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size:8.0pt'>Im(b) Im =Im(A)</span> <span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>Re(b) + Re(A)</span> <span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size:8.0pt'>Im(b) </span></p> </td> </tr> </table> <p class="MsoBodyText">A<span style='font-size:8.0pt'>÷</span>b denotes an image where each pixel C <sub>i,j</sub> =A<sub>i,j</sub><span style='font-size:8.0pt'>÷</span>b</p> <p class="MsoBodyText">|b| denotes a norm of multi-component scalar. For the rgb image it is (R+G+B)/3,</p> <p class="MsoBodyText">floor(b) is the largest integer smaller than b</p> <p class="MsoBodyText">Re(b) denotes the real component of the complex number b</p> <p class="MsoBodyText"> <b>a</b> mod <b>b</b> is a modulus <b>b</b> operation on <b>a</b></p> <p class="MsoBodyText"><b> </b></p> <p class="MsoBodyText"><b>Table of operation results for each element in the operation A ÷ B, where A and B are images</b></p> <table class="MsoNormalTable" border="1" cellspacing="0" cellpadding="0" style='border-collapse:collapse;border:none'> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText">Operand</p> <p class="MsoBodyText">Type</p> </td> <td width="97" valign="top" style= 'width:72.55pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷b) mod 256</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷ b )mod 256</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷|b|) mod 256</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷ b) mod 256</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>[a÷b] mode 256</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>[a÷Re(b)] mod 256</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷ b) mod 65536</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷ b )mod 65536</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷|b|) mod 65536</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷ b) mod 65536</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷ b) mode 65536</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>[a÷Re(b)] mod 65536</span></p> </td> </tr> <tr style='height:17.0pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a÷b mod 256 for each channel R,G,B</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷b) mod 256 for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>R =(a<sub>R</sub>÷b<sub>R</sub>) mod 256 G =(a<sub>G</sub>÷b<sub>G</sub>) mod 256 B =(a<sub>B</sub>÷b<sub>B</sub>) mod 256</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷b ) mod 256 for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷b) mode 256 for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>[a÷ Re(b)] mod 256 for each channel R,G,B</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷b) mod 4294967296</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷b) mod 4294967296</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷|b|) mod 4294967296</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷b ) mod 4294967296</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>(a÷b) mode 4294967296</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>[a÷ Re(b)] mod 4294967296</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a÷b</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a÷b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a÷|b|</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a÷b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a÷b truncated to float</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a÷Re(b)</span></p> </td> </tr> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a÷b</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a÷b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a÷|b|</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a÷b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>a÷b</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>a÷Re(b)</span></p> </td> </tr> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(a)÷b Im =0 </span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(a)÷b Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(a)÷|b| Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(a)÷b Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(a)÷b Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=Re(a)</span> <span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>Re(b) +Im(a)</span> <span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size:8.0pt'>Im(b) Im =Im(a)</span> <span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size: 8.0pt'>Re(b) + Re(a)</span> <span style= 'font-size:8.0pt;font-family:Symbol'>´</span><span style= 'font-size:8.0pt'>Im(b) </span></p> </td> </tr> </table> <p class="MsoBodyText">a and b denote pixel values of matching pixels A<sub>i,j</sub> and B<sub>i,j</sub> of images A and B</p> <p class="MsoBodyText"> </p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node176" id= "node176"></a>Maximum</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image160.jpg" alt= "image">. This arithmetic operation takes either two image operands, or one image and one scalar operand, or two scalar operands. If both operands are images they have to have the same size. Images can be of different types, have different bit-per-pixel counts. The output image has the same type as the first operand. If the source operand is an image, the result is clipped at maximum grey level permissible for source image type.</p> <p class="MsoBodyText"><b>Table of operation results for the operation max(A , b), where A is image and b is scalar</b></p> <table class="MsoNormalTable" border="1" cellspacing="0" cellpadding="0" style='border-collapse:collapse;border:none'> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText">Operand</p> <p class="MsoBodyText">Type</p> </td> <td width="95" valign="top" style= 'width:71.1pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b scalar</span></p> </td> <td width="73" valign="top" style= 'width:55.1pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b scalar</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b scalar</span></p> </td> <td width="101" valign="top" style= 'width:75.5pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float scalar</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>double scalar</span></p> </td> <td width="99" valign="top" style= 'width:74.35pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex scalar</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A,b)</span></p> </td> <td width="73" valign="top" style= 'width:55.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max(A,b) mod 256</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A,|b| )</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max(A,b) mod 256</span></p> </td> <td width="101" valign="top" style= 'width:75.5pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[A, floor(b)] mod 256</span></p> </td> <td width="99" valign="top" style= 'width:74.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[A, floor {Re(b)}] mod 256</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A,b)</span></p> </td> <td width="73" valign="top" style= 'width:55.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max(A,b) mod 65536</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A,|b| )</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max(A,b) mod mod 65536</span></p> </td> <td width="101" valign="top" style= 'width:75.5pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[A, floor(b)] mod 65536}</span></p> </td> <td width="99" valign="top" style= 'width:74.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[A, floor {Re(b)}] 65536}</span></p> </td> </tr> <tr style='height:17.55pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A,b) for each channel R,G,B</span></p> </td> <td width="73" valign="top" style= 'width:55.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max{A, [min (b,256)] mod 256}</span> <span style= 'font-size:8.0pt'>for each channel R,G,B</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A,b )</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>R = max(A,b <sub>R</sub>) G = max(A,b <sub>G</sub>) B = max(A,b <sub>B</sub>)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max(A,b) mod 256</span> <span style= 'font-size:8.0pt'>for each channel R,G,B</span></p> </td> <td width="101" valign="top" style= 'width:75.5pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[A, floor(b)] mod 256 for each channel R,G,B</span></p> </td> <td width="99" valign="top" style= 'width:74.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[A, floor {Re(b)}] 256 for each channel R,G,B</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A,b)</span></p> </td> <td width="73" valign="top" style= 'width:55.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max(A,b) mod 4294967296</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(A,|b| )</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max(A,b) mod 4294967296</span></p> </td> <td width="101" valign="top" style= 'width:75.5pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[A, floor(b)] mod 4294967296</span></p> </td> <td width="99" valign="top" style= 'width:74.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[A, floor {Re(b)}] mod 4294967296</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A,b)</span></p> </td> <td width="73" valign="top" style= 'width:55.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A,b)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A,|b|)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A,b)</span></p> </td> <td width="101" valign="top" style= 'width:75.5pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[max(A,b), FLOAT_MAX)</span></p> </td> <td width="99" valign="top" style= 'width:74.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max[max(A,Re(b)), FLOAT_MAX)</span></p> </td> </tr> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A,b)</span></p> </td> <td width="73" valign="top" style= 'width:55.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A,b)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A,|b|)</span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A,b)</span></p> </td> <td width="101" valign="top" style= 'width:75.5pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A,b)</span></p> </td> <td width="99" valign="top" style= 'width:74.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(A,Re(b))</span></p> </td> </tr> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= max(A,b) Im =0 </span></p> </td> <td width="73" valign="top" style= 'width:55.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=max(A,b) Im =0 </span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= max(A,|b|) Im =0 </span></p> </td> <td width="82" valign="top" style= 'width:61.4pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= max(A,b) Im =0 </span></p> </td> <td width="101" valign="top" style= 'width:75.5pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= max(A,b) Im =0 </span></p> </td> <td width="99" valign="top" style= 'width:74.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= max(A,Re(b)) </span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'> Im =max(A,Im(b)) </span></p> </td> </tr> </table> <p class="MsoBodyText">max(A<span style= 'font-size:8.0pt'>,</span>b) denotes an image where each pixel C <sub>i,j</sub> =max(A<sub>i,j</sub><span style= 'font-size:8.0pt'>,</span>b )</p> <p class="MsoBodyText">|b| denotes a norm of multi-component scalar. For the rgb image it is (R+G+B)/3,</p> <p class="MsoBodyText">floor(b) is the largest integer smaller than b</p> <p class="MsoBodyText">Re(b) denotes the real component of the complex number b</p> <p class="MsoBodyText"> <b>a</b> mod <b>b</b> is a modulus <b>b</b> operation on <b>a</b></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>FLOAT_MAX = 3.402823466e+38F maximum 32-bit floating point number</span></p> <p class="MsoBodyText"><b>Table of operation results for each element in the operation max(A ,B), where A and B are images</b></p> <table class="MsoNormalTable" border="1" cellspacing="0" cellpadding="0" style='border-collapse:collapse;border:none'> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText">Operand</p> <p class="MsoBodyText">Type</p> </td> <td width="97" valign="top" style= 'width:72.55pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="76" valign="top" style= 'width:57.25pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="89" valign="top" style= 'width:66.85pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a,b)</span></p> </td> <td width="76" valign="top" style= 'width:57.25pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max(a,b) mod 256</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a,|b| )</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max(a,b) mod 256</span></p> </td> <td width="89" valign="top" style= 'width:66.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[a, floor(b)] mod 256</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[a, floor {Re(b)}] mod 256</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a,b)</span></p> </td> <td width="76" valign="top" style= 'width:57.25pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max(a,b) mod 65536</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a,|b| )</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max(a,b) mod mod 65536</span></p> </td> <td width="89" valign="top" style= 'width:66.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[a, floor(b)] mod 65536}</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[a, floor {Re(b)}] 65536}</span></p> </td> </tr> <tr style='height:17.0pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a,b) for each channel R,G,B</span></p> </td> <td width="76" valign="top" style= 'width:57.25pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max{a, [min (b,256)] mod 256}</span> <span style= 'font-size:8.0pt'>for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a,b )</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>R = max(a,b <sub>R</sub>) G = max(a,b <sub>G</sub>) B = max(a,b <sub>B</sub>)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max(a,b) mod 256</span> <span style= 'font-size:8.0pt'>for each channel R,G,B</span></p> </td> <td width="89" valign="top" style= 'width:66.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[a, floor(b)] mod 256 for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[a, floor {Re(b)}] 256 for each channel R,G,B</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a,b)</span></p> </td> <td width="76" valign="top" style= 'width:57.25pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max(a,b) mod 4294967296</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max(a,|b| )</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>max(a,b) mod 4294967296</span></p> </td> <td width="89" valign="top" style= 'width:66.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[a, floor(b)] mod 4294967296</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[a, floor {Re(b)}] mod 4294967296</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a,b)</span></p> </td> <td width="76" valign="top" style= 'width:57.25pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a,b)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a,|b|)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a,b)</span></p> </td> <td width="89" valign="top" style= 'width:66.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>max[max(a,b), FLOaT_MaX)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max[max(a,Re(b)), FLOaT_MaX)</span></p> </td> </tr> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a,b)</span></p> </td> <td width="76" valign="top" style= 'width:57.25pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a,b)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a,|b|)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a,b)</span></p> </td> <td width="89" valign="top" style= 'width:66.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a,b)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>max(a,Re(b))</span></p> </td> </tr> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= max(a,b) Im =0 </span></p> </td> <td width="76" valign="top" style= 'width:57.25pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=max(a,b) Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= max(a,|b|) Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= max(a,b) Im =0 </span></p> </td> <td width="89" valign="top" style= 'width:66.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= max(a,b) Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= max(a,Re(b)) </span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'> Im =max(a,Im(b)) </span></p> </td> </tr> </table> <p class="MsoBodyText">a and b denote pixel values of matching pixels A<sub>i,j</sub> and B<sub>i,j</sub> of images A and B</p> <p class="MsoBodyText"><b> </b></p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node177" id= "node177"></a>Minimum</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image162.jpg" alt= "image">. This arithmetic operation takes either two image operands, or one image and one scalar operand, or two scalar operands. If both operands are images they have to have the same size. Images can be of different types, have different bit-per-pixel counts. The output image has the same type as the first operand. If the source operand is an image, the result is clipped at minimum grey level permissible for source image type.</p> <p class="MsoBodyText"><b>Table of operation results for the operation min(A , b), where A is image and b is scalar</b></p> <table class="MsoNormalTable" border="1" cellspacing="0" cellpadding="0" style='border-collapse:collapse;border:none'> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText">Operand</p> <p class="MsoBodyText">Type</p> </td> <td width="95" valign="top" style= 'width:71.1pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b scalar</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b scalar</span></p> </td> <td width="71" valign="top" style= 'width:53.05pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b scalar</span></p> </td> <td width="76" valign="top" style= 'width:2.0cm;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b scalar</span></p> </td> <td width="95" valign="top" style= 'width:70.9pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float scalar</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>double scalar</span></p> </td> <td width="101" valign="top" style= 'width:75.8pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex scalar</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A,b)</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min(A,b) mod 256</span></p> </td> <td width="71" valign="top" style= 'width:53.05pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A,|b| )</span></p> </td> <td width="76" valign="top" style= 'width:2.0cm;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min(A,b) mod 256</span></p> </td> <td width="95" valign="top" style= 'width:70.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[A, floor(b)] mod 256</span></p> </td> <td width="101" valign="top" style= 'width:75.8pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[A, floor {Re(b)}] mod 256</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A,b)</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min(A,b) mod 65536</span></p> </td> <td width="71" valign="top" style= 'width:53.05pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A,|b| )</span></p> </td> <td width="76" valign="top" style= 'width:2.0cm;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min(A,b) mod mod 65536</span></p> </td> <td width="95" valign="top" style= 'width:70.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[A, floor(b)] mod 65536}</span></p> </td> <td width="101" valign="top" style= 'width:75.8pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[A, floor {Re(b)}] 65536}</span></p> </td> </tr> <tr style='height:17.55pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A,b) for each channel R,G,B</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min{A, [min (b,256)] mod 256}</span> <span style= 'font-size:8.0pt'>for each channel R,G,B</span></p> </td> <td width="71" valign="top" style= 'width:53.05pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A,b )</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>R = min(A,b <sub>R</sub>) G = min(A,b <sub>G</sub>) B = min(A,b <sub>B</sub>)</span></p> </td> <td width="76" valign="top" style= 'width:2.0cm;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min(A,b) mod 256</span> <span style= 'font-size:8.0pt'>for each channel R,G,B</span></p> </td> <td width="95" valign="top" style= 'width:70.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[A, floor(b)] mod 256 for each channel R,G,B</span></p> </td> <td width="101" valign="top" style= 'width:75.8pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.55pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[A, floor {Re(b)}] 256 for each channel R,G,B</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A,b)</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min(A,b) mod 4294967296</span></p> </td> <td width="71" valign="top" style= 'width:53.05pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(A,|b| )</span></p> </td> <td width="76" valign="top" style= 'width:2.0cm;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min(A,b) mod 4294967296</span></p> </td> <td width="95" valign="top" style= 'width:70.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[A, floor(b)] mod 4294967296</span></p> </td> <td width="101" valign="top" style= 'width:75.8pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[A, floor {Re(b)}] mod 4294967296</span></p> </td> </tr> <tr style='height:18.2pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A,b)</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A,b)</span></p> </td> <td width="71" valign="top" style= 'width:53.05pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A,|b|)</span></p> </td> <td width="76" valign="top" style= 'width:2.0cm;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A,b)</span></p> </td> <td width="95" valign="top" style= 'width:70.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[min(A,b) , -FLOAT_MAX)</span></p> </td> <td width="101" valign="top" style= 'width:75.8pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:18.2pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min[min(A,Re(b)), -FLOAT_MAX)</span></p> </td> </tr> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A,b)</span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A,b)</span></p> </td> <td width="71" valign="top" style= 'width:53.05pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A,|b|)</span></p> </td> <td width="76" valign="top" style= 'width:2.0cm;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A,b)</span></p> </td> <td width="95" valign="top" style= 'width:70.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A,b)</span></p> </td> <td width="101" valign="top" style= 'width:75.8pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(A,Re(b))</span></p> </td> </tr> <tr style='height:25.9pt'> <td width="82" valign="top" style= 'width:61.4pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> <td width="95" valign="top" style= 'width:71.1pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= min(A,b) </span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>Im =0 </span></p> </td> <td width="72" valign="top" style= 'width:53.75pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=min(A,b) Im =0 </span></p> </td> <td width="71" valign="top" style= 'width:53.05pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= min(A,|b|) Im =0 </span></p> </td> <td width="76" valign="top" style= 'width:2.0cm;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= min(A,b) Im =0 </span></p> </td> <td width="95" valign="top" style= 'width:70.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= min(A,b) Im =0 </span></p> </td> <td width="101" valign="top" style= 'width:75.8pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.9pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= min(A,Re(b)) </span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'> Im =min(A,Im(b)) </span></p> </td> </tr> </table> <p class="MsoBodyText">min(A<span style= 'font-size:8.0pt'>,</span>b) denotes an image where each pixel C <sub>i,j</sub> =min(A<sub>i,j</sub><span style= 'font-size:8.0pt'>,</span>b )</p> <p class="MsoBodyText">|b| denotes a norm of multi-component scalar. For the rgb image it is (R+G+B)/3,</p> <p class="MsoBodyText">floor(b) is the largest integer smaller than b</p> <p class="MsoBodyText">Re(b) denotes the real component of the complex number b</p> <p class="MsoBodyText"> <b>a</b> mod <b>b</b> is a modulus <b>b</b> operation on <b>a</b></p> <p class="MsoBodyText"><b>Table of operation results for each element in the operation min(A ,B), where A and B are images</b></p> <table class="MsoNormalTable" border="1" cellspacing="0" cellpadding="0" style='border-collapse:collapse;border:none'> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText">Operand</p> <p class="MsoBodyText">Type</p> </td> <td width="97" valign="top" style= 'width:72.55pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>8b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a,b)</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min(a,b) mod 256</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a,|b| )</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min(a,b) mod 256</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[a, floor(b)] mod 256</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[a, floor {Re(b)}] mod 256</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>16b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a,b)</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min(a,b) mod 65536</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a,|b| )</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min(a,b) mod mod 65536</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[a, floor(b)] mod 65536}</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[a, floor {Re(b)}] 65536}</span></p> </td> </tr> <tr style='height:17.0pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>24b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a,b) for each channel R,G,B</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min{a, [min (b,256)] mod 256}</span> <span style= 'font-size:8.0pt'>for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a,b )</span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>R = min(a,b <sub>R</sub>) G = min(a,b <sub>G</sub>) B = min(a,b <sub>B</sub>)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min(a,b) mod 256</span> <span style= 'font-size:8.0pt'>for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[a, floor(b)] mod 256 for each channel R,G,B</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.0pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[a, floor {Re(b)}] 256 for each channel R,G,B</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>32b image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a,b)</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min(a,b) mod 4294967296</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min(a,|b| )</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span lang="NL" style= 'font-size:8.0pt'>min(a,b) mod 4294967296</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[a, floor(b)] mod 4294967296</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[a, floor {Re(b)}] mod 4294967296</span></p> </td> </tr> <tr style='height:17.65pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>float image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a,b)</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a,b)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a,|b|)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a,b)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>min[min(a,b) , -FLOAT_MAX)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:17.65pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min[min(a,Re(b)), -FLOAT_MAX)</span></p> </td> </tr> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>double image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a,b)</span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a,b)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a,|b|)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a,b)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a,b)</span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>min(a,Re(b))</span></p> </td> </tr> <tr style='height:25.1pt'> <td width="84" valign="top" style= 'width:62.65pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>complex image</span></p> </td> <td width="97" valign="top" style= 'width:72.55pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= min(a,b) </span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'>Im =0 </span></p> </td> <td width="73" valign="top" style= 'width:54.85pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style= 'font-size:8.0pt'>Re=min(a,b) Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= min(a,|b|) Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= min(a,b) Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= min(a,b) Im =0 </span></p> </td> <td width="84" valign="top" style= 'width:62.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:25.1pt'> <p class="MsoBodyText"><span style='font-size:8.0pt'>Re= min(a,Re(b)) </span></p> <p class="MsoBodyText"><span style='font-size:8.0pt'> Im =min(a,Im(b)) </span></p> </td> </tr> </table> <p class="MsoBodyText">a and b denote pixel values of matching pixels A<sub>i,j</sub> and B<sub>i,j</sub> of images A and B</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2><a name="node178" id="node178"></a>Binary Bitwise Operations</h2> <h3 style='page-break-after:auto'><a name="node179" id= "node179"></a>Bitwise AND</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image176.jpg" alt= "image">. This bitwise operation takes either two image operands or one image and one scalar operand. If both operands are images they have to have the same size and type (number of bits per pixel). The output image has the same type as the first operand. This operation applies only to images of integral type: 1, 8,16, 24 bits per pixel and 32 bits per pixel integral.</p> <h3 style='page-break-after:auto'><a name="node180" id= "node180"></a>Bitwise OR</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image177.jpg" alt= "image">. This bitwise operation takes either two image operands or one image and one scalar operand. If both operands are images they have to have the same size and type (number of bits per pixel). The output image has the same type as the first operand. This operation applies only to images of integral type: 1, 8,16, 24 bits per pixel and 32 bits per pixel integral.</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node181" id= "node181"></a>Bitwise exclusive OR</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image178.jpg" alt= "image">. This bitwise operation takes either two image operands or one image and one scalar operand. If both operands are images they have to have the same size and type (number of bits per pixel). The output image has the same type as the first operand.</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2><a name="node182" id="node182"></a>Binary Thresholding and Segmentation Operations</h2> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node183" id= "node183"></a>Simple Threshold</h3> <p class="MsoBodyText">Operation icon <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image179.jpg" alt="image">. The operation converts a grey scale or multi-component image to a binary image with pixels having their grey level above a given value set to foreground (1) while the rest set to background (0). For RGB images the operation is applied to individual components and the resulting binary images are ANDed. The operation takes one image and one scalar operand.</p> <h3 style='page-break-after:auto'><a name="node184" id= "node184"></a>Precise Threshold</h3> <p class="MsoBodyText">Operation icon <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image180.jpg" alt="image">. The operation converts a grey scale or multi-component image to a binary image with pixels having their grey level equal to a given value set to foreground (1) while the rest set to background (0). The operation takes either two image operands or one image and one scalar operand. During the operand selection process the background selection is prompted by a special cursor marked <sub>BG</sub>. This operation is useful for selecting particular blob in a labelled image, e.g. largest. It can be applied to floating point images too but it is the user’s responsibility to make sure that the same levels are indistinguishable within the tolerances of the selected type.</p> <h3 style='page-break-after:auto'><a name="node185" id= "node185"></a>Threshold Image by Tracing Local Maxima of Intensity </h3> <p class="MsoBodyText">Operation icon <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image181.jpg" alt="image">. This operation takes a grey-scale or colour image as one input and a binary skeleton-marker image as another input. It uses the marker skeleton as a seed to trace the "ridges" of the first operand and extend the skeleton along the ridges until ridge stops. The operation result is a binary (0/1) image of the extended skeleton of the "ridges", the bright lines on the first input image. This operation is useful for tracing, extending edges with reduced contrast emanating from the edges of higher contrast. The later ones after thresholding and skeletonisation can be used for creation of marker skeleton.</p> <h3 style='page-break-after:auto'><a name="node186" id= "node186"></a>Fuzzy C-means Clustering</h3> <p class="MsoBodyText">Operation icon <img border="0" width= "31" height="31" src="PIPUserManualNoFootnotes_files/image182.jpg" alt="image">. This is a classical image clustering method. For description see J.C.Bezdek “Pattern Recognition With Fuzzy Objective Function Algorithms” New York, Plenum Press, 1982. Number of clusters is the second input parameter and is limited by 255. The resulting image is displayed using palette that corresponds to the central intensities/colours of the clusters. The indices into the palette are ranging from 1 to the number of clusters. Due to recursive nature of the algorithm it can be slow.</p> <h3 style='page-break-after:auto'><a name="node187" id= "node187"></a>Segment by Skeleton</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image183.jpg" alt= "image">. This operation takes a source image and a binary image (0/1) of the same size. The binary image is expected to be the image of a skeletal lines associated with the source image. The segmentation consists in assignment of the same intensity to the area enclosed by each closed contour within the skeleton image. Thus the skeleton guides the segmentation. The value assigned is the average value of the pixels inside the skeletal contour.</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2><a name="node188" id="node188"></a>Binary Morphological Operations</h2> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node189" id= "node189"></a>Dilation with Symmetric Kernel</h3> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image184.jpg" alt= "image">. Morphological image dilation on binary, grey scale or multi-component images. For multi-component images each component is dilated individually. During the operand selection process the kernel selection is prompted by a special cursor marked <sub>KER</sub>. Kernel has to be supplied as an image of the same type (bits per pixel) as the image to be dilated. Kernel may have either odd or even number of rows and columns. Prior to application of the operation a border of half-width of kernel size is created around the original image. Values of pixels within the frame repeat the values of the original image border extending the original image border by half-width of the kernel in each direction. This treatment of the image edges is most appropriate for preservation of boundary features during morphological operations. The dimensions of the kernel cannot exceed half of the corresponding dimensions of the image operand.</p> <p class="MsoNormal"> </p> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="node190" id= "node190"></a>Erosion with Symmetric Kernel</h3> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image185.jpg" alt= "image">. Morphological image erosion on binary, grey scale or multi-component images. For multi-component images each component is eroded individually. During the operand selection process the kernel selection is prompted by a special cursor marked <sub>KER</sub>. Kernel has to be supplied as an image of the same type (bits per pixel) as the image to be eroded. Kernel may have either odd or even number of rows and columns. Prior to application of the operation a border of half-width of kernel size is created around the original image. Values of pixels within the frame repeat the values of the original image border extending the original image border by half-width of the kernel in each direction. This treatment of the image edges is most appropriate for preservation of boundary features during morphological operations. The dimensions of the kernel cannot exceed half of the corresponding dimensions of the image operand.</p> <h3 style='page-break-after:auto'><a name="node191" id= "node191"></a>Opening with Symmetric Kernel</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image186.jpg" alt= "image">. Morphological image opening on binary, grey scale or multi-component images. For multi-component images each component is opened individually. During the operand selection process the kernel selection is prompted by a special cursor marked <sub>KER</sub>. Kernel has to be supplied as an image of the same type (bits per pixel) as the image to be closed. Kernel may have either odd or even number of rows and columns. Treatment of the image border pixels is the same as in erosion and dilation operations. The dimensions of the kernel cannot exceed half of the corresponding dimensions of the image operand.</p> <h3 style='page-break-after:auto'><a name="node192" id= "node192"></a>Closing with Symmetric Kernel</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image187.jpg" alt= "image">. Morphological image closing on binary, grey scale or multi-component images. For multi-component images each component is closed individually. During the operand selection process the kernel selection is prompted by a special cursor marked <sub>KER</sub>. Kernel has to be supplied as an image of the same type (bits per pixel) as the image to be opened. Kernel may have either odd or even number of rows and columns. Treatment of the image border pixels is the same as in erosion and dilation operations. The dimensions of the kernel cannot exceed half of the corresponding dimensions of the image operand.</p> <h3 style='page-break-after:auto'><a name="node193" id= "node193"></a>Dilation with flat kernel and mask</h3> <p class="MsoNormal">Operation icon for the binary kernel mask is <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image188.jpg" alt="image">. Morphological image dilation on grey scale or multi-component images. The kernel is flat that is it has the value 0 for integral image types and minimum image intensity for the images of floating point types. This value for the kernel is selected as the most popular for morphological dilations and erosions because they would not introduce any values absent in the image source. Unlike dilation with symmetrically shaped kernel, this operation allows use of kernels of complex shape. The shape of the kernel is controlled by the binary mask supplied as the second operand of the operation. The pixels whose mask values equal 1 (foreground) are included in the operation, the pixel whose mask values set to 0 (background) are ignored during the operation. For multi-component images each component is dilated individually. The diameter of the mask can be any positive integer odd or even.</p> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="node194" id= "node194"></a>Erosion with flat kernel and mask</h3> <p class="MsoNormal">Operation icon for the binary kernel mask is <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image189.jpg" alt="image">. Morphological image erosion on grey scale or multi-component images. The kernel is flat that is it has the value 0 for integral image types and minimum image intensity for the images of floating point types. This value for the kernel is selected as the most popular for morphological dilations and erosions because they would not introduce any values absent in the image source. Unlike erosion with symmetrically shaped kernel, this operation allows use of kernels of complex shape. The shape of the kernel is controlled by the binary mask supplied as the second operand of the operation. The pixels whose mask values equal 1 (foreground) are included in the operation, the pixel whose mask values set to 0 (background) are ignored during the operation. For multi-component images each component is dilated individually. The diameter of the mask can be any positive integer odd or even.</p> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="node195" id= "node195"></a>Opening with flat kernel and mask</h3> <p class="MsoNormal">Operation icon for the binary kernel mask is <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image190.jpg" alt="image">. Morphological image opening on grey scale or multi-component images. The kernel is flat that is it has the value 0 for integral image types and minimum image intensity for the images of floating point types. This value for the kernel is selected as the most popular for morphological dilations and erosions because they would not introduce any values absent in the image source. Unlike opening with symmetrically shaped kernel, this operation allows use of kernels of complex shape. The shape of the kernel is controlled by the binary mask supplied as the second operand of the operation. The pixels whose mask values equal 1 (foreground) are included in the operation, the pixel whose mask values set to 0 (background) are ignored during the operation. For multi-component images each component is dilated individually. The diameter of the mask can be any positive integer odd or even.</p> <p class="MsoNormal"> </p> <h3 style='page-break-after:auto'><a name="node196" id= "node196"></a>Closing with flat kernel and mask</h3> <p class="MsoNormal">Operation icon for the binary kernel mask is <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image191.jpg" alt="image">. Morphological image closing on grey scale or multi-component images. The kernel is flat that is it has the value 0 for integral image types and minimum image intensity for the images of floating point types. This value for the kernel is selected as the most popular for morphological dilations and erosions because they would not introduce any values absent in the image source. Unlike closing with symmetrically shaped kernel, this operation allows use of kernels of complex shape. The shape of the kernel is controlled by the binary mask supplied as the second operand of the operation. The pixels whose mask values equal 1 (foreground) are included in the operation, the pixel whose mask values set to 0 (background) are ignored during the operation. For multi-component images each component is dilated individually. The diameter of the mask can be any positive integer odd or even.</p> <h3 style='page-break-after:auto'><a name="node197" id= "node197"></a>Morphological reconstruction</h3> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image192.jpg" alt= "image"> for mask and <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image193.jpg" alt= "image"> for marker. Morphological reconstruction of one image (mask) by another (marker). .Algorithms and application described in <i>Luc Vincent</i>, Morphological Grayscale Reconstruction in Image Analysis: Applications and Efficient Algorithms. IEEE TRANS on Image Processing, v 2, April 1993, pp176-20. During the operand selection process the marker image selection is prompted by a special cursor marked <sub>MKR</sub>. The marker image has to have the same type (bits per pixel) as the image to be reconstructed. Prior to application of the operation the image is inflated by the 2 pixels and an artificial background (0) frame is created.</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2><a name="node198" id="node198"></a>Binary Filtering Operations</h2> <h3 style='page-break-after:auto'><a name="node199" id= "node199"></a>Convolution with rectangular/square kernel</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image194.jpg" alt= "image">. General convolution operation can be applied to all image types. The restriction is put on the kernel image type. This image can only be of type Double (64 bit) or Float (32-bit) and can have either odd or even dimensions. The resulting image type is the same as source image type. For odd-sized kernel dimension the centre of the kernel in that dimension is the central pixel, for even-sized kernels the centre is between the pixels in the centre of the corresponding dimension of the kernel Use <a href= "start.htm#_Convolution_Kernel_Designer">Kernel Designer</a> to build even-dimensioned kernels.</p> <h3 style='page-break-after:auto'><a name="node200" id= "node200"></a>Convolution with elliptic/circular kernel</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image195.jpg" alt= "image">. General convolution operation can be applied to all image types. The restriction is put on the kernel image type. This image can only be of type Double (64 bit) or Float (32-bit can have either odd or even dimensions. The resulting image type is the same as source image type. If the kernel image supplied as a rectangular image the kernel actually used is the ellipse inscribed into the rectangle.</p> <p class="MsoNormal"><img border="0" width="45" height="35" src= "PIPUserManualNoFootnotes_files/image196.gif" alt="image"></p> <p class="MsoNormal">. For odd-sized kernel dimension the centre of the kernel in that dimension is the central pixel, for even-sized kernels the centre is between the pixels in the centre of the corresponding dimension of the kernel Use <a href= "start.htm#_Convolution_Kernel_Designer">Kernel Designer</a> to build even-dimensioned kernels. In case of square kernel image the kernel used is the circular. Parts of the kernel outside the inscribed ellipse/circle are not used.</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node201" id= "node201"></a>Median Filter with Square Kernel</h3> <p class="MsoBodyText">Operation icon<img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image197.jpg" alt= "image">. Median filter is a non-linear filter belonging to the class of rank filters. It removes noise but preserves the edges within the original image better than linear filtering techniques. First operand in this operation is an image, second is the size of the square filtering kernel, i.e. the length in pixels of the side of the square around each pixel within the image where the ranking is performed. The length can be either odd or even. The pixel which receives the result is in the centre of the square. For RGB images the operator is applied to each component. . Prior to application of the operation the image is inflated by the kernel size and an artificial frame is created by repeating pixels in the original boundary. Other applications mirror the boundaries but in case of very large kernels it leads to loss of edges near the boundary. Repeating the last known pixel outside the boundary of the image preserves the original edges near the image boundary. Kernel dimensions cannot exceed half of the source image dimensions.</p> <h3 style='page-break-after:auto'><a name="node202" id= "node202"></a>Median Filter with Circular Kernel</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image198.jpg" alt= "image">. This is an isotropic version of median filter. Unlike the square kernel version it does not introduce geometric distortion but runs slightly slower. First operand in this operation is an image, second is the diameter of the kernel. This diameter can be either odd or even. For RGB images the operator is applied to each component. Boundary action is the same as in filter with square kernel.</p> <h3 style='page-break-after:auto'><a name="node203" id= "node203"></a>Separable Median Filter</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image199.jpg" alt= "image">. This operation runs single dimensional median filter in X direction, then the result is subject to the single directional median in Y direction. First operand in this operation is an image, second is the diameter of the kernel. The diameter can be either odd or even. For RGB images the operator is applied to each component. Boundary action is the same as in filter with square kernel. This operation is faster than both previous median filters. It distorts the features but tend to preserve vertical and horizontal edges. It is useful for calculation of illumination trends in an image.</p> <h3 style='page-break-after:auto'><a name="node204" id= "node204"></a>Fast Isotropic Low Pass Filter with Kernel Equivalent to Box Filter</h3> <p class="MsoBodyText"><span style= 'position:relative;z-index:8;left:-3px; top:0px;width:512px;height:512px'> <img width="512" height="512" src= "PIPUserManualNoFootnotes_files/image200.gif" alt= "image"></span><br clear="all"> Operation icon <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image201.jpg" alt="image">. Fast isotropic smoothing filter with the kernel similar to a box filter. It has much stronger high frequency suppression, steeper slope of frequency response curve than the binomial filter below with very similar calculation speed, that is close to separable filter. Its proximity to a box filter is illustrated using the test pattern from Bernd Jahne “ Digital Image Processing” Springer-Verlag 2002, p.289. Here we present a test image after application of the filter of the kernel size 9x9 pixels. Unlike traditional box filter it shows no anisotropy and cross section at the centre of the image exhibits a distinct pattern of the <i><span style= 'font-size:12.0pt'>sinc</span></i> function.</p> <p class="MsoBodyText"><img border="0" width="218" height="164" src="PIPUserManualNoFootnotes_files/image202.jpg" alt="image"></p> <h3 style='page-break-after:auto'><a name="node205" id= "node205"></a>Smoothing Filter with Binomial Kernel</h3> <p class="MsoBodyText">Operation icon <img border="0" width="31" height="31" src="PIPUserManualNoFootnotes_files/image203.jpg" alt= "image">. This is a separable isotropic smoothing filter. For description see Bernd Jahne “Image Processing for Scientific Applications” p. 372. Second operand is the size of the smoothing kernel. Treatment of the image border pixels is the same as in median filter operation. Kernel horizontal and vertical size are limited by the integer arithmetic used and cannot exceed 25 pixels. One can stack them to emulate increased kernel size.</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2><a name="node206" id="node206"></a>Binary Transforms</h2> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node207" id= "node207"></a>Variance Transform</h3> <p class="MsoBodyText">Operation icon for radius of the transform’s kernel is <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image204.jpg" alt="image">. Variance transform operation generates an image consisting of variance in the given neighbourhood of each pixel of the source image. The neighbourhood is a circle defined by its radius as the second operand. Transform is useful for texture analysis. The operation conserves the image type. For example, variance transform of the 8-bit image is an 8-bit image. Values outside 0-0xFF range are set to 0 and 0xFF respectively. If precise variance is required, use images of floating point types.</p> <h3 style='page-break-after:auto'><a name="node208" id= "node208"></a>Normalised Sum of Squared Differences Transform</h3> <p class="MsoBodyText">Operation icon for the radius of the transform’s kernel is <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image205.jpg" alt="image">. Normalised sum of squared differences transform operation generates an image consisting of sum of squared differences of the pixels in the given neighbourhood from the central pixel of the neighbourhood. The neighbourhood is a circle defined by its radius as the second operand. The resulting sum is divided by the number of pixels in the neighbourhood. Transform is useful for texture analysis. It does not suffer from apparent resolution reduction observed in Variance transform caused by implicit averaging built into the variance transform. The operation conserves the image type.</p> <h3 style='page-break-after:auto'><a name="node209" id= "node209"></a>Deviation Trend Transform</h3> <p class="MsoBodyText">Operation icon for the radius of the transform’s kernel is <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image206.jpg" alt="image">. This operation is intended as a texture measure. It generates an image of the trend in the intensity deviation from the central pixel value in given neighbourhood of each pixel of the source image. The neighbourhood is a circle defined by its radius as the second operand. The operation produces image of floating point type. For 8, 16 and 24-bit images the result is a 32-bit floating point image. For higher bit count image types it is an image of type double. For multi-component images the operation is applied to the intensity component of the image.</p> <h3 style='page-break-after:auto'><a name="node210" id= "node210"></a>Texture Directionality</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image207.jpg" alt= "image">. Texture directionality transform generates an image with pixel values representing strength of texture directionality in the neighbourhood of a given pixel. The strength of directionality measure is obtained as follows:</p> <p class="MsoBodyText">1. In the square of the edge size <i>N</i> given by the user <i>N</i> darkest and <i>N</i> brightest pixels are calculated.</p> <p class="MsoBodyText">2. From each set of pixels, the darkest and the brightest a fitted line are obtained together with the values of</p> <p class="MsoBodyText"><sub><img border="0" width="80" height="48" src="PIPUserManualNoFootnotes_files/image208.gif" alt= "image"></sub></p> <p class="MsoBodyText">explained variances <sub><img border="0" width="23" height="24" src= "PIPUserManualNoFootnotes_files/image209.gif" alt= "image"></sub> and <sub><img border="0" width="23" height="24" src="PIPUserManualNoFootnotes_files/image210.gif" alt= "image"></sub>.</p> <p class="MsoBodyText">3. The texture directionality measure is calculated as the cosine of the angle between those 2 line scaled by the explained variances and the ratio of the dynamic range<sub><img border="0" width="20" height="24" src= "PIPUserManualNoFootnotes_files/image211.gif" alt="image"></sub> of the neighbourhood to the dynamic range <sub><img border="0" width="13" height="17" src= "PIPUserManualNoFootnotes_files/image212.gif" alt= "image"></sub> of the image type. For example for 8-bit images <i>I</i> =255. For floating point image types the value of <i>I</i> is set to 1.</p> <p class="MsoBodyText"><sub><img border="0" width="300" height="86" src="PIPUserManualNoFootnotes_files/image213.gif" alt= "image"></sub></p> <p class="MsoBodyText">For the images of integral types this measure is scaled to the dynamic range of the image type. Usefulness of this operation is demonstrated in the following test project. Here different textures from the set of Bordatz Textures are processed with this operation. The texture in operand 1 has more directional features than the one in operands 5 or 11 but same directionality with less contrast than in operand 5.</p> <p class="MsoBodyText"><img border="0" width="478" height="653" src="PIPUserManualNoFootnotes_files/image214.jpg" alt="image"></p> <p class="MsoBodyText">Average intensity of the resulting image indicates that the operation ranks the textures according to the presence of the directionality in the texture and contrast of the directional information.</p> <h3 style='page-break-after:auto'><a name="node211" id= "node211"></a>Forward Fast Fourier Transform on Kernel Image</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image215.jpg" alt= "image">. This is a supportive operation for frequency domain processing. This operation is designed to synchronise the frequency range of an image of a convolution kernel (first operand) with the frequency range of a given image (second operand) for future processing in frequency domain. The term convolution refers to spatial domain. Usually convolution kernel of a finite impulse response (FIR) filter is an image smaller in size than the intended processing target. Direct FFT of that image will produce in general case a frequency domain image of smaller frequency range. This operation will set the frequency range of the result to that of the second operand.</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2><a name="node212" id="node212"></a>Binary Interpolation Operations</h2> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node213" id= "node213"></a>Interpolate under a mask anisotropic</h3> <p class="MsoNormal">Operation icon for the mask image is<img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image216.jpg" alt="image">. This operation takes a source image and a binary image of the same size. The foreground pixels of the binary image make the mask of the area that needs to be interpolated from the pixels outside the masked area. This is a fast operation for anisotropic interpolation inside the area defined by the mask somewhat similar to inpainting technique described in "Fast Digital Image Inpainting., Manuel M. Oliveira & all, Proceedings on the International Conference on Visualization, Marbella 2001, Spain.” The difference is in expanding kernel size depending on the local thickness of the mask and inverse distance weighing of the pixels. The thickness of the mask in this operation cannot exceed 255 pixels.</p> <h3 style='page-break-after:auto'><a name="node214" id= "node214"></a>Interpolate under a mask tangent to mask</h3> <p class="MsoNormal">Operation icon for the mask image is <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image217.jpg" alt="image">. This operation takes a source image and a binary image of the same size. The foreground pixels of the binary image make the mask of the area that needs to be interpolated from the pixels outside the masked area. This is a fast operation for isotropic interpolation inside the area defined by the mask. During the interpolation process the values of the pixels are propagated from the edge into the masked region along the line tangent to the mask in this point. Tangent is deduced from the distance transform of the mask. The thickness of the mask in this operation cannot exceed 255 pixels.</p> <h3 style='page-break-after:auto'><a name="node215" id= "node215"></a>Fill mask with bright background</h3> <p class="MsoNormal">Operation icon for the mask image is <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image218.jpg" alt="image">. This operation takes a source image and a binary image of the same size. The foreground pixels of the binary image make the mask of the area that needs to be “guessed” from the pixels outside the masked area. The goal of this operation is to create a blended into background replacement for the masked out area. The area outside the mask is not affected. This operation fills the area under the mask with the bright local background. The intensity of the bright local background is calculated for each pixel of the mask as follows: neighbourhood of the mask of radius <i>R</i> is selected, this neighbourhood is thresholded into 2 classes, bright and dark, average of the bright class makes the resulting value. The radius <i>R = 3·<b>d</b></i>, where <b><i>d</i></b> is the maximum thickness of the mask. The thickness of the mask in this operation cannot exceed 255 pixels. The operation uses simple image statistic, SIS threshold in order to make the operation as fast as possible.</p> <h3 style='page-break-after:auto'><a name="node216" id= "node216"></a>Fill mask with neighbouring pixels</h3> <p class="MsoNormal">Operation icon for the mask image is <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image219.jpg" alt="image">. This operation takes a source image and a binary image of the same size. The foreground pixels of the binary image make the mask of the area that needs to be “guessed” from the pixels outside the masked area. The goal of this operation is to create a blended into background replacement for the masked out area in case when the image consists of the areas with the same intensity, e.g. labelled image. The area outside the mask is not affected. This operation fills the area under the mask with the closest most representative neighbour starting from the edges of the mask down to its skeleton. The thickness of the mask in this operation cannot exceed 255 pixels. Intended use of the operation is suppression of small areas in the labelled image.</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2><a name="node217" id="node217"></a>Binary Auxiliary Operations</h2> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node218" id= "node218"></a>Build Gaussian kernel</h3> <p class="MsoNormal">This is an image generation operation. Operation icons are <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image220.jpg" alt="image"> for the kernel size and <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image221.jpg" alt="image"> for standard deviation. The operation creates the image of Gaussian function centred in the image centre, normalised so that the area of the image is equal 1.The image created is of a type of floating point</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2><a name="node219" id="node219"></a>Binary Geometric Operations</h2> <h3 style='page-break-after:auto'><a name="node220" id= "node220"></a>Crop by mask</h3> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image222.jpg" alt= "image"> . This operation reduces the image to a rectangular region of interest. The region of interest is the largest rectangle which can fit into the mask of the object of interest. The mask of the object of interest, a binary image is supplied as the second operand.</p> <h3 style='page-break-after:auto'><a name="node221" id= "node221"></a>Augment Image Mirror Border</h3> <p class="MsoNormal">Operation icons are: <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image223.jpg" alt="image"> for the image source and <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image224.jpg" alt="image"> for the border size. This operation produces an image of augmented size with the border region mirroring the adjacent internal region of the image.</p> <h3 style='page-break-after:auto'><a name="node222" id= "node222"></a>Crop Image Border</h3> <p class="MsoNormal">Operation icons are: <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image225.jpg" alt="image"> for the image source and <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image226.jpg" alt="image"> for the border size. This operation produces an image of reduced size with the border region of specified size removed. It complements Augment Image Mirror Border operation.</p> <p class="MsoNormal"> </p> <p class="MsoNormal"> </p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2><a name="node223" id="node223"></a>Binary Statistical Operations</h2> <h3 style='page-break-after:auto'><a name="node224" id= "node224"></a><span style= 'font-size:10.0pt;font-family: "Times New Roman"'>This class of operations takes works on images, takes scalar or image as a parameter and returns a scalar.</span></h3> <h3 style='page-break-after:auto'><a name="node225" id= "node225"></a>Pixel Count for Given Grey Level</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image227.jpg" alt= "image">. Operation calculates the number of pixels corresponding to a given grey in the histogram. For RGB images the histogram is calculated on the intensity component of the image.</p> <h3 style='page-break-after:auto'><a name="node226" id= "node226"></a>Number of Pixels Exceeding Given Grey Level</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image228.jpg" alt= "image">. Operation calculates the number of pixels in the image histogram higher than a given grey level. For RGB images the operation is performed on the histogram of the intensity component of the image.</p> <h3 style='page-break-after:auto'><a name="node227" id= "node227"></a>Per Element Maximum of Two Operands</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image160.jpg" alt= "image">. Calculates per element maximum of 2 operands. If both operands are images calculates per pixel maximum of 2 images. For RGB images it calculates per pixel maximum for each channel.</p> <h3 style='page-break-after:auto'><a name="node228" id= "node228"></a>Per Element Maximum of Two Operands</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image162.jpg" alt= "image">. Calculates per element minimum of 2 operands. If both operands are images calculates per pixel maximum of 2 images. For RGB images it calculates per pixel minimum for each channel</p> <h3 style='page-break-after:auto'><a name="node229" id= "node229"></a>Mean within Masked Area</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image229.jpg" alt= "image">. This operation calculates mean of the image pixel grey values within the area marked by the supplied mask. Mask foreground indicates the pixels of interest, participating in the calculation of mean. For RGB images calculates mean of the brightness, intensity component of the image within the mask.</p> <h3 style='page-break-after:auto'><a name="node230" id= "node230"></a>Standard Deviation within Masked Area</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image230.jpg" alt= "image">. This operation calculates standard deviation of the image pixel grey values within the area marked by the supplied mask. Mask foreground indicates the pixels of interest, participating in the calculation of standard deviation. For RGB images calculates standard deviation of the brightness, intensity component of the image within the mask.</p> <h3 style='page-break-after:auto'><a name="node231" id= "node231"></a>Maximum Grey Level within Masked Area</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image231.jpg" alt= "image">. This operation calculates maximum intensity, maximum grey level of the image pixel grey values within the area marked by the supplied mask. For RGB images it calculates maximum of the brightness, intensity component of the image within the mask.</p> <h3 style='page-break-after:auto'><a name="node232" id= "node232"></a>Median Grey Level within Masked Area</h3> <p class="MsoBodyText">Operation icon<img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image232.jpg" alt= "image">. This operation calculates median intensity, median grey level of the image pixel grey values within the area marked by the supplied mask. For RGB images it calculates median of the brightness, intensity component of the image within the mask</p> <h3 style='page-break-after:auto'><a name="node233" id= "node233"></a>Minimum Grey Level within Masked Area</h3> <p class="MsoNormal"> </p> <p class="MsoNormal">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image233.jpg" alt= "image">. This operation calculates minimum intensity, minimum grey level of the image pixel grey values within the area marked by the supplied mask. For RGB images it calculates minimum of the brightness, intensity component of the image within the mask.</p> <b><i><span style='font-size:12.0pt;font-family:Arial'><br clear= "all" style='page-break-before:always'></span></i></b> <h2><a name="node234" id="node234"></a>Binary Operations Applicable Only To Binary Images</h2> <h3 style='page-break-after:auto'><a name= "_Threshold_by_Blob"></a>Threshold by Blob Area, Preserve Blobs of Large Area</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image234.jpg" alt= "image">. The operation takes one image and one scalar operand. Operation identifies 8-connected blobs within the given binary image. Blobs of the area, number of pixels larger than given by the second operand are preserved in the resulting binary image. Smaller blobs have their pixels assigned to background.</p> <h3 style='page-break-after:auto'><a name="node235" id= "node235"></a>Threshold by Blob Area, Preserve Blobs of Small Area</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image235.jpg" alt= "image">. The operation takes one image and one scalar operand. Operation identifies 8-connected blobs within the given binary image. Blobs of the area, number of pixels larger than given by the second operand are preserved in the resulting binary image. Smaller blobs have their pixels assigned to background.</p> <h3 style='page-break-after:auto'><a name="node236" id= "node236"></a>Threshold by Blob Eccentricity, Preserve Blobs of Large Eccentricity</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image236.jpg" alt= "image">. The operation takes one image and one scalar operand. Operation identifies 8-connected blobs within the given binary image. An ellipse in inscribed into the blob. Blobs of the eccentricity larger than given by the second operand are preserved in the resulting binary image. Blobs with smaller eccentricity, close in shape to a circle have their pixels assigned to background.</p> <h3 style='page-break-after:auto'><a name="node237" id= "node237"></a>Threshold by Blob Eccentricity, Preserve Blobs of Large Eccentricity</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image237.jpg" alt= "image">. The operation takes one image and one scalar operand. Operation identifies 8-connected blobs within the given binary image. An ellipse in inscribed into the blob. Blobs of the eccentricity smaller than given by the second operand are preserved in the resulting binary image. Blobs with larger eccentricity, more elongated have their pixels assigned to background.</p> <span style= 'font-size:10.0pt;font-family:"Times New Roman"'><br clear="all" style='page-break-before:always'></span> <p class="MsoBodyText"> </p> <h2 style='margin-left:0cm;text-indent:0cm'><a name="node238" id= "node238"></a>Binary Operations Applicable Only To 24-bit Images</h2> <h3 style='page-break-after:auto'><a name="node239" id= "node239"></a>Segment image by Red-Green histogram</h3> <p class="MsoBodyText">Operation icons are: <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image238.jpg" alt="image"> for the RGB image source (first input) and <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image239.jpg" alt="image"> for the labelled 256x256 image of 2-dimensional red-green histogram of the source image (second input). Areas of the histogram attributed t the same label are marked in the output image with the same colour, average to each cluster in the labelled histogram. Note that the labelled image cannot have more than 256x256 levels. Hence it can be at most a 16-bit image. A raw 2D histogram of a large image can be a 32-bit image. The operation is not design to work with those and will generate and error.</p> <h3 style='page-break-after:auto'><a name="node240" id= "node240"></a>Segment image by Red-Blue histogram</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image240.jpg" alt= "image">. Takes an RGB image source <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image238.jpg" alt= "image"> as the first input and the labelled 256x256 image of 2-dimensional red-blue histogram of the this image as the second input. Areas of the histogram attributed t the same label are marked in the output image with the same colour, average to each cluster in the labelled histogram.</p> <h3 style='page-break-after:auto'><a name="node241" id= "node241"></a>Segment image by Green-Blue histogram</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image241.jpg" alt= "image">. Takes an RGB image source <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image238.jpg" alt= "image"> as the first input and the labelled 256x256 image of 2-dimensional green-blue histogram of the this image as the second input. Areas of the histogram attributed t the same label are marked in the output image with the same colour, average to each cluster in the labelled histogram.</p> <h3 style='page-break-after:auto'><a name="node242" id= "node242"></a>Segment image by Hue-Intensity histogram</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image242.jpg" alt= "image">. Takes an RGB image source <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image238.jpg" alt= "image"> as the first input and the labelled 256x256 image of 2-dimensional hue-intensity histogram of the this image as the second input. Areas of the histogram attributed t the same label are marked in the output image with the same colour, average to each cluster in the labelled histogram.</p> <h3 style='page-break-after:auto'><a name="node243" id= "node243"></a>Segment image by Hue-Saturation histogram</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image243.jpg" alt= "image">. Takes an RGB image source <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image238.jpg" alt= "image"> as the first input and the labelled 256x256 image of 2-dimensional hue-saturation histogram of the this image as the second input. Areas of the histogram attributed t the same label are marked in the output image with the same colour, average to each cluster in the labelled histogram.</p> <h3 style='page-break-after:auto'><a name="node244" id= "node244"></a>Segment image by Intensity-Saturation histogram</h3> <p class="MsoBodyText">Operation icon <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image244.jpg" alt= "image">. Takes an RGB image source <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image238.jpg" alt= "image"> as the first input and the labelled 256x256 image of 2-dimensional intensity-saturation histogram of the this image as the second input. Areas of the histogram attributed t the same label are marked in the output image with the same colour, average to each cluster in the labelled histogram.<br clear="all" style= 'page-break-before:always'></p> <h2><a name="_Ternary_Filter_Operations"></a>Ternary Filter Operations</h2> <h3 style='page-break-after:auto'><a name="node245" id= "node245"></a>Local Image Smoothing with Intensity Range Constraint</h3> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image245.jpg" alt="image"> for the diameter of the kernel and <img border= "0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image246.jpg" alt="image"> for the intensity constraint. This is a filter inspired by the popular Bilateral Filter, described in C. Tomasi and R. Manduchi, "Bilateral Filtering for Gray and Color Images", <i>Proceedings of the 1998 IEEE International Conference on Computer Vision</i>, Bombay, India. The operation takes one image and two scalar operands. First operand is the diameter of the kernel. It has to be odd. The second operand is <i><span style= 'font-family:Symbol'>k</span></i>=<i>δ,</i> if <i>δ</i><i><span style='font-family:Symbol'>³</span> 1,</i> where <i>δ</i> is an intensity range or <i><span style= 'font-family:Symbol'>k</span></i>=<i><span style= 'font-family:Symbol'>g</span>,</i> if <i>0<</i> <i><span style= 'font-family:Symbol'>g</span><1,</i> where <span style= 'font-family:Symbol'>g</span> is the fraction of the intensity of the reference pixel (see below). The filter belongs to so called Intensity Constrained Flat Kernel (ICFK) filters, whose output is described by the formula:</p> <p class="Text"><span lang="EN-US" style= 'color:red'><sub><img border="0" width="260" height="56" src= "PIPUserManualNoFootnotes_files/image247.gif" alt= "image"></sub></span><span lang="EN-US">,</span></p> <p class="Text"><span lang="EN-US">where</span></p> <p class="MsoBodyText"><sub><img border="0" width="24" height="27" src="PIPUserManualNoFootnotes_files/image248.gif" alt= "image"></sub> <sub>is a histogram</sub> of the part of the image, which is masked by the kernel χ with the centre at <sub><img border="0" width="16" height="25" src= "PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub>,</p> <p class="MsoBodyText"><sub><img border="0" width="16" height="25" src="PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub> is a vector describing the spatial position of the pixels <sub><img border="0" width="40" height="25" src= "PIPUserManualNoFootnotes_files/image250.gif" alt="image"></sub>, where <i>S</i> is the spatial domain,</p> <p class="MsoBodyText">The constraint <i>K(p)</i> takes 2 forms:</p> <p class="MsoBodyText"><i>K(p) = I<sub>p</sub> ± δ ( δ</i><i><span style='font-family:Symbol'>³</span> 1)</i></p> <p class="MsoBodyText"><i>K(p) = I<sub>p</sub> ± I<sub>p</sub> ·</i><i><span style='font-family:Symbol'>g</span> ( 0<</i> <i><span style='font-family: Symbol'>g</span><1)</i>.</p> <p class="MsoBodyText">The later makes the filter applicable to images of any type because image dynamic range does no appear explicitly in the constraint expression,</p> <p class="Text"><span lang="EN-US"><sub><img border="0" width="91" height="32" src="PIPUserManualNoFootnotes_files/image251.gif" alt= "image"></sub></span></p> <p class="Text"><span lang="EN-US">is the average intensity within that part of the histogram under the kernel mask, which satisfies the constraint <i>K(p)</i>,</span></p> <p class="Text"><span lang="EN-US"><sub><img border="0" width="114" height="26" src="PIPUserManualNoFootnotes_files/image252.gif" alt= "image"></sub> </span></p> <p class="Text" style='text-indent:0cm'><span lang="EN-US">is the median of the area under the kernel mask.</span></p> <p class="Text" style='text-indent:0cm'><span lang= "EN-US"> The filter is described in detail in A. Gutenev “Intensity Constrained Flat Kernel Image Filtering Scheme - Definition and Applications”, submitted to <i>Proceedings of the 2010 International Conference of Signal and Image Engineering, London, U.K., 30 June - 2 July, 2010</i>. </span></p> <h3 style='page-break-after:auto'><a name="node246" id= "node246"></a>Local Image Median with Intensity Range Constraint</h3> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image245.jpg" alt="image"> for the diameter of the kernel and <img border= "0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image253.jpg" alt="image"> for the intensity constraint. The operation takes one image and two scalar operands. First operand is the diameter of the kernel. It has to be odd. The second operand is <i><span style= 'font-family:Symbol'>k</span></i>=<i>δ,</i> if <i>δ</i><i><span style='font-family:Symbol'>³</span> 1,</i> where <i>δ</i> is an intensity range or <i><span style= 'font-family:Symbol'>k</span></i>=<i><span style= 'font-family:Symbol'>g</span>,</i> if <i>0<</i> <i><span style= 'font-family:Symbol'>g</span><1,</i> where <span style= 'font-family:Symbol'>g</span> is the fraction of the intensity of the reference pixel (see below). The filter belongs to so called Intensity Constrained Flat Kernel (ICFK) filters, whose output is described by the formula:</p> <p class="Text"><span lang="EN-US" style= 'color:red'><sub><img border="0" width="260" height="56" src= "PIPUserManualNoFootnotes_files/image247.gif" alt= "image"></sub></span><span lang="EN-US">,</span></p> <p class="Text"><span lang="EN-US">where</span></p> <p class="MsoBodyText"><sub><img border="0" width="24" height="27" src="PIPUserManualNoFootnotes_files/image248.gif" alt= "image"></sub> <sub>is a histogram</sub> of the part of the image, which is masked by the kernel χ with the centre at <sub><img border="0" width="16" height="25" src= "PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub>,</p> <p class="MsoBodyText"><sub><img border="0" width="16" height="25" src="PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub> is a vector describing the spatial position of the pixels <sub><img border="0" width="40" height="25" src= "PIPUserManualNoFootnotes_files/image250.gif" alt="image"></sub>, where <i>S</i> is the spatial domain,</p> <p class="MsoBodyText"><i>K(p) = I<sub>p</sub> ± I<sub>p</sub> ·</i><i><span style='font-family:Symbol'>g</span></i>, is the constraint. Selection of constraint in this form makes the filter applicable to images of any type because image dynamic range does no appear explicitly in the constraint expression,</p> <p class="Text"><span lang="EN-US"><sub><img border="0" width="129" height="27" src="PIPUserManualNoFootnotes_files/image254.gif" alt= "image"></sub></span></p> <p class="Text"><span lang="EN-US">is the median of the intensity within that part of the histogram under the kernel mask, which satisfies the constraint <i>K(p)</i>,</span></p> <p class="Text"><span lang="EN-US"><sub><img border="0" width="97" height="25" src="PIPUserManualNoFootnotes_files/image255.gif" alt= "image"></sub> </span></p> <p class="Text" style='text-indent:0cm'><span lang="EN-US">is the median of the area under the kernel mask.</span></p> <p class="Text" style='text-indent:0cm'><span lang= "EN-US"> </span></p> <h3 style='page-break-after:auto'><a name="node247" id= "node247"></a>Local Exclusive Median with Intensity Range Constraint</h3> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image245.jpg" alt="image"> for the diameter of the kernel and <img border= "0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image256.jpg" alt="image"> for the intensity constraint. This is another operation falling within definition of Intensity Constrained Flat Kernel filtering scheme. It is designed to suppress features falling within the intensity constraint of central pixel. Pixels within the given range are replaced with median of the area under the kernel with intensities outside the range. The operation takes one image and two scalar operands. First operand is the diameter of the kernel. It has to be odd. The second operand is <i><span style= 'font-family:Symbol'>k</span></i>=<i>δ,</i> if<i>δ</i><i><span style='font-family:Symbol'>³</span> 1,</i> where <i>δ</i> is an intensity range or <i><span style= 'font-family:Symbol'>k</span></i>=<i><span style= 'font-family:Symbol'>g</span>,</i> if <i>0<</i> <i><span style= 'font-family:Symbol'>g</span><1,</i> where <span style= 'font-family:Symbol'>g</span> is the fraction of the intensity of the reference pixel. Operator’s output is described by the formula:</p> <p class="Text"><span lang="EN-US" style= 'color:red'><sub><img border="0" width="239" height="52" src= "PIPUserManualNoFootnotes_files/image257.gif" alt= "image"></sub> </span> <span lang= "EN-US">, </span></p> <p class="Text"><span lang="EN-US">where</span></p> <p class="Text"><span lang="EN-US"><sub><img border="0" width="47" height="25" src="PIPUserManualNoFootnotes_files/image258.gif" alt= "image"></sub> <sub>is the pixel count of the histogram at the level</sub> <i>I<sub>p</sub></i>,</span></p> <p class="Text"><span lang="EN-US"><sub><img border="0" width="53" height="27" src="PIPUserManualNoFootnotes_files/image259.gif" alt= "image"></sub><sub>is the part of the histogram </sub> <sub><img border="0" width="23" height="25" src= "PIPUserManualNoFootnotes_files/image260.gif" alt= "image"></sub><sub>satisfying the constraint</sub> <i>K(p)</i></span></p> <p class="MsoBodyText"><span lang="EN-US"> </span></p> <p class="Text"><span lang="EN-US"><sub><img border="0" width="279" height="52" src="PIPUserManualNoFootnotes_files/image261.gif" alt= "image"></sub>, </span></p> <p class="Text"><span lang="EN-US">where <sub><img border="0" width="39" height="25" src= "PIPUserManualNoFootnotes_files/image262.gif" alt= "image"></sub><i> </i>is the compliment of the constraint <i>K(p</i>), that is the set of all intensities within the histogram <sub><img border="0" width="23" height="25" src= "PIPUserManualNoFootnotes_files/image260.gif" alt= "image"></sub>lying outside the <i>K(p</i>) range defined around the pixel at <sub><img border="0" width="13" height="23" src= "PIPUserManualNoFootnotes_files/image263.gif" alt= "image"></sub>;</span></p> <p class="Text"><span lang="EN-US">sup{ <i>K(p</i>)} is the top of the range <i>K(p</i>); for example for <i>K(p</i>) written as</span></p> <p class="Text"><span lang= "EN-US"> <i>K(p)=</i>{<sub><img border="0" width="196" height= "23" src="PIPUserManualNoFootnotes_files/image264.gif" alt= "image"></sub>} it is <sub><img border="0" width="59" height="23" src="PIPUserManualNoFootnotes_files/image265.gif" alt= "image"></sub> </span></p> <p class="Text"><i><span lang="EN-US">G</span></i> <span lang= "EN-US">= <i>F<sub> </sub></i> . </span></p> <p class="MsoBodyText">Detailed description of the operator and one of its applications is given in <i>“Alex A. Gutenev., Intensity Constrained Flat Kernel Filter for Local Dark Feature Suppression. Application to Removal of Hair Artifacts in Dermatoscopic Images., in Image Processing: Algorithms and Systems X; and Parallel Processing for Imaging Applications II Proceedings of the SPIE, Volume 8295, pp. 829517-829517-9 (2012).”</i></p> <p class="Text" style='text-indent:0cm'> </p> <h3 style='page-break-after:auto'><a name="node248" id= "node248"></a>Maximize Contrast within Intensity Range</h3> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image245.jpg" alt="image"> for the diameter of the kernel and <img border= "0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image266.jpg" alt="image"> for the intensity constraint. This is another filter falling within the definition of Intensity Constrained Flat Kernel filtering scheme. The operation takes one image and two scalar operands. First operand is the diameter of the kernel. It has to be odd. The second operand is <i><span style= 'font-family:Symbol'>k</span></i>=<i>δ,</i> if <i>δ</i><i><span style='font-family:Symbol'>³</span> 1,</i> where <i>δ</i> is an intensity range or <i><span style= 'font-family:Symbol'>k</span></i>=<i><span style= 'font-family:Symbol'>g</span>,</i> if <i>0<</i> <i><span style= 'font-family:Symbol'>g</span><1,</i> where <span style= 'font-family:Symbol'>g</span> is the fraction of the intensity of the reference pixel (see below). The operation is aiming to increase the contrast of the pixels in the output image. The output of the filter is described by the formula:</p> <p class="Text"><span lang="EN-US" style= 'color:red'><sub><img border="0" width="260" height="56" src= "PIPUserManualNoFootnotes_files/image247.gif" alt= "image"></sub></span><span lang="EN-US">,</span></p> <p class="Text"><span lang="EN-US">where</span></p> <p class="MsoBodyText"><sub><img border="0" width="24" height="27" src="PIPUserManualNoFootnotes_files/image248.gif" alt= "image"></sub> <sub>is a histogram</sub> of the part of the image, which is masked by the kernel χ with the centre at <sub><img border="0" width="16" height="25" src= "PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub>,</p> <p class="MsoBodyText"><sub><img border="0" width="16" height="25" src="PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub> is a vector describing the spatial position of the pixels <sub><img border="0" width="40" height="25" src= "PIPUserManualNoFootnotes_files/image250.gif" alt="image"></sub>, where <i>S</i> is the spatial domain,</p> <p class="MsoBodyText"><i>K(p) = I<sub>p</sub> ± I<sub>p</sub> ·</i><i><span style='font-family:Symbol'>g</span></i>, is the constraint. Selection of constraint in this form makes the filter applicable to images of any type because image dynamic range does no appear explicitly in the constraint expression,</p> <p class="MsoBodyText"><sub><img border="0" width="114" height="26" src="PIPUserManualNoFootnotes_files/image252.gif" alt= "image"></sub></p> <p class="Text" style='text-indent:0cm'><i><span lang="EN-US" style='line-height: 105%'>F</span></i> <span lang="EN-US" style= 'line-height:105%'>=</span> <span lang="EN-US" style= 'font-size:11.0pt;line-height:105%;color:red'><sub><img border="0" width="195" height="64" src= "PIPUserManualNoFootnotes_files/image267.gif" alt= "image"></sub></span><span lang="EN-US" style= 'line-height:105%'> , </span></p> <p class="MsoBodyText">where <sub><img border="0" width="27" height="29" src="PIPUserManualNoFootnotes_files/image268.gif" alt= "image"></sub>is the average intensity of the area under the kernel χ at <sub><img border="0" width="16" height="25" src= "PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub></p> <p class="MsoBodyText">The filter is described in A. Gutenev “Intensity Constrained Flat Kernel Image Filtering Scheme - Definition and Applications”, submitted to <i>Proceedings of the 2010 International Conference of Signal and Image Engineering, London, U.K., 30 June - 2 July, 2010</i>.</p> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node249" id= "node249"></a>Local Maximum within Intensity Range</h3> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image245.jpg" alt="image"> for the diameter of the kernel and <img border= "0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image269.jpg" alt="image"> for the intensity constraint. This is another filter falling within the definition of Intensity Constrained Flat Kernel filtering scheme. The operation takes one image and two scalar operands. First operand is the diameter of the kernel. It has to be odd. The second operand is <i><span style= 'font-family:Symbol'>k</span></i>=<i>δ,</i> if <i>δ</i><i><span style='font-family:Symbol'>³</span> 1,</i> where <i>δ</i> is an intensity range or <i><span style= 'font-family:Symbol'>k</span></i>=<i><span style= 'font-family:Symbol'>g</span>,</i> if <i>0<</i> <i><span style= 'font-family:Symbol'>g</span><1,</i> where <span style= 'font-family:Symbol'>g</span> is the fraction of the intensity of the reference pixel. It can be viewed as intensity constrained morphological dilation and is defined by the formula:</p> <p class="Text"><span lang="EN-US" style= 'color:red'><sub><img border="0" width="260" height="56" src= "PIPUserManualNoFootnotes_files/image247.gif" alt= "image"></sub></span><span lang="EN-US">,</span></p> <p class="Text"><span lang="EN-US">where</span></p> <p class="MsoBodyText"><sub><img border="0" width="24" height="27" src="PIPUserManualNoFootnotes_files/image248.gif" alt= "image"></sub> <sub>is a histogram</sub> of the part of the image, which is masked by the kernel χ with the centre at <sub><img border="0" width="16" height="25" src= "PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub>,</p> <p class="MsoBodyText"><sub><img border="0" width="16" height="25" src="PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub> is a vector describing the spatial position of the pixels <sub><img border="0" width="40" height="25" src= "PIPUserManualNoFootnotes_files/image250.gif" alt="image"></sub>, where <i>S</i> is the spatial domain,</p> <p class="MsoBodyText"><i>K(p) = I<sub>p</sub> ± I<sub>p</sub> ·</i><i><span style='font-family:Symbol'>g</span></i>, is the constraint. Selection of constraint in this form makes the filter applicable to images of any type because image dynamic range does no appear explicitly in the constraint expression,</p> <p class="MsoBodyText"><sub><img border="0" width="114" height="26" src="PIPUserManualNoFootnotes_files/image252.gif" alt= "image"></sub></p> <p class="Text" style='text-indent:0cm'><i><span lang="EN-US" style='line-height: 105%'>F</span></i> <span lang="EN-US" style= 'line-height:105%'>=</span> <span lang="EN-US" style= 'font-size:11.0pt;line-height:105%;color:red'><sub><img border="0" width="103" height="29" src= "PIPUserManualNoFootnotes_files/image270.gif" alt= "image"></sub></span><span lang="EN-US" style= 'line-height:105%'> </span></p> <p class="MsoBodyText">where <sub><img border="0" width="27" height="29" src="PIPUserManualNoFootnotes_files/image268.gif" alt= "image"></sub>is the average intensity of the area under the kernel χ at <sub><img border="0" width="16" height="25" src= "PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub></p> <p class="MsoBodyText">At the time of creation this filter presented only a theoretical interest, no applications were found for it. The operation takes one image and two scalar operands. First operand is the diameter of the kernel. It has to be odd. The second operand is the fraction (0,1) of intensity used for constraining the intensity range within the kernel.</p> <h3 style='page-break-after:auto'><a name="node250" id= "node250"></a>Local Minimum within Intensity Range</h3> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image245.jpg" alt="image"> for the diameter of the kernel and <img border= "0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image269.jpg" alt="image"> for the intensity constraint. This is another filter falling within the definition of Intensity Constrained Flat Kernel filtering scheme. The operation takes one image and two scalar operands. First operand is the diameter of the kernel. It has to be odd. The second operand is <i><span style= 'font-family:Symbol'>k</span></i>=<i>δ,</i> if<i>δ</i><i><span style='font-family:Symbol'>³</span> 1,</i> where <i>δ</i> is an intensity range or <i><span style= 'font-family:Symbol'>k</span></i>=<i><span style= 'font-family:Symbol'>g</span>,</i> if <i>0<</i> <i><span style= 'font-family:Symbol'>g</span><1,</i> where <span style= 'font-family:Symbol'>g</span> is the fraction of the intensity of the reference pixel. It can be viewed as intensity constrained morphological erosion and is defined by the formula:</p> <p class="Text"><span lang="EN-US" style= 'color:red'><sub><img border="0" width="260" height="56" src= "PIPUserManualNoFootnotes_files/image247.gif" alt= "image"></sub></span><span lang="EN-US">,</span></p> <p class="Text"><span lang="EN-US">where</span></p> <p class="MsoBodyText"><sub><img border="0" width="24" height="27" src="PIPUserManualNoFootnotes_files/image248.gif" alt= "image"></sub> <sub>is a histogram</sub> of the part of the image, which is masked by the kernel χ with the centre at <sub><img border="0" width="16" height="25" src= "PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub>,</p> <p class="MsoBodyText"><sub><img border="0" width="16" height="25" src="PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub> is a vector describing the spatial position of the pixels <sub><img border="0" width="40" height="25" src= "PIPUserManualNoFootnotes_files/image250.gif" alt="image"></sub>, where <i>S</i> is the spatial domain,</p> <p class="MsoBodyText"><i>K(p) = I<sub>p</sub> ± I<sub>p</sub> ·</i><i><span style='font-family:Symbol'>g</span></i>, is the constraint. Selection of constraint in this form makes the filter applicable to images of any type because image dynamic range does no appear explicitly in the constraint expression,</p> <p class="MsoBodyText"><sub><img border="0" width="114" height="26" src="PIPUserManualNoFootnotes_files/image252.gif" alt= "image"></sub></p> <p class="Text" style='text-indent:0cm'><i><span lang="EN-US" style='line-height: 105%'>F</span></i> <span lang="EN-US" style= 'line-height:105%'>=</span> <span lang="EN-US" style= 'font-size:11.0pt;line-height:105%;color:red'><sub><img border="0" width="99" height="29" src= "PIPUserManualNoFootnotes_files/image271.gif" alt= "image"></sub></span><span lang="EN-US" style= 'line-height:105%'> </span></p> <p class="MsoBodyText">where <sub><img border="0" width="27" height="29" src="PIPUserManualNoFootnotes_files/image268.gif" alt= "image"></sub>is the average intensity of the area under the kernel χ at <sub><img border="0" width="16" height="25" src= "PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub></p> <p class="MsoBodyText">At the time of creation this filter presented only a theoretical interest, no applications were found for it. The operation takes one image and two scalar operands. First operand is the diameter of the kernel. It has to be odd. The second operand is the fraction (0,1) of intensity used for constraining the intensity range within the kernel.</p> <h3 style='page-break-after:auto'><a name="node251" id= "node251"></a>Directional low pass filter</h3> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image272.jpg" alt="image"> for the length of the kernel and <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image273.jpg" alt="image"> for the direction of the smoothing. This operation applies smoothing along a line to a source given as a first operand. The kernel is a line whose size is given by the second operand and the direction is specified by the third operand. The direction is specified in radians.</p> <p class="MsoBodyText"> </p> <h2><a name="node252" id="node252"></a>Ternary Threshold Operations</h2> <h3 style='page-break-after:auto'><a name="node253" id= "node253"></a>Threshold at Local Average within Intensity Range</h3> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image245.jpg" alt="image"> for the diameter of the kernel and <img border= "0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image274.jpg" alt="image"> for the intensity constraint. This is another filter falling within the definition of Intensity Constrained Flat Kernel filtering scheme. The operation takes one image and two scalar operands. First operand is the diameter of the kernel. It has to be odd. The second operand is <i><span style= 'font-family:Symbol'>k</span></i>=<i>δ,</i> if <i>δ</i><i><span style='font-family:Symbol'>³</span> 1,</i> where <i>δ</i> is an intensity range or <i><span style= 'font-family:Symbol'>k</span></i>=<i><span style= 'font-family:Symbol'>g</span>,</i> if <i>0<</i> <i><span style= 'font-family:Symbol'>g</span><1,</i> where <span style= 'font-family:Symbol'>g</span> is the fraction of the intensity of the reference pixel. Its output is described by the formula:</p> <p class="Text"><span lang="EN-US" style= 'color:red'><sub><img border="0" width="260" height="56" src= "PIPUserManualNoFootnotes_files/image247.gif" alt= "image"></sub></span><span lang="EN-US">,</span></p> <p class="Text"><span lang="EN-US">where</span></p> <p class="MsoBodyText"><sub><img border="0" width="24" height="27" src="PIPUserManualNoFootnotes_files/image248.gif" alt= "image"></sub> <sub>is a histogram</sub> of the part of the image, which is masked by the kernel χ with the centre at <sub><img border="0" width="16" height="25" src= "PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub>,</p> <p class="MsoBodyText"><sub><img border="0" width="16" height="25" src="PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub> is a vector describing the spatial position of the pixels <sub><img border="0" width="40" height="25" src= "PIPUserManualNoFootnotes_files/image250.gif" alt="image"></sub>, where <i>S</i> is the spatial domain,</p> <p class="MsoBodyText"><i>K(p) = I<sub>p</sub> ± I<sub>p</sub> ·</i><i><span style='font-family:Symbol'>g</span></i>, is the constraint. Selection of constraint in this form makes the filter applicable to images of any type because image dynamic range does no appear explicitly in the constraint expression,</p> <p class="Text"><i><span lang="EN-US">F =G=</span></i><span lang= "EN-US" style= 'font-size:11.0pt;line-height:105%;color:red'><sub><img border="0" width="148" height="64" src= "PIPUserManualNoFootnotes_files/image275.gif" alt= "image"></sub></span><span lang= "EN-US">, </span></p> <p class="MsoBodyText">where <sub><img border="0" width="27" height="29" src="PIPUserManualNoFootnotes_files/image268.gif" alt= "image"></sub> is the average intensity of the area under the kernel χ at <sub><img border="0" width="16" height="25" src= "PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub></p> <p class="MsoBodyText">The operation takes one image and two scalar operands. First operand is the diameter of the kernel. It has to be odd. The second operand is the fraction (0,1) of intensity used for constraining the intensity range within the kernel. The operation finds the average intensity within the kernel and assigns to the central pixel to the foreground if its intensity is within the given range of the average, otherwise it assigns the corresponding output pixel to the background. The threshold operation is described in detail in A. Gutenev “Intensity Constrained Flat Kernel Image Filtering Scheme - Definition and Applications”, submitted to <i>Proceedings of the 2010 International Conference of Signal and Image Engineering, London, U.K., 30 June - 2 July, 2010</i>.</p> <h3 style='page-break-after:auto'><a name="node254" id= "node254"></a>Threshold Below Local Average within Intensity Range</h3> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image245.jpg" alt="image"> for the diameter of the kernel and <img border= "0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image276.jpg" alt="image"> for the intensity constraint. This is one of the possible inverses of the previous operation, where the output is assigned to foreground, if local average is below the infimum of the range around the central pixel:</p> <p class="Text"><i><span lang="EN-US">F =G=</span></i><span lang= "EN-US" style= 'font-size:11.0pt;line-height:105%;color:red'><sub><img border="0" width="173" height="64" src= "PIPUserManualNoFootnotes_files/image277.gif" alt= "image"></sub></span><span lang= "EN-US">, </span></p> <p class="MsoBodyText">where <sub><img border="0" width="27" height="29" src="PIPUserManualNoFootnotes_files/image268.gif" alt= "image"></sub> is the average intensity of the area under the kernel χ at <sub><img border="0" width="16" height="25" src= "PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub></p> <p class="MsoBodyText"><i>K(p) = I<sub>p</sub> ± I<sub>p</sub> ·</i><i><span style='font-family:Symbol'>g</span></i>, is the constraint</p> <p class="MsoBodyText">The operation takes one image and two scalar operands. First operand is the diameter of the kernel. It has to be odd. The second operand is the fraction (0,1) of intensity used for constraining the intensity range within the kernel.</p> <h3 style='page-break-after:auto'><a name="node255" id= "node255"></a>Threshold Above Local Average within Intensity Range</h3> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image245.jpg" alt="image"> for the diameter of the kernel and <img border= "0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image278.jpg" alt="image"> for the intensity constraint. This is another of the possible inverses of the Threshold at Local Average within Intensity Range operation, where the output is assigned to foreground if local average is above the supremum of the range around the central pixel:</p> <p class="Text"><i><span lang="EN-US">F =G=</span></i><span lang= "EN-US" style= 'font-size:11.0pt;line-height:105%;color:red'><sub><img border="0" width="179" height="64" src= "PIPUserManualNoFootnotes_files/image279.gif" alt= "image"></sub></span><span lang= "EN-US">, </span></p> <p class="MsoBodyText">where <sub><img border="0" width="27" height="29" src="PIPUserManualNoFootnotes_files/image268.gif" alt= "image"></sub> is the average intensity of the area under the kernel χ at <sub><img border="0" width="16" height="25" src= "PIPUserManualNoFootnotes_files/image249.gif" alt= "image"></sub></p> <p class="MsoBodyText"><i>K(p) = I<sub>p</sub> ± I<sub>p</sub> ·</i><i><span style='font-family:Symbol'>g</span></i>, is the constraint</p> <p class="MsoBodyText">The operation takes one image and two scalar operands. First operand is the diameter of the kernel. It has to be odd. The second operand is the fraction (0,1) of intensity used for constraining the intensity range within the kernel.</p> <h3 style='page-break-after:auto'><a name="node256" id= "node256"></a>Pixel Clustering in Local Neighbourhood</h3> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image245.jpg" alt="image"> for the diameter of the kernel and <img border= "0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image280.jpg" alt="image"> for the intensity range. This operation performs local clustering on neighbouring pixels based on given definition of neighbourhood and on the image intensity range defining intensity equivalence within the cluster. This is an experimental procedure in the process of evolution and it will be modified. We do not recommend using it as yet in a production environment.</p> <h3 style='page-break-after:auto'><a name="node257" id= "node257"></a>Threshold by Statistics of another Image</h3> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image238.jpg" alt="image"> for the diameter of the image source, <img border="0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image281.jpg" alt="image"> for the second, usually smaller sized image and <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image282.jpg" alt="image"> for the standard deviation multiplier. This operation is designed to take the mean and standard deviation of a second operand, presumably a smaller image or a sub-image of the first operand, multiply the standard deviation by the supplied multiplier. The results of the multiplication define a range around the calculated mean. This range is the threshold range defining the foreground in the output binary image. For multi-component images the ranges obtained from different components yield the axis of the ellipse or ellipsoid defining the foreground of the resulting binary image. </p> <h2><a name="node258" id="node258"></a>Ternary Threshold Operations Applicable to Multi-component Images</h2> <h3 style='page-break-after:auto'><a name="node259" id= "node259"></a>Threshold by Relative Statistics of another Image</h3> <p class="MsoNormal"> </p> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image238.jpg" alt="image"> for the diameter of the image source <img border= "0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image283.jpg" alt="image">, for the second, usually smaller sized image and <img border="0" width="32" height="32" src="PIPUserManualNoFootnotes_files/image284.jpg" alt= "image"> for the standard deviation multiplier. This operation is designed to take the mean and standard deviation for each component of a second operand, presumably a smaller image or a sub-image of the first operand, multiply the components standard deviations by the supplied multiplier. The ratios of the component means are calculated together with scaled standard deviations. The scaled standard deviations yield the axis of the ellipse or ellipsoid. The calculated ratios of component means make the centre of the ellipse/ellipsoid. The ratios of the components of each the pixel are compared against the ellipse/ellipsoid thus being assigned to the foreground or background of the resulting binary image.</p> <p class="MsoBodyText"> </p> <h2><a name="node260" id="node260"></a>Ternary Transforms</h2> <p class="MsoBodyText"> </p> <h3 style='page-break-after:auto'><a name="node261" id= "node261"></a>Local Image Variance with Intensity Range Constraint</h3> <p class="MsoBodyText">Operation icons are <img border="0" width= "32" height="32" src="PIPUserManualNoFootnotes_files/image245.jpg" alt="image"> for the diameter of the kernel and <img border= "0" width="32" height="32" src= "PIPUserManualNoFootnotes_files/image285.jpg" alt="image"> for the intensity constraint. This is another operation falling within definition of Intensity Constrained Flat Kernel filtering scheme. It is designed as a texture measure. The operation takes one image and two scalar operands. First operand is the diameter of the kernel. It has to be odd. The second operand is <i><span style= 'font-family:Symbol'>k</span></i>=<i>δ,</i> if <i>δ</i><i><span style='font-family:Symbol'>³</span> 1,</i> where <i>δ</i> is an intensity range or <i><span style= 'font-family:Symbol'>k</span></i>=<i><span style= 'font-family:Symbol'>g</span>,</i> if <i>0<</i> <i><span style= 'font-family:Symbol'>g</span><1,</i> where <span style= 'font-family:Symbol'>g</span> is the fraction of the intensity of the reference pixel. Detailed description will be provided following pending publication.</p> <b><span style='font-size:14.0pt;font-family:Arial'><br clear="all" style='page-break-before:always'></span></b> <h1 style='page-break-after:auto'><a name="node262" id= "node262"></a>Special tasks</h1> <h3 style='page-break-after:auto'><a name= "_Determining_Average_Grain"></a>Determining Average Grain Size From Metallographic Images</h3> <p class="MsoBodyText">This feature is available in Full Size image view of a calibrated binary image. </p> <p class="MsoNormal"><img border="0" width="342" height="79" src= "PIPUserManualNoFootnotes_files/image286.jpg" alt="image"></p> <p class="MsoBodyText"> </p> <p class="MsoBodyText">If the project is not calibrated the menu is greyed out.</p> <p class="MsoBodyText">In this feature it is assumed that the binary image is a two-phase metallographic image, where one phase is represented by the foreground (white) and another with the background (black). The background is assumed consisting of thing lines separating the grains of the foreground. The average size of these grains is calculated according to the ASTM standard E 112-96 and close to it Australian Standard AS 1733-1976. ASTM standard employs formula for calculation of the grain size while the Australian standard employs a look up table.</p> <p class="MsoNormal">The results of the calculations are presented in the following form</p> <p class="MsoNormal"> </p> <p class="MsoNormal"><img border="0" width="502" height="437" src= "PIPUserManualNoFootnotes_files/image287.jpg" alt="image"></p> <p class="MsoBodyText"> </p> <p class="MsoBodyText">Two calculation methods of the grain size calculations are employed: Planimetric Method and Intercept Method. These methods are described in detail in the standards. In the Planimetric Method the size of the 3-dimensional grain is deduced from the average area of the grain in the image. In the Intercept Method the size is deduced from the average length of the line segments intercepted by the grain body.</p> <p class="MsoBodyText">In Supplementary Information section we present the data used in calculation for both methods as well as additional grain size calculation based on fully visible grains only. The standard methods make use of partially usable grains as well.</p> <p class="MsoBodyText"> </p> <p class="MsoBodyText">Pressing “Save” button user can save the results in comma delimited .csv text file. The name of the file is specified interactively.</p> <b><span style='font-size:14.0pt;font-family:Arial'><br clear="all" style='page-break-before:always'></span></b> <h1 style='page-break-after:auto'><a name="node263" id= "node263"></a>Memory management</h1> <p class="MsoBodyText">With advent of megapixel cameras size of images quickly increased to the point of filling all available address space of 32-bit Windows operating system. In these circumstances any image processing application without memory management is self-limiting. In Pictorial Image Processor© the objects responsible for the largest memory consumption are the images. For example, 5 megapixel image converted to type double precision floating point takes 40 megabyte. Keeping in RAM even a small algorithm comprising this type of images exerts a significant stress on operating system and ultimately performance of the computer.</p> <p class="MsoBodyText">Memory manager of Pictorial Image Processor© performs the following tasks:</p> <p class="MsoList">1. Monitors memory consumption of the Pictorial Image Processor© application</p> <p class="MsoList">2. If a preset limit of the system memory is reached, caches into a temp directory image stores of the images</p> <p class="MsoList">3. If a Pictorial Image Processor© project loses focus the image store for the whole project is cached to a temp directory.</p> <p class="MsoNormal"> </p> <p class="MsoBodyText">Memory management tasks are performed on background minimising impact on application performance in its principal task. The pixel stores are cached into a subdirectory “/pip” of the system directory holding temporary files, defined by environment variable TEMP. The cache is cleaned when application terminates normally. On application’s start up it attempts to clean up cache directory. This may not happen, if TEMP system variable has been changed since last execution of the application.</p> <p class="MsoBodyText">The memory manager also operates on 64-bit operating systems reducing the need for use of virtual memory.</p> <p class="MsoNormal"> </p> </div> <!-- And the content tree: --> <ul id="contentsTree" class="contentTree"> <li><a href="start.htm#node0">Introduction</a> <ul> <li><a href="start.htm#node1">Version Info</a></li> </ul> </li> <li><a href="start.htm#node2">Using Pictorial Image Processor</a> <ul> <li><a href="start.htm#_Basic_steps">Basic steps</a></li> <li><a href="start.htm#node3">Project window navigation</a></li> <li><a href="start.htm#node4">Project Edit functions</a></li> <li><a href="start.htm#node5">Project attributes</a></li> <li><a href="start.htm#_Convolution_Kernel_Designer">Convolution Kernel Designer</a></li> <li><a href="start.htm#node6">Logging execution time for project operations</a></li> <li><a href="start.htm#_Viewing_full_size">Viewing full size image</a> <ul> <li><a href="start.htm#node7">Image Information</a></li> <li><a href="start.htm#node8">Viewing Zoomed Image</a></li> <li><a href="start.htm#node9">Copying Image to Clipboard</a></li> <li><a href="start.htm#node10">Viewing Palette Selection</a></li> <li><a href="start.htm#node11">Mapping Image into Viewing Range</a></li> <li><a href="start.htm#node12">Viewing Neighbourhood of Pixel under Cursor</a></li> <li><a href="start.htm#node13">Cross-section Line profiles</a></li> <li><a href="start.htm#node14">Component view</a></li> </ul> </li> <li><a href="start.htm#_Intensity_Histogram_Window">Intensity Histogram Window</a></li> <li><a href="start.htm#node15">2D Histogram Window</a></li> <li><a href="start.htm#_Intensity_Profile_Window">Spatial Statistics Histogram Window</a></li> <li><a href="start.htm#node16">Intensity Profile Window</a></li> <li><a href="start.htm#_Batch_processing_of">Batch processing of file lists</a></li> </ul> </li> <li><a href="start.htm#_Operands">Operands</a> <ul> <li><a href="start.htm#node17">Scalar Operand</a></li> <li><a href="start.htm#node18">Image Operand</a></li> </ul> </li> <li><a href="start.htm#_Operations">Operations</a> <ul> <li><a href="start.htm#_Input/Output">Input/Output</a> <ul> <li><a href="start.htm#_Open_Image">Open Image</a></li> <li><a href="start.htm#node19">Image List</a></li> <li><a href="start.htm#node20">Save Operand</a></li> <li><a href="start.htm#node21">Save Image Histogram</a></li> <li><a href="start.htm#node22">Replace Image</a></li> <li><a href="start.htm#node23">Enter Scalar</a></li> <li><a href="start.htm#node24">Edit Scalar</a></li> <li><a href="start.htm#node25">Select Subimage</a></li> </ul> </li> <li><a href="start.htm#_Type_Conversion_Operations">Type Conversion Operations</a> <ul> <li><a href="start.htm#node26">1-bit to 8-bit</a></li> <li><a href="start.htm#node27">1-bit to 16-bit</a></li> <li><a href="start.htm#node28">1-bit to 24-bit</a></li> <li><a href="start.htm#node29">1-bit to 32-bit</a></li> <li><a href="start.htm#node30">1-bit to Float, 32-bit single precision floating point</a></li> <li><a href="start.htm#node31">1-bit to 64-bit double precision floating point</a></li> <li><a href="start.htm#node32">1-bit to 128-bit complex</a></li> <li><a href="start.htm#node33">8-bit to 16-bit</a></li> <li><a href="start.htm#node34">8-bit to 24-bit</a></li> <li><a href="start.htm#node35">8-bit to 32-bit</a></li> <li><a href="start.htm#node36">8-bit to Float, 32-bit single precision floating point</a></li> <li><a href="start.htm#node37">8-bit to 64-bit double precision floating point</a></li> <li><a href="start.htm#node38">8-bit to 128-bit complex</a></li> <li><a href="start.htm#node39">16-bit to 8-bit</a></li> <li><a href="start.htm#node40">16-bit to 32-bit</a></li> <li><a href="start.htm#node41">16-bit to Float, 32-bit single precision floating point</a></li> <li><a href="start.htm#node42">16-bit to 64-bit double precision floating point</a></li> <li><a href="start.htm#node43">16-bit to 128-bit complex</a></li> <li><a href="start.htm#node44">24-bit to 8-bitt</a></li> <li><a href="start.htm#node45">24-bit to 16-bit</a></li> <li><a href="start.htm#node46">24-bit to 32-bit</a></li> <li><a href="start.htm#node47">Extract 1st principal component from 24-bit image</a></li> <li><a href="start.htm#node48">Extract red component of 24-bit image</a></li> <li><a href="start.htm#node49">Extract green component of 24-bit image</a></li> <li><a href="start.htm#node50">Extract blue component of 24-bit image</a></li> <li><a href="start.htm#node51">Combine 3 grey components into 24-bit image</a></li> <li><a href="start.htm#node52">Extract hue component of 24-bit image</a></li> <li><a href="start.htm#node53">Extract saturation component of 24-bit image</a></li> <li><a href="start.htm#node54">Extract intensity component of 24-bit image</a></li> <li><a href="start.htm#node55">Combine 3 HSI components into 24-bit image</a></li> <li><a href="start.htm#node56">32-bit integral to 8-bit</a></li> <li><a href="start.htm#node57">32-bit integral to 16-bit</a></li> <li><a href="start.htm#node58">32-bit integral to 32-bit single precision floating point</a></li> <li><a href="start.htm#node59">32-bit integral to 64-bit double precision floating point</a></li> <li><a href="start.htm#node60">32-bit integral to 128-bit complex</a></li> <li><a href="start.htm#node61">32-bit single precision floating point to 8-bit</a></li> <li><a href="start.htm#node62">32-bit single precision floating point to 16-bit</a></li> <li><a href="start.htm#node63">32-bit single precision floating point to 32-bit integral</a></li> <li><a href="start.htm#node64">32-bit single precision floating point to 64-bit double precision floating point</a></li> <li><a href="start.htm#node65">32-bit single precision floating point to 128-bit complex</a></li> <li><a href="start.htm#node66">64-bit double precision floating point to 8-bit</a></li> <li><a href="start.htm#node67">64-bit double precision floating point to 16-bit</a></li> <li><a href="start.htm#node68">64-bit double precision floating point to 32-bit integral</a></li> <li><a href="start.htm#node69">64-bit double precision floating point to 32-bit single precision floating point</a></li> <li><a href="start.htm#node70">64-bit double precision floating point to 128-bit complex</a></li> <li><a href="start.htm#node71">128-bit complex to 8-bit</a></li> <li><a href="start.htm#node72">128-bit complex to 16-bit</a></li> <li><a href="start.htm#node73">128-bit complex to 32-bit integral</a></li> <li><a href="start.htm#node74">128-bit complex to 32-bit single precision floating point</a></li> <li><a href="start.htm#node75">128-bit complex to 64-bit double precision floating point</a></li> <li><a href="start.htm#node76">Extract real component of 128-bit complex image</a></li> <li><a href="start.htm#node77">Extract imaginary component of 128-bit complex image</a></li> <li><a href="start.htm#node78">Extract magnitude component of 128-bit complex image</a></li> <li><a href="start.htm#node79">Extract argument component of 128-bit complex image</a></li> <li><a href="start.htm#node80">Combine 2 images of the same size into 128-bit complex image</a></li> <li><a href="start.htm#node81">Extract red component interpolating Bayer mosaic image</a></li> <li><a href="start.htm#node82">Extract green component interpolating Bayer mosaic image</a></li> <li><a href="start.htm#node83">Extract blue component interpolating Bayer mosaic image</a></li> </ul> </li> <li><a href="start.htm#_Function_Operations">Function Operations</a> <ul> <li><a href="start.htm#node84">Histogram Equalisation</a></li> <li><a href="start.htm#node85">Absolute value</a></li> <li><a href="start.htm#node86">Power function</a></li> <li><a href="start.htm#node87">Reassign dark outliers</a></li> <li><a href="start.htm#node88">Reassign bright outliers</a></li> <li><a href="start.htm#node89">Reassign dark and bright outliers</a></li> </ul> </li> <li><a href="start.htm#_Unary_Operations">Unary Operations</a> <ul> <li><a href="start.htm#node90">Invert Image</a></li> <li><a href="start.htm#node91">Add Image to Itself</a></li> <li><a href="start.htm#node92">Exclusive OR on Image</a></li> <li><a href="start.htm#node93">Multiply Image by Itself</a></li> <li><a href="start.htm#node94">Automatic Thresholding Using Simple Image Statistic</a></li> <li><a href="start.htm#node95">Automatic Segmentation Using Simple Image Statistic</a></li> <li><a href="start.htm#node96">Automatic Thresholding using Maximum between Class Variance</a></li> <li><a href="start.htm#node97">Automatic Thresholding using Isodata algorithm</a></li> <li><a href="start.htm#node98">Modified Roberts Cross Filter</a></li> <li><a href="start.htm#node99">Sobel Filter</a></li> <li><a href="start.htm#node100">Elementary Dilation with 8-connected kernel</a></li> <li><a href="start.htm#node101">Elementary Dilation with 4-connected kernel</a></li> <li><a href="start.htm#node102">Elementary Erosion with 8-connected kernel</a></li> <li><a href="start.htm#node103">Elementary Erosion with 4-connected kernel</a></li> <li><a href="start.htm#node104">Elementary Opening with 8-connected kernel</a></li> <li><a href="start.htm#node105">Elementary Opening with 4-connected kernel</a></li> <li><a href="start.htm#node106">Elementary Closing with 8-connected kernel</a></li> <li><a href="start.htm#node107">Elementary Closing with 4-connected kernel</a></li> <li><a href="start.htm#node108">Watershed</a></li> <li><a href="start.htm#node109">Label Disjoint Histogram Blobs</a></li> <li><a href="start.htm#node110">Direction of gradient</a></li> <li><a href="start.htm#node111">Create circular 1-bit per pixel kernel</a></li> <li><a href="start.htm#node112">Create vertical 1-bit per pixel line</a></li> <li><a href="start.htm#node113">Create horizontal 1-bit per pixel line</a></li> </ul> </li> <li><a href="start.htm#node114">Unary Operations Applicable Only To Binary Images</a> <ul> <li><a href="start.htm#node115">Fill Closed Contours</a></li> <li><a href="start.htm#node116">Fill Small Holes</a></li> <li><a href="start.htm#node117">Outline Foreground Blobs</a></li> <li><a href="start.htm#node118">Skeletonise</a></li> <li><a href="start.htm#node119">Prune</a></li> <li><a href="start.htm#node120">Prune Not Closed Lines</a></li> <li><a href="start.htm#_Label_4-connected_Blobs">Label 4-connected Blobs in the Binary Image</a></li> <li><a href="start.htm#node121">Label 8-connected Blobs in the Binary Image</a></li> <li><a href="start.htm#node122">Label 4-connected Blobs in the Binary Image by the Blob Area</a></li> <li><a href="start.htm#node123">Label 8-connected Blobs in the Binary Image by the Blob Area</a></li> <li><a href="start.htm#node124">Distance Transform with Outside Assumed Background</a></li> <li><a href="start.htm#node125">Distance Transform with Outside Assumed Foreground</a></li> </ul> </li> <li><a href="start.htm#node126">Unary Operations Applicable Only To 24-bit Images</a> <ul> <li><a href="start.htm#node127">Extract Red-Green Histogram Image</a></li> <li><a href="start.htm#node128">Extract Red-Blue Histogram Image</a></li> <li><a href="start.htm#node129">Extract Blue-Green Histogram Image</a></li> <li><a href="start.htm#node130">Extract Hue-Intensity Histogram Image</a></li> <li><a href="start.htm#node131">Extract Hue-Saturation Histogram Image</a></li> <li><a href="start.htm#node132">Extract Intensity-Saturation Histogram Image</a></li> </ul> </li> <li><a href="start.htm#node133">Unary Transforms</a> <ul> <li><a href="start.htm#node134">Forward Fast Fourier Transform</a></li> <li><a href="start.htm#node135">Reverse Fast Fourier Transform</a></li> </ul> </li> <li><a href="start.htm#node136">Unary Geometric Operations</a> <ul> <li><a href="start.htm#node137">Crop image removing dark border</a></li> <li><a href="start.htm#node138">Get Crop Mask</a></li> <li><a href="start.htm#node139">Rotate image by 90o</a></li> <li><a href="start.htm#node140">Rotate image by -90o</a></li> <li><a href="start.htm#node141">Get Top Border Mask for the Image</a></li> <li><a href="start.htm#node142">Get Bottom Border Mask for the Image</a></li> <li><a href="start.htm#node143">Get Top Border Mask for the Image</a></li> <li><a href="start.htm#node144">Get Right Border Mask for the Image</a></li> <li><a href="start.htm#node145">Expand Image Half Size in Each Direction</a></li> <li><a href="start.htm#node146">Contract Image Quarter Size in Each Direction</a></li> <li><a href="start.htm#node147">Circular Shift of Origin by Half-Image</a></li> <li><a href="start.htm#node148">Upsample Image by Linear Interpolation</a></li> <li><a href="start.htm#node149">Downsample Image by Linear Interpolation</a></li> <li><a href="start.htm#node150">Upsample Image by Duplicating Each Pixel</a></li> <li><a href="start.htm#node151">Downsample Image by Removing Each Second Pixel</a></li> </ul> </li> <li><a href="start.htm#node152">Unary Statistical Operations</a> <ul> <li><a href="start.htm#node153">Mean</a></li> <li><a href="start.htm#node154">Standard Deviation</a></li> <li><a href="start.htm#node155">Width</a></li> <li><a href="start.htm#node156">Height</a></li> <li><a href="start.htm#node157">Histogram Maximum</a></li> <li><a href="start.htm#node158">Peak Grey Level</a></li> <li><a href="start.htm#node159">Maximum Grey Level of the Image</a></li> <li><a href="start.htm#node160">Median Grey Level of the Image</a></li> <li><a href="start.htm#node161">Minimum Grey Level of the Image</a></li> <li><a href="start.htm#node162">Total sum of intensities</a></li> </ul> </li> <li><a href="start.htm#node163">Unary Statistical Operations Applicable Only To Binary Images</a> <ul> <li><a href="start.htm#node164">Blob count</a></li> <li><a href="start.htm#node165">Mean blob area</a></li> <li><a href="start.htm#node166">Mean diagonal of minimum enclosing rectangle (MER)</a></li> <li><a href="start.htm#node167">Total foreground area</a></li> <li><a href="start.htm#node168">Minimum distance of foreground blobs to the image right border</a></li> <li><a href="start.htm#node169">Minimum distance of foreground blobs to the image left border</a></li> <li><a href="start.htm#node170">Minimum distance of foreground blobs to the image top border</a></li> <li><a href="start.htm#node171">Minimum distance of foreground blobs to the image bottom border</a></li> </ul> </li> <li><a href="start.htm#_Binary_Arithmetic_Operations">Binary Arithmetic Operations</a> <ul> <li><a href="start.htm#node172">Add</a></li> <li><a href="start.htm#node173">Subtract</a></li> <li><a href="start.htm#node174">Multiply</a></li> <li><a href="start.htm#node175">Divide</a></li> <li><a href="start.htm#node176">Maximum</a></li> <li><a href="start.htm#node177">Minimum</a></li> </ul> </li> <li><a href="start.htm#node178">Binary Bitwise Operations</a> <ul> <li><a href="start.htm#node179">Bitwise AND</a></li> <li><a href="start.htm#node180">Bitwise OR</a></li> <li><a href="start.htm#node181">Bitwise exclusive OR</a></li> </ul> </li> <li><a href="start.htm#node182">Binary Thresholding and Segmentation Operations</a> <ul> <li><a href="start.htm#node183">Simple Threshold</a></li> <li><a href="start.htm#node184">Precise Threshold</a></li> <li><a href="start.htm#node185">Threshold Image by Tracing Local Maxima of Intensity</a></li> <li><a href="start.htm#node186">Fuzzy C-means Clustering</a></li> <li><a href="start.htm#node187">Segment by Skeleton</a></li> </ul> </li> <li><a href="start.htm#node188">Binary Morphological Operations</a> <ul> <li><a href="start.htm#node189">Dilation with Symmetric Kernel</a></li> <li><a href="start.htm#node190">Erosion with Symmetric Kernel</a></li> <li><a href="start.htm#node191">Opening with Symmetric Kernel</a></li> <li><a href="start.htm#node192">Closing with Symmetric Kernel</a></li> <li><a href="start.htm#node193">Dilation with flat kernel and mask</a></li> <li><a href="start.htm#node194">Erosion with flat kernel and mask</a></li> <li><a href="start.htm#node195">Opening with flat kernel and mask</a></li> <li><a href="start.htm#node196">Closing with flat kernel and mask</a></li> <li><a href="start.htm#node197">Morphological reconstruction</a></li> </ul> </li> <li><a href="start.htm#node198">Binary Filtering Operations</a> <ul> <li><a href="start.htm#node199">Convolution with rectangular/square kernel</a></li> <li><a href="start.htm#node200">Convolution with elliptic/circular kernel</a></li> <li><a href="start.htm#node201">Median Filter with Square Kernel</a></li> <li><a href="start.htm#node202">Median Filter with Circular Kernel</a></li> <li><a href="start.htm#node203">Separable Median Filter</a></li> <li><a href="start.htm#node204">Fast Isotropic Low Pass Filter with Kernel Equivalent to Box Filter</a></li> <li><a href="start.htm#node205">Smoothing Filter with Binomial Kernel</a></li> </ul> </li> <li><a href="start.htm#node206">Binary Transforms</a> <ul> <li><a href="start.htm#node207">Variance Transform</a></li> <li><a href="start.htm#node208">Normalised Sum of Squared Differences Transform</a></li> <li><a href="start.htm#node209">Deviation Trend Transform</a></li> <li><a href="start.htm#node210">Texture Directionality</a></li> <li><a href="start.htm#node211">Forward Fast Fourier Transform on Kernel Image</a></li> </ul> </li> <li><a href="start.htm#node212">Binary Interpolation Operations</a> <ul> <li><a href="start.htm#node213">Interpolate under a mask anisotropic</a></li> <li><a href="start.htm#node214">Interpolate under a mask tangent to mask</a></li> <li><a href="start.htm#node215">Fill mask with bright background</a></li> <li><a href="start.htm#node216">Fill mask with neighbouring pixels</a></li> </ul> </li> <li><a href="start.htm#node217">Binary Auxiliary Operations</a> <ul> <li><a href="start.htm#node218">Build Gaussian kernel</a></li> </ul> </li> <li><a href="start.htm#node219">Binary Geometric Operations</a> <ul> <li><a href="start.htm#node220">Crop by mask</a></li> <li><a href="start.htm#node221">Augment Image Mirror Border</a></li> <li><a href="start.htm#node222">Crop Image Border</a></li> </ul> </li> <li><a href="start.htm#node223">Binary Statistical Operations</a> <ul> <li><a href="start.htm#node224">This class of operations takes works on images, takes scalar or image as a parameter and returns a scalar.</a></li> <li><a href="start.htm#node225">Pixel Count for Given Grey Level</a></li> <li><a href="start.htm#node226">Number of Pixels Exceeding Given Grey Level</a></li> <li><a href="start.htm#node227">Per Element Maximum of Two Operands</a></li> <li><a href="start.htm#node228">Per Element Maximum of Two Operands</a></li> <li><a href="start.htm#node229">Mean within Masked Area</a></li> <li><a href="start.htm#node230">Standard Deviation within Masked Area</a></li> <li><a href="start.htm#node231">Maximum Grey Level within Masked Area</a></li> <li><a href="start.htm#node232">Median Grey Level within Masked Area</a></li> <li><a href="start.htm#node233">Minimum Grey Level within Masked Area</a></li> </ul> </li> <li><a href="start.htm#node234">Binary Operations Applicable Only To Binary Images</a> <ul> <li><a href="start.htm#_Threshold_by_Blob">Threshold by Blob Area, Preserve Blobs of Large Area</a></li> <li><a href="start.htm#node235">Threshold by Blob Area, Preserve Blobs of Small Area</a></li> <li><a href="start.htm#node236">Threshold by Blob Eccentricity, Preserve Blobs of Large Eccentricity</a></li> <li><a href="start.htm#node237">Threshold by Blob Eccentricity, Preserve Blobs of Large Eccentricity</a></li> </ul> </li> <li><a href="start.htm#node238">Binary Operations Applicable Only To 24-bit Images</a> <ul> <li><a href="start.htm#node239">Segment image by Red-Green histogram</a></li> <li><a href="start.htm#node240">Segment image by Red-Blue histogram</a></li> <li><a href="start.htm#node241">Segment image by Green-Blue histogram</a></li> <li><a href="start.htm#node242">Segment image by Hue-Intensity histogram</a></li> <li><a href="start.htm#node243">Segment image by Hue-Saturation histogram</a></li> <li><a href="start.htm#node244">Segment image by Intensity-Saturation histogram</a></li> </ul> </li> <li><a href="start.htm#_Ternary_Filter_Operations">Ternary Filter Operations</a> <ul> <li><a href="start.htm#node245">Local Image Smoothing with Intensity Range Constraint</a></li> <li><a href="start.htm#node246">Local Image Median with Intensity Range Constraint</a></li> <li><a href="start.htm#node247">Local Exclusive Median with Intensity Range Constraint</a></li> <li><a href="start.htm#node248">Maximize Contrast within Intensity Range</a></li> <li><a href="start.htm#node249">Local Maximum within Intensity Range</a></li> <li><a href="start.htm#node250">Local Minimum within Intensity Range</a></li> <li><a href="start.htm#node251">Directional low pass filter</a></li> </ul> </li> <li><a href="start.htm#node252">Ternary Threshold Operations</a> <ul> <li><a href="start.htm#node253">Threshold at Local Average within Intensity Range</a></li> <li><a href="start.htm#node254">Threshold Below Local Average within Intensity Range</a></li> <li><a href="start.htm#node255">Threshold Above Local Average within Intensity Range</a></li> <li><a href="start.htm#node256">Pixel Clustering in Local Neighbourhood</a></li> <li><a href="start.htm#node257">Threshold by Statistics of another Image</a></li> </ul> </li> <li><a href="start.htm#node258">Ternary Threshold Operations Applicable to Multi-component Images</a> <ul> <li><a href="start.htm#node259">Threshold by Relative Statistics of another Image</a></li> </ul> </li> <li><a href="start.htm#node260">Ternary Transforms</a> <ul> <li><a href="start.htm#node261">Local Image Variance with Intensity Range Constraint</a></li> </ul> </li> </ul> </li> <li><a href="start.htm#node262">Special tasks</a> <ul> <li><a href="start.htm#_Determining_Average_Grain">Determining Average Grain Size From Metallographic Images</a></li> </ul> </li> <li><a href="start.htm#node263">Memory management</a></li> </ul>
