Mango User Guide
Contents
1. 3 4 Grid of Images 2D Image generation IN tomographic data OUT jpeg files written to the working directory Name slice axis X Y or Z filemame_base jpg standard for all gridders If one is interested in more than one plane Grid of Images can be used Planes can be created on the x y z or all three axis direction toggle Enter the desired number of planes and unless auto choose planes is true enter a valid middle plane and plane spacing The files are written to the working directory 6 3 5 Intensity Gradient Plot IN tomographic data OUT jpeg file in working directory The Intensity Gradient Plot is a scatter plot in which each voxel contributes a point where its intensity provides the x value and its gradient the y value The brighter a certain area is the more voxels map to it A file prepended with IntensityGradientPlot to the suffix and with a jpg extension is written to the working directory This plot can help to determine the gradient threshold for 3 phase CAC segmentation See section 3 Phase Converging Active Contours Segmentation below for an example of the output and how to estimate the gradient threshold from the plot 14 6 3 6 Cylindrical Intensity Profile IN tomographic data OUT data in log_PO file Given a cylindrical data set like a drill core plug for example it may be useful to determine an intensity histog2. This function calculates for each voxel the euclidean distance to the nearest voxel of the other phase Note that if the distance map data is to be used for the creation of medial axis data it is important that cluster removal is carried out on the segmented data If do statistics is true the distance distribution of the data is written to the log_PO file Currently only the original method should be used Make sure write data is set to true to obtain an output file The toggle make maximal voxel file should be left to false The output file will have the name distance_map prepended to the suffix The phase whose distance is to be calculated must be set accordingly in the Top Section menu parameter phase_to_check 8 Label Data 8 1 Compare Label Data Files IN label data OUT label difference information This function takes two data sets of the same domain Set the file name base of the second file in the file name base window All corresponding voxels that have a different label in the two input files and their values are listed in the log_PO file Note that the same data set when run with a different number of processors with Label Clusters will result in different labelling of the clusters 32 8 2 Subset 8 3 Format Conversion 8 4 Intensity Cut Plane 8 5 Grid of Images 8 6 Sort Cluster Lables IN label data OUT sorted label data Functions that produce label data will create dif
3. are convert_clusters must be set to true for both pore and grain If write data is true a file with the suffix extended by IC is written 30 to the data directory Parameters need to be set for both Pore and Grain to control which clusters are removed Either the single largest cluster is kept keep one cluster only set to true or a minimum and maximum cluster size can be set and clusters are kept accordingly Note that an isolated cluster removal is advised if the dataset is to be processed for a medial axis or fiducial 7 2 9 Erosion Dilation IN segmented data OUT segmented data This function can erode dilate or dilate erode objects in a dataset by a ra dius specified in the radius parameter where the order is set with the order parameter toggle If write data is true a file with the letters Ed appended to the original file name is created with the eroded dilated data If do statis tics is true the number of voxels and their percentage that has changed is given in the log files If the object is close to the dataset borders halo size should be set to a number larger than the radius to avoid incorrect process ing at the border 7 2 10 Fiducial IN segmented data OUT fiducial segmented data The Fiducial function under Segmented data attempts to make a surface around the segmented object s It does this through repeated dilation erosion steps with i
4. eg threshold such that a segmentation is achieved Performing this process on the original tomographic data does in fact not lead to a satisfying segmentation Instead the initial region growing is car ried out on edge data ie Sobel and then these regions are analysed and merged on the original data For this reason two input files are required for this method of segmentation The file entered in the Top section must be the edge Sobel processed data and the second file entered in the Watershed Input data file parameter corresponds to the original data A threshold value that gives desired results for a simple segmentation is a good value to choose for the region average threshold Watershed segmentation has been found to perform well on cortical bone mostly solid with fine branching structure Currently this method is not yet implemented in parallel 23 6 6 6 Converging Active Contours Segmentation IN tomographic data optional fiducial data file OUT segmented data The paper Techniques for image enhancement and segmentation of tomo graphic images of porous materials Sheppard Sok Averdunk Physica A Volume 339 p 145 151 describes this segmentation method in some de tail The method requires two threshold values lower threshold and upper threshold which bound the uncertain intensity region Voxels with an in tensity less than lower threshold are immediately assigned void and voxel intensities ab
5. parameter determines the maximum file size in Megabytes larger data sets are written as multiple files 4 1 MPI If Mango is to run in multi processor mode the MPI parameters need to be set How many processors are needed depends on what is to be done and the particular hardware configuration that the job is running on Note that the total number of processors used is determined by the multiplication of the numbers entered for num_processors x y and z In order to minimise parallel processing overhead the sub domains created by X Y Z eg 8 sub domains if x y z 2 should be as close to a cube as possible such that the communication surfaces sub domain boundaries are as small as possible For example x 2 y 2 z 2 8 processors and sub domains communication area 12 is better than x 4 y 2 z 1 8 processors and sub domains com munication area 16 num_bytes_in chunk The file reading utility reads a part of the data file then distributes it to the processors then reads another part distributes it and so on The chunk size must be small enough to fit in the memory of a single processor but otherwise needs to be reasonably large for good perfor mance Any number greater than 1MB should be sufficient 5 Top Section controls verbosity_level Allows for the control of how much processing information is written to stdout the log files during the execution of the program phase to check Sets the phase that is a
6. 7 Threshold Quality Usd ere Ea one BBR on 6 3 8 Compare Tom Data gan oo kee lr aa Hoke aos 6 4 Preprocessing Filters and Convolvers 6 amp 1 WEA A A ye A ee 6 4 2 Median a a do ee hk a A IA 6 43 Conservative Median 6 4 4 Conservative Smoothing 10 10 10 12 12 12 12 12 12 12 12 12 6 4 5 Gaussian cele eds A EN ee Bt 16 6 4 6 Selective Gaussian 2 6 6 be ee ees 17 6 4 7 Convolution FFT lt a AR See 17 6 4 8 Sobel Gradient Edge Detection 17 6 4 9 Kuwahara Edge Enhancing 18 6 4 10 Anisotropic Diffusion 2 era wha Bw Oe 18 64 11 Un sh rp Mask s t e a nce ay ia Se da ee ap 18 6 5 Preprocessing Data wit x ade aaa as a 19 Gil escale Data esii y d e DEA x ee 19 6 5 2 Beam Hardening Correction BHC 19 Gi SUM e aa a a UG 19 6 5 4 Subset OOC Out of core o 20 6 5 5 Format Conversion iia ale y de e 20 6 5 6 Format Conversion OOC 20 6 5 7 Dif Tom Data Files ai A 20 6 5 8 Edge Detection tios cl bnew Gly bee Boag a 20 6 6 Segmentation 0d di Ya ene eng 21 6 6 1 The Problem ls a AA A wae 21 6 6 2 Simple Segmentation 22 6 6 3 Level Set Segmentation 4 22 6 6 4 Metropolis Segmentation 23 6 6 5 Watershed Segmentation 23 6 6 6 Converging Active Contours Segmentation 24 6 6 7 3 Phase Converging Active Contours Seg
7. Mango User Guide APPLIED MATHEMATICS ANU Holger AVERDUNK 2004 2005 v 1 1 ql am A os 8 E 8 E nn an aaa Eng E Nono my e np E fig OL En a a A E yl Mm no E E a a Pt Fy a a Ti mango medial axis and network generation Contents 1 Introduction dl The Software a a ea we Be Sa eer oe eg 1 2 Data Formats 4 04 2 be wk og edad St ew bo Pane ee as Log Fil sid a a is Set Th het A et eh se The GUI Data Flow Chart Top Section Menus AMPL 4 Go de e lea fh waite a Oh Kehoe Sb Top Section controls 51 Input Data sa sea p ose A ate RH oA eo BS ee Sil ANECA eeu ge aah San a ng he oe nd Bak Ny a geen he Seas la ASCI yee te once so bead ck ale eee ale oe Sid A Sa TAME IM a an hea eas a delia Se edo Tas Se olaa SLL Binary eae A IA a ma SLS A a a hg eee UG awe A ee gs 5 1 6 binary 22 34 ese lt Alea a de Bos a de Ba Bo Sr Dinary short s saieti ae ee ea he ee oe e 5 1 8 binary ushort 2s eek Bae eee ae Se AS oth Tomographic Data 6 1 Input Data File n sses e ads nepa ew cat deo el Pos ee a et 6 2 Generate Geometric Fiducial 63 Analysis Cd ae Gk A e De A 6 3 1 Intensity Histogram imita wii ie we elas 6 3 2 Intensity Cut Line ie ei Se ie he pa 6 3 3 Intensity Cut Plane 2D Image generation 6 3 4 Grid of Images 2D Image generation 6 3 5 Intensity Gradient Plot e patata is la het wale 6 3 6 Cylindrical Intensity Profile 6 3
8. _PO file do statistics has currently no effect 11 Medial Axis Data 11 1 Analysis 11 1 1 Compare Medial Axis Data Files IN medial axis data 2 different files with the same domain OUT location and value of all voxels that differ between the files listed in the log_PO file To compare two medial axis data files of the same domain enter the base name of the second file in the file_name_base field and examine the compar ison results in the log_PO file 11 1 2 Measure Medial Axis Quality IN medial axis data and corresponding segmented data OUT statistics in the log_PO file A measure of the quality of the medial axis is calculated by creating an object consisting of the union of spheres with the radius of each sphere given by the distance transform of the corresponding medial axis voxel at its center This object is then compared to the segmented data from which the medial axis 37 was created The number and percentage of correct missing and spurious voxels listed gives an indication of the quality of the medial axis 11 1 3 Intensity Cut Plane 2D Picture generation IN medial axis data OUT jpeg of a plane A gray level jpeg picture of a plane x y or z of medial axis data can be generated by this function Set the desired position of the cut plane in the position window Gray levels are well spread if auto scale is set to true If auto_scale is false the manual minimum value and manu
9. al maximal value are used to determine the gray levels The jpeg file is written to the working directory 11 1 4 Grid of Images IN medial axis data OUT jpegs of planes This function does the same as Intensity Cut Plane 2D Picture generation but allows multiple planes to be produced in one run The input windows for direction the number of planes and the middle plane and plane spacing control this additional functionality 11 1 5 Medial Axis Percolation IN medial axis data OUT percolation threshold for X Y Z or all three written to log_PO This function calculates the percolation threshold using a bisection binary search method It is the threshold at which the medial axis or rather the geometry it represents disconnects one face from another Toggle the direc tion switch to find the threshold for X Y Z or all three axes The tolerance parameter determines to what accuracy the threshold is calculated the lower the value the more accurate the threshold at the cost of longer time taken to compute Note that if the threshold is less than 1 or the tolerance value is within the thresholds then the axis is not spanning in that direction Therefore in usual circumstances the tolerance value should be below 1 If a flow tube has been added to the input file remove flow tube should be set to true in the Medial Axis creation otherwise it will not span Dur ing medial axis c
10. allocated data to its log file If normalise is set to true the data is normalised such that the sum of the histogram is 1 6 3 2 Intensity Cut Line IN tomographic data OUT intensity cut line data written to log_P0 This function is useful for determining sub set sizes and getting a general idea of the dataset like heterogeneity for example If the averaging radius is 1 0 the analysis axis is one voxel in diameter An averaging out of local heterogeneity can be achieved by increasing this radius Set the direction to the axis of interest and fill in the desired coordinates from which the cut line originates The coordinates toggle is only meaningful for a previously 13 subsetted data set In this case if coordinates is set to global the refer ence frame is that of the original file 6 3 3 Intensity Cut Plane 2D Image generation IN tomographic data OUT jpeg file written to the working directory Name slice axis X Y or Z filemame_base jpg Here a two dimensional slice along one of three axis of the dataset is con verted into a gray level jpeg file which is written to the working directory Choose the desired axis using the toggle switches and enter a valid position in the dataset If auto scale is set to false enter appropriate manual min imum value and manual maximum value parameters from which the scale intensity is calculated 6
11. ax delta aps or rms to complete 6 4 7 Convolution FFT IN tomographic data OUT filtered tomographic data does aps or rms to complete 6 4 8 Sobel Gradient Edge Detection IN tomographic data OUT filtered tomographic data The Sobel gradient edge detector not really a filter convolutes the dataset with the following kernel over the 26 neighbourhood of the central voxel x kernel 1 3 1 o O 0 1 3 1 3 6 3 o O 0 3 6 3 1 3 1 o O 0 1 3 1 x 1 x x 1 y kernel 1 3 1 3 6 3 1 3 1 o o o o o o o o o 1 3 1 3 6 3 1 3 1 y 1 y y i z kernel 1 0 1 3 0 3 1 O 1 3 0 3 6 0 6 3 0 3 1 0 1 3 0 3 1 O 1 z 1 Zz z 1 Visually the resulting output corresponds to the outlines of objects Usually the Sobel output would not be used as input for a segmentation It is used in conjunction with the original tomographic data in CAC perfect and Wa tershed Segmentation No parameters taken 17 6 4 9 Kuwahara Edge Enhancing IN tomographic data OUT filtered tomographic data This filter is an edge preserving enhancing filter Consider the following 2D labelling of a 5 5 matrix aa ab b b aa ab b b ac ac abcd bd bd cc cdd d cccdd d In each of the four regions a b c d the mean brightness and the variance are calculated The output value of the center pixel overlapping all four regions abcd in the window is the mean value of the region
12. ction the number of planes and the middle plane and plane spacing control this additional functionality 39 9 2 Processing 9 2 1 Distance Map Watershed IN distance map data optional fiducial OUT label data labelsWS This method carries out a Watershed algorithm similar to the one described in Watershed Segmentation above In this case distance map data serves as the input leading to label data output where each label number corresponds to a region found by the Watershed algorithm This function can be used for finding the volume of separate but connected air bubbles in foam or the volume of individual beads in a bead pack for example The do statistics toggle currently has no effect The seed checking radius defines the radius of the volume that is searched to find the seed voxel with the highest distance value It should be set to the radius of the smallest object that is to be la belled as a single region yet it must be within the parameters of 1 0 to 50 0 If the seed checking radius is too small more smaller undesirable regions may be formed in a sense over segmentation occurs The threshold incre ment value affects how quickly regions grow into areas with lower distance Usually lower threshold increment values will result in better results but at the cost of computation time 9 2 2 Maximal Covering Spheres IN distance map data optional fiducial OUT max_included_
13. different parameters are often necessary to achieve good results The following flow chart gives an overview of what needs to be done The tutorial at the end of this user guide explains the issues in more detail DATA PROCESSING ANALYSIS TOMOGRAPHIC DATA gt does the data need subsetting or a fiducial Intensity Cut Plane Intensity Histogram Intensity Cut Line Cylindrical Intensity Profile Intensity Gradient Plot Visualise whole or part subset strided subset of the data set get a feel and look of the data set quality size shape phases etc V filter Anisotropic Diffusion gt Intensity Cut Plane Intensity Histogram Unsharp Mask gt check effect of filter V segment choose segmentation method based on data V SEGMENTED DATA gt Intensity Cut Plane Subset Is the segmentation acceptable does the set need Isolated Cluster Removal create distance data V DISTANCE MAP DATA create medial axis V MEDIAL AXIS DATA gt visualise is the data OK create network V NETWORK Filtering the data first with Anisotropic Diffusion usually 20 iterations followed by Unsharp Mask is advised 4 Top Section Menus Input Data File This menu needs to be used only if the input data is in ascii format Enter the exact x y and z dimensions of the input data set Output Data File compression choose method of compression num_mbytes_per file This
14. e directory di alog box which allows setting the data directory the directory from which the data is read By default the data directory is the same as the working directory file name_suffix Sets the string which together with the type of expected data input is used to construct the file name that is searched for in the data directory For example suppose a dataset has been processed with Beam Hardening Correction and one wishes to load the segmented file thereof the file name suffix can be set to BHC and the program will expect a file called segmentedBHC nc 11 5 1 Input Data 5 1 1 NetCDF The NetCDF network Common Data Form is an interface for array oriented data access and a library that provides an implementation of the interface See the NetCDF website at http my unidata ucar edu content software netcdf index html or google NetCDF Files in this format have nc as suffix parameters required in the header 5 1 2 ASCII If data is read into Mango in ASCII format the dimensions of the dataset must be entered into the GUI Input Data File section right below Top Sec tion The file must be terminated by a newline after each row of dimension x and every number must be separated by a whitespace X Y Z must equal the number of numbers in the input file Files in this format have ai as suffix 5 1 3 rawPGM rawPGM 5 1 4 binary int 5 1 5 binary char 5 1 6 binary uchar Files in un
15. e which extends from the first to the last slice of the dataset in any axis If do statistics is true the log file will list the number of clusters in the phase under investigation and in what size range they are Setting convert clusters to true removes all non spanning clusters from the dataset which will be written to a file if write file is true which has SC added to its file name suffix Spanning clusters can be checked for each axis individually or for all three axes at once by the direction toggle 7 2 7 Label Clusters IN segmented data OUT label data integer Label Clusters assigns a unique integer number to each isolated cluster and writes out a file named labels concatenated with the input file suffix exten sion if write data is true where each voxel is numbered according to which cluster it belongs to If do statistics is true the log file will list the number of clusters in the phase under investigation and in what size range they are Note that the same data set when run with a different number of processors will result in different labelling of the clusters 7 2 8 Isolated Clusters IN segmented data OUT segmented data The Isolated Clusters function allows for the analysis and removal of iso lated clusters of the void solid or both phases If do statistics is set to true the log file will list the number of clusters in both phases and in what size range they
16. ect to the boundary It is the radius of the region that is searched when deciding if a potential pinning point is a local maximum A pinning point is a point that connects the medial axis to the boundary and it must be a local maximum in the distance map The parameter is only effective if connect boundary is true 9 1 Analysis 9 1 1 Euclidean Voronoi 9 1 2 Compare Distance Map Data Files IN distance map data 2 data sets OUT difference information This function takes two data sets of the same domain Set the file name base of the second file in the file name base window All corresponding voxels that have a different distance data in the two input files and their values are listed in the log_P0 file 9 1 3 Intensity Cut Plane 2D Picture generation IN distance map data OUT jpeg file A gray level jpeg picture of a plane x y or z of Distance Map Data can be generated by this function Set the desired position of the cut plane in the position window Gray levels are well spread if auto scale is set to true If auto_scale is false the manual minimum value and manual maximal value are used to determine the gray levels The jpeg file is written to the working directory 9 1 4 Grid of Images IN distance map data OUT jpeg files This function does the same as Intensity Cut Plane 2D Picture generation but allows multiple planes to be produced in one run The input windows for dire
17. ed data OUT subsetted segmented data Strided or unstrided subsets of segmented data can be prepared by entering the appropriate offsets and sizes Note that a strided subset does not neces sarily accurately represent the original due to downscaling A new file with the letters SS appended to the suffix is written to the data directory 7 2 3 Format Conversion IN segmented data OUT segmented data in set format This function performs the conversion of segmented data to netcdf ascii and binary bit pack unsigned char format with the respective file suffixes of nc ai not yet and seg 7 2 4 Add Flowtube IN segmented data OUT segmented data with flow tube This function adds a halo around a segmented dataset by extending the bor der in the x and y direction by one voxel and setting these areas to solid 1 These areas are also extended in the z direction ie the top and bottom ends by an amount scaled on the original z size This is a preparatory step of the segmented data in order to create medial axis and networks aimed at studying flow in the z axis The letters FT are added to the suffix of the output file which will be created if write data is true 29 7 2 5 Add Boundary Layer IN segmented data OUT segmented data with extra added layer 7 2 6 Spanning Clusters IN segmented data OUT cluster information in log file A spanning cluster is defined as an object of one phas
18. etc can and should be used to confirm the segmentation How to judge a segmentation Looking at a number of Intensity Cut Planes of tomographic and segmented data is a good first step to check the segmentation It should be kept in mind that the human visual system is not able to distinguish between various gray levels all that well Next a visualisation tool eg mayavi which can display tomographic data as contour lines and seg mented data as isosurfaces simultaneously should be used to verify the results Isosurfaces should lie along dense contour lines Visualising the data in 3D is important as this is the true nature of the data Seg Quality study in progress 6 6 2 Simple Segmentation IN tomographic data optional fiducial OUT segmented data pros fast and simple given perfect data this is the method of choice cons does not deal well with noise Simple threshold segmentation requires lower threshold and upper thresh old parameters Every voxel with a value below and equal to the lower threshold and everything equal and above the upper threshold is set to 0 Void and the rest is set to 1 Grain Note therefore that unless a certain phase is to be segmented out of the data ie an intermediate phase is the phase of interest the upper threshold should be 65536 the highest input value possible A careful choice of the lower threshold is crucial for a good simple segmentation Filtering of
19. ferent labels depending on the processor layout number of cpus and x y z layout This function sorts the label numbers of the various clusters thus allowing for a better compar ison between labelled datasets 8 7 Cluster Size Distribution IN label data OUT statistics of clusters 8 8 Smooth Label Data IN label data OUT smoothed label data Performs a euclidean voronoi tessellation on the label data followed by ma jority filtering 8 9 Triple Label Contact IN label data OUT cluster contact statistics and label data containing interface surfaces Examines the contact areas of differently labelled clusters at the voxel level The three neighbours of a voxel are counted in the x y and z planes 33 8 10 Network from Labels IN label data OUT pore throat network 9 Distance Map Data 9 0 1 Subset 9 0 2 Format Conversion 9 0 3 Medial Axis IN distance map data optional fiducial OUT medial axis data describe data format Top Section phase to check must correspond with distance data The Medial Axis function requires Euclidean Distance data as input The axis is created through homotopic thinning of the distance map data where strict voxel ordering is provided by the distance map and the bit reversed value of the voxel s global coordinates If do statistics is true the coordi nation number distribution and their spatial distributions are written to the log PO file If write data
20. gle should be left to false work in progress The four vertical lines indicate the intensity thresholding also compare to the previous intensity histogram The solid horizontal line indicates the gradient threshold Notice the arches at about the hight of the dashed lines connecting the three main bulk voxel populations These arches rep resent high gradient voxels In general appropriate gradient thresholds can be found in the area just above the main bulk voxels 25 Figure 3 Three phase intensity histogram with thresholding values To find the gradient threshold number load the plot into an application which shows pixel row and column numbers eg Gimp Let x be the y coordinate representing the right hight for the gradient threshold Then given that the top left pixel is 0 0 gradient threshold 2048 x 32 The 65536 x axis intensity x 65536 y axis max gradient pixel picture is scaled by a factor of 32 Note that the rectangles bordered by the solid horizontal line and the bottom of the Figure from left to right correspond to pore pore or intermediate to be determined intermediate intermediate or solid to be determined and solid Everything above that line is edge data which will be determined as the three regions grow The dashed lines indicate the effect of setting the optional 2nd gradient threshold This parameter has to be above the gradient threshold and is u
21. gmentation using the Marching Cubes algo rithm 21 7 1 5 Minkowski Analysis IN segmented data OUT Minkowski functionals Calculate the Minkowski functionals of the segmented data 7 1 6 Resultant Distribution IN segmented data and corresponding tomographic data OUT histogram data Resultant Distribution produces output in the log_PO file of two sets of numbers which can be plotted to show the distribution of original tomo graphic values and their corresponding segmented values It is useful for segmentations other than simple segmentation as the resulting distribution is trivial in the simple case The histogram bin size can be set as desired 7 1 7 Compare Seg Data Files IN segmented data 2 data sets of the same domain OUT difference information Compare Seg Data Files is a tool to compare two different segmentations It takes two segmented input files which have to have the same domains and lists in the log_PO file all voxels and their coordinates which differ between the two segmentations The second input file name base can be entered in the file name base parameter output spread between log files how about a difference seg file 7 1 8 Cluster Tracking not working 7 1 9 Analyse Crevice Pore Space not working 28 7 2 Processing 7 2 1 Compare Seg Data Files IN 2 segmented data sets of the same domain OUT differences between input datasets 7 2 2 Subset IN segment
22. hreshold values and one gradient threshold value These parameters divide the input data initially into six groups pore pore or intermediate to be determined intermediate intermediate or solid to be determined solid and edge data high gradient to be determined Pore intermediate and solid regions then grow until all voxels have been determined It may be helpful to carry out a simple segmentation first to determine reasonable threshold intervals 24 0 05 i T T T T 0 04 i j 0 03 i i 0 02 i i af AM i fi f l 4000 5000 6000 7000 8000 9000 10000 11000 Figure 2 Three phase intensity histogram with thresholding values Figure x shows a fairly well separated three phase intensity histogram The two solid vertical lines indicate good simple thresholding values and the dashed lines indicate appropriate intervals for 3 phase CAC segmentation To determine the gradient threshold an Intensity Gradient Plot see sec tion x above can be used The Intensity Gradient Plot is a scatter plot in which each voxel contributes a point where its intensity provides the x value and its gradient the y value Figure x shows an Intensity Gradient Plot black and white have been inverted which has the thresholding parameters indicated as lines on it Segmentation 3 Phase currently only uses gradient information for calculating growth speed The use_intensity tog
23. ic data OUT tomographic data in format selected OOC do format conversion running on one processor only without reading the complete dataset into memory 6 5 7 Diff Tom Data Files 6 5 8 Edge Detection IN tomographic data OUT distance map data ED 20 6 6 Segmentation Segmentation output files have the word segmented followed by the suffix of the input file as file name and the files are written to the data directory 6 6 1 The Problem There is no known general theory of segmentation Put simply segmentation can be defined as the process of changing a multi phase object into one of low phase and high phase 0 and 1 Today there are a multitude of different segmenta tion methods which seek to eliminate the shortcomings of a simple thresholding approach ie x lt threshold x 0 x gt threshold x 1 So what are the difficulties in this seemingly trivial process What is a good segmentation and what is a bad one What is the best segmentation method for a given data set and purpose The issues here are the original data that serves as input and the desired output and what is to be done with it The quick cliched answers are The devil is in the details and different horses for different courses Noise Data collected from x ray computerised tomography suffers from a num ber of sources of noise These include beam hardening ring artifacts cosmic rays and artifacts caused by 3D reconstruction methods and data c
24. is true a file prepended with medial_axis to the suffix is written to the data directory There are a number of ways in which the medial axis can be created at the boundary volumes In particular the parameters connect boundary remove flow tube and distance averaging radius affect medial axis construction at the boundary How those param eters are chosen depends on the purpose of the medial axis construction If fluid flow studies are to be carried out along the z axis of the object a flow tube should be added prior to making the distance map data If connect boundary is false medial axis along the inside boundary may be created but they will never connect or extend point through the boundary This option should only be used by the informed user The distance increment parameter affects the ordering and the speed with which the medial axis is created The smaller the number the more strict the ordering and the longer it will take and vice versa If prune dead ends is true all dead ends of the medial axis are removed This results in a less cluttered medial axis Currently a medial surface can not be made The min axis cluster size parameter sets the size below which medial axis clusters are removed The remove flow tube toggle should only be set to true if the input file contains a flow tube and the output file should be without it 34 The distance averaging radius affects how axis conn
25. ius the correction is to be carried out Data past this radius is set to Fiducial outside right If the correction is not to start immediately from the center set the correction start radius accordingly The tomographic output files from Beam Hardening Correc tion have the letters BHC added to the file name suffix of the input file 6 5 3 Subsetting IN tomographic data OUT subsetted tomographic data Cutting down of the original dataset to one which contains only the regions of interest has several advantages A smaller dataset is processed faster and 19 outside regions do not clutter the intensity histogram Small subsets can also be used to determine what filtering and segmentation parameters are best for a given dataset Downscaling of a subset can be achieved by entering stride numbers greater than 1 which as a consequence reduces resolution A new file with the letters SS appended to the suffix is written to the data directory 6 5 4 Subset OOC Out of core IN tomographic data OUT subsetted tomographic data OOC Out of Core Create a subset running on one processor only without reading the complete dataset into memory 6 5 5 Format Conversion IN tomographic data OUT tomographic data in format selected This function can convert tomographic input into netcdf nc binary un signed short bs binary unsigned character ubc and ascii ai 6 5 6 Format Conversion OOC IN tomograph
26. ks dina dede paa dao 12 1 3 Connection Matrix 13 MPE Timings 14 Algorithms and Optimisations 15 From Tomogram to Network A short Tutorial 16 Conclusion 17 Appendix iste SOM plans ta us a 40 40 40 40 40 41 41 41 41 41 1 Introduction Mango is a software tool for parallel Segmentation and Network Generation and the pre and post processing and analysis of associated data The ini tial input for Mango is Tomographic Data of porous or multi phase objects Mango has been build to process tomographic data from x ray computerised tomography but any voxelated data can be used as input Processing of the Tomographic Data leads to Segmented Distance Map Fiducial Medial Axis and Network Data This User Guide adheres strongly to the logical processing layout found in the Mango GUI General User Interface Quota tion marks are used to indicate parameters and sections which correspond to methods functions of the software Other descriptors for low phase include void pore and 0 and for high phase solid grain and 1 are used interchange ably 1 1 The Software The Mango Software is implemented in C and is controlled by a GUI written in Python Mango can be compiled on Unix and Linux systems Most importantly it can be run in parallel allowing for the processing of up to 2048 cube voxel data sets Parallel processing is implemented using the MPI Message Passing Interface see http www u
27. l Datos pets sita ra ido op oe Se 8 9 Triple Label Contact ico ense es 8 10 Network from Labels 9 Distance Map Data TOD Subset sad a E RAG EE oS 9 0 2 Format Conversion lt 4 a b A ake els BRS 9 0 3 Medial Axis ack os Se ee eS OS RIO OS 9T Analysis o ah dogs hod a yi Sie i oe ee ck a eae ae we a Rea Re A 9 1 1 Euclidean Voronoi uses ae 4 8 eS 9 1 2 Compare Distance Map Data Files 9 1 3 Intensity Cut Plane 2D Picture generation 9 1 4 Grid of Images is dare AA 9 2 Processing o poegi ae hot mod a a aoe HK Ea EGE a oS 9 2 1 Distance Map Watershed 9 2 2 Maximal Covering Spheres o aoaaa 9 2 3 Maximal Spheres o o ate oo Ga we Fo 10 Fiducial Data TOL Shrink Fid ci l re dae A AREA 11 Medial Axis Data TIL AMAS A O O A as 11 1 1 Compare Medial Axis Data Files 11 1 2 Measure Medial Axis Quality 11 1 3 Intensity Cut Plane 2D Picture generation TLIA Grd of Images a Lr ere Shy Mel ee chen GP Erie eke a E 11 1 5 Medial Axis Percolation bo acy te be hikes ee ana 11 1 6 Medial Axis Neighbour Anisotropy Measurement I2 UE TOR CS SING ani es Maa Sete act E dah Se rs OA Ge aed 11 2 1 Format Conversion a a Ane wtp ere SU eos 11 22 SUBSE oa ald a Se Bo GY a Se Oe Aud SS ZR Oe 11 2 3 Network Construction y Aula ake e 12 Pore Throat Network Data AN O 12 1 1 Convert File Format 12 1 2 Compare Networ
28. mentation 24 7 Segmented Data 27 TE Analysis a a a Oe ee RP eS aa S EA 27 7 1 1 Intensity Cut Plane 2D Picture generation De 7 1 2 Grid of Images lacio Ga ete tee oi bone Bok BSS 27 7 1 3 Calculate Porosity adidas Apu a 27 Rd MCO Jsos urfa c ja ts se a o ate oe 27 7 1 5 Minkowski Analysis oaa 28 7 1 6 Resultant Distribution ara a 28 7 1 7 Compare Seg Data Files ye ech eA eR 28 7 1 8 Cluster Tracking ira a a a 28 7 1 9 Analyse Crevice Pore Space 28 4 2 PYOCCSSING od a OY een ge Soh eB a aad T 29 7 2 1 Compare Seg Data Files 29 zozobra en PS A ohn sio 29 7 2 3 Format Conversion ra Se eck SEES 29 7 2 4 Add dobla 29 7 2 5 Add Boundary Layer cra ee ee ges da 7 2 6 Spanning Clusters or cought Goce eed oo gad os ey 7 2 7 Label Clusters gt ac coe dae el exe oe o alee oe oe Bee 7 2 8 Isolated Clusters Yegros Ha Dela ta a en de aed Erosion Dali sl e SA ee GATA E evs aoe 7 2 11 Write Crevice Pore Space erp Ge ete ie et ene od 7 2 12 Euclidean Distance 2 4 prisa Sw ae eS eee as 8 Label Data 8 1 Compare Label Data Files 5 44 44 4 ase Bx Gate BAS als Sa UES Uy es sway Rew eas gs AB Ber ued aw The se cal Gi ee od Pea ens T 8 3 Format Conversion erro erica ee aly Beko baw ee 8 4 Intensity Cut Plane told ate oe hE ae rs Geo Gid Ok MAESTRA eked kw ae 8 6 Sort Cluster Lables 2 Sii its es o o es 8 7 Cluster Size Distribution o 8 8 Smooth Labe
29. mographic data OUT filtered tomographic data The Median filter replaces the value of each voxel with the median of the surrounding voxels where filter range determines the surrounding spherical volume The parameters filter sigma and max delta do not apply 6 4 3 Conservative Median IN tomographic data OUT filtered tomographic data The Conservative Median filter replaces the value of each voxel with the median of the surrounding voxels where filter range determines the sur rounding spherical volume if its value is outside the minimum and maximum values of the surrounding The parameters filter sigma and max delta do not apply 6 4 4 Conservative Smoothing IN tomographic data OUT filtered tomographic data The Conservative Smoothing filter replaces the value of each voxel with the maximum minimum of the surrounding voxels if it is larger smaller than the maximum minimum where filter range determines the surrounding spherical volume The parameters filter sigma and max delta do not apply 6 4 5 Gaussian IN tomographic data OUT filtered tomographic data gaussianPassFilter h says it is not working but gaussian does something ie different histogram distance map data optional fiducial uses filter sigma as well aps or rms to complete 16 6 4 6 Selective Gaussian IN tomographic data OUT filtered tomographic data does uses filter sigma and m
30. nalysed by the Euclidean Distance and Medial Axis functions In addition the checked phase is 26 connected while the background phase is 6 connected in Isolated Cluster analysis 10 phase to check affects CrevicePoreSpace ErosionDilation EuclideanDistance IsolatedClusters LabelClusters MajorityFilter MeasureMedAxQuality MedialAxis MinkowskiAnalysis SpanningClusters use_ fiducial and read_ fiducial_from_file In Mango a fiducial means a surface which completely encloses a volume If processing is to occur only in the volume enclosed by a fiducial then the appropriate toggles must be set in the Top Section There are two types of fiducial data If a dataset is processed with Beam Hardening Correction data outside the specified radius is set to a flag value indicating outside fidu cial The second type of fiducial data is a file which is in fact segmented data which serves as a mask for a corresponding dataset Fiducial files can be generated geometrically Generate Geometric Fiducial in the tomographic menu or a form fitting fiducial can be generated from Fiducial in the seg mented data menu Therefore if a file has been processed with Beam Hard ening Correction use_fiducial should be set to true If a file fiducial is to be used both use_fiducial and read_fiducial_from_file must be set to true data_ directory Press the Browse button to open a choos
31. ncreasing radii If do statistics is true the log files will contain cluster statistics and the number of voxels that changed If write data is true and a fiducial is created successfully one object cluster and one background cluster remain after dilation erosion steps a file beginning with fiducial and the input file suffix is written to the data directory do we really need break on failure Usually the max concavity radius should be set to a greater number than max convexity radius The action of the max concavity radius can be imagined as rolling a sphere around the outside of the object and converting to l any voxel that the sphere cannot reach The max convexity radius is equivalent to rolling a sphere around the inside of the object and converting to 0 any voxel that the sphere cannot reach If the object is close to the dataset borders halo size should be set to a number larger than the largest radius to avoid incorrect processing at the border The radius increment 31 factor determines by how much the radii are are increased after each unsuc cessful step The fiducial should be checked to see if it has the desired shape 7 2 11 Write Crevice Pore Space IN segmented data not working 7 2 12 Euclidean Distance IN segmented data optional fiducial OUT distance map A Euclidean Distance data file is needed as input for the creation of medial axis data
32. nix mcs anl gov mpi and http www lam mpi org Standard Furthermore use of the NetCDF library is made to deal with large data sets and a FFT library is used also see http www fftw org Boost and jpeg libraries are also used Compi lation therefore requires an appropriate environment Currently the Mango core source code amounts to more than 100 000 lines of code Developers and Contributers Dr Adrian Sheppard Dr Rob Sok Holger Averdunk Boris Breidenbach Dr Gerd Schroeder 1 2 Data Formats Tomographic data must be in integer values ranging from 0 to 65536 where higher values indicate higher density and vice versa Segmented data consists of 0 s and 1 s Distance Map data floating point numbers Medial axis data floating point numbers for distance and row index for voxel location Network data Input Data formats are described in the following sections Metadata Non ascii data files contain metadata which contains informa tion about the dataset size the original data collection and reconstruction and the history of processing that has been carried out on the data set eg filtering subsetting etc NetCDF files can be converted to ascii with the ncdump command Ascii files can be converted to netCDF files with ncgen 1 3 Log Files For each processor that is used during a run a log file with the number of the corresponding processor appended to log_P is written to the working direct
33. ollection instruments themselves Furthermore resolution and contrast are hardly ever ideal Specific algorithms and methods are able to ameliorate these artifacts eg Beam Hardening Correction Probably the most important step after data collection and prior to segmentation is filtering A combination of Anisotropic Diffusion and Unsharp Mask usually leads to good results Visual inspection and validation of original and filtered data possibly followed by improving fil tering by trying different parameters is necessary Post segmentation isolated cluster removal see section Isolated Clusters can be used in some cases to remove objects judged spurious or unwanted Resolution the half voxel problem Border areas between the low and high phase will have voxels with intermediate values These voxels may not be correctly assigned to one phase or another In essence this is a resolution prob lem if the resolution were to be increased in these border areas phases could be assigned more accurately 21 Post Segmentation Analysis Segmentation should be objective yet what is to be done with the segmented data should be kept in mind during the seg mentation A small change in the segmentation threshold can lead to enormous effects and differences in post segmentation analysis eg surface area con nectedness of fine structures etc Any prior knowledge of the actual object composition density void volume structure
34. ory Processor O is the master processor and the log_PO file contains collated information from all processors The verbosity_level set in the GUI top section affects how much information is written to those log files 2 The GUI The GUI is divided into two main areas The function selection area is on the left starting with Top Section To the right the control parameters of the selected function are displayed Subsection menus can be minimised and maximised by double clicking the left mouse button Options are selected by right clicking once and then the selected option is displayed in red To en sure the corresponding parameter window is displayed and highlighted on the right single click the option again with the left mouse button The required parameters can then be entered and toggles can be switched As the GUI just acts as a way to write an input file for Mango named parms in each time parameters have changed and a new processing run is to be started ensure that the Save button has been pressed The bottom message win dow should then display Saved parms in The Run button can currently be ignored The File field at the top above the Save button has three menus The Save menu has the same effect as pressing the Save button Change Working Directory opens a dialog box to change the working di rectory Exit terminates the GUI The help buttons may provide helpful info
35. ove upper threshold are set to high phase The set phases represent seed regions which grow into the undecided phase until all voxels are assigned 0 or 1 The speed with which these regions grow is calculated form gradient and intensity information of the immediate voxel neighbour hood Where the growing regions meet usually represents the void solid boundaries of the object 6 6 7 3 Phase Converging Active Contours Segmentation IN tomographic data optional fiducial data file OUT segmented data low and intermediate phase or low intermediate and high phase Extracting an intermediate phase from a dataset by simple segmentation with two thresholds can be problematic If high phase voxels directly border low phase areas simple thresholding is likely to assign some of these border voxels to the intermediate phase half voxel problem This can result in segmentations which include unwanted high low phase border voxels in the intermediate phase The 3 Phase Converging Active Contours Segmentation method can achieve a much better result by firstly identifying voxels with high gradient values Then regions of pore intermediate and solid phase grow depending on the gradient the same method as for Converging Active Contours High low border voxels are more likely to be assigned either as low or high phase as one of these phases grows into the border area and not assigned falsely as intermediate The method requires four intensity t
36. ram of increasing radii from a center to the outside Should this histogram indicate unexpected density increases from the inside to the outside the input xct data may suffer from Beam Hardening Artifacts If this is the case Beam Hardening Correction may minimise these artifacts 6 3 7 Threshold Quality IN tomographic data OUT data in log_PO file Study in progress 6 3 8 Compare Tom Data IN tomographic data 2 data files of the same domain OUT data in log_PO file Compare Tom Data takes 2 tomographic data files which have to be of the same domain as input and reports all voxels that differ This function can be used for example to compare pre and post filtered data 6 4 Preprocessing Filters and Convolvers With the exception of Sobel all filters use the parameter filter range which defines the surrounding spherical volume of a center voxel For example for range 1 6 neighbours range 1 5 18 neighbours range 1 8 26 neighbours range 2 32 neighbours The tomographic output files from Arithmetic Filters have the letters AF added to the file name suffix of the input files 6 4 1 Mean IN tomographic data OUT filtered tomographic data The Mean filter replaces the value of each voxel with the mean of the sur rounding voxels where filter range determines the surrounding spherical 15 volume The parameters filter sigma and max delta do not apply 6 4 2 Median IN to
37. reation the connect boundary switch obviously also has a 38 strong bearing on percolation 11 1 6 Medial Axis Neighbour Anisotropy Measurement IN medial axis data OUT 26 neighbour percentage written to log_PO file This analysis tool adds any of the 26 neighbours of each voxel in the medial axis and then normalises the values such that the maximum value is 100 An indication of axis direction and an example output follows Up East z 1 y 1 Il I North x 1 ii x 1 South y 1 z 1 West Down 46 19 2 43 82 44 32 9T 32 2 3 98 oN 93 01 55 68 47 78 42 41 335052 a 24 84 37 4 100 E 100 of dee 2 24 84 5 33 8 A241 24 47 78 55 68 I 93 201 88 9 7 5 97 32 44 32 43 82 46 79 Here the major direction of the medial axis is north south 100 That means on average more voxels have neighbours north and south than in the other directions Therefore this represents a very simple and basic measure of anisotropy of the medial axis 11 2 Processing 11 2 1 Format Conversion IN medial axis data in netCDF format OUT medial axis data in ascii format With this function medial axis data in netCDF format can be converted to ascii where each line has the x y and z coordinates of a voxel written in brackets followed by the distance value associa
38. rmation vi File Save Run Halt Top Section Input_Data_File Output_Data_File MPI Tomographic_Data Input_Data_File Generate_Geometric_Fiducial Intensity_Histogram Intensity_Cut_Line Intensity_Cut_Plane Intensity GradientPiot Grid_Of_Images Cylindrical_Intensity_Profile Threshold_Quality Compare_Tom_Data_Files Arithmetic_Filter Anisotropic_Diffusion Unsharp_Mask Rescale_Data Subset Format_Conversion Beam_Hardening_Correction Diff_Tom_Data_Files Edge_Detection Metropolis_Segmentation Level_Set_Segmentation Segmentation_3_Phase WatershedSegmentation Segmentation Segmented_Data Input_Data_File Intensity Cut_Plane Grid_Of_Images CAlneintn Maun nites Ido_statistics method make_maximal_voxel_file write data A true w fast marching origin w false w true false help help y true false help help Saved Saved Saved paved parms in parms in parms in parms in Figure 1 The Graphical User Interface 3 Data Flow Chart Converting tomographic data into a realistic network requires many steps Unfortunately complete automation of this process yielding a good end result cannot be achieved Furthermore although some functions can be chained ie the output of one function directly serves as input to another results have to be examined and further runs with
39. sed as a refinement Voxels with high gradient but low or high intensities can be directly assigned to pore or grain solid Since this affects the seeding of the growing regions segmentation results differ if this parameter is set 26 7 Segmented Data 7 1 Analysis 7 1 1 Intensity Cut Plane 2D Picture generation IN segmented data OUT jpeg file in working directory Here a two dimensional slice along one of three axis of the dataset is con verted into a black and white jpeg file which is written to the working di rectory Choose the desired axis using the toggle switches and enter a valid position in the dataset 7 1 2 Grid of Images IN segmented data OUT jpeg files in working directory If one is interested in more than one plane Grid of Images can be used Planes can be created on the x y z or all three axes direction toggle Enter the desired number of planes and unless auto choose planes is true enter a valid middle plane and plane spacing The files are written to the working directory 7 1 3 Calculate Porosity IN segmented data OUT Porosity data in log PO file This function calculates the number of void 0 and grain 1 voxels and their percentages Note that unless an appropriate Fiducial or subset is used regions outside the object proper will contribute to the fractions 7 1 4 MC Isosurface IN segmented data OUT isosurface Create an isosurface from a se
40. signed character format have ubc as suffix 5 1 7 binary short 5 1 8 binary ushort Files in unsigned short format have bs as suffix 6 Tomographic Data 6 1 Input Data File This menu allows setting the expected format of the input file and the base name of the file filemame_base The expected file name is the concatena 12 tion of filemame_base file name _suffix format type suffix eg nc for netCDF 6 2 Generate Geometric Fiducial IN tomographic data OUT a fiducial file of type segmented data This function generates a fiducial file which encloses some volume of the tomographic dataset The fiducial is either a cylinder running along any of the three axis with any radius that fits within the dataset also taking account of the mid point chosen or a rectangle where offset and size can be set 6 3 Analysis 6 3 1 Intensity Histogram IN tomographic data OUT intensity histogram data written to log_PO The Intensity Histogram of a tomographic data set is the crucial preanalysis tool for segmentation In order to benefit most from this tool it is helpful to only analyse the volumes of interest this can be achieved through ap propriate subsetting or the use of a fiducial Given a normal value range a default bin size of 32 results in a smooth histogram but other bin sizes can be chosen If per_ process is true each processor writes the intensity histogram of its
41. sphere data float The function finds the largest inscribed euclidean distance sphere that cov ers each voxel in the object This gives an indication of the wetting and non wetting phases capillary pressure hydraulic radius If do statistics is set to true a distance distribution of the radii is written to the log_PO file The fast method is more efficient as it avoids unnecessary calculations yet gives the same results as brute_force and should therefore be used prefer ably The output file has max_included_sphere prepended to the original suffix 9 2 3 Maximal Spheres IN distance map data optional fiducial OUT medial axis data Given the euclidean distance transform of an object this function extracts 36 the voxels whose euclidean distance spheres are not contained within those of their neighbours The output file has medial_axis prepended to its suffix The number of maximal spheres is reported in the log file do statistics currently has no effect 10 Fiducial Data 10 1 Shrink Fiducial IN fiducial segmented data OUT fiducial segmented data Shrink Fiducial allows for the volume reduction of a fiducial shrink wrap The shrink_by parameter determines the amount by which the original fidu cial gets eroded If write_data is true a file with fiducialSH prepended to the suffix will be written to the data directory The number of voxels changed are reported in the log
42. ssian 2 subtract the blurred image from the original which results in the mask 18 3 add the mask to the original controlled by the strength parameter This filter requires three parameters and the defaults of radius 2 5 cut off 8 0 and strength 2 0 are usually suitable Too much sharpening can cause a halo effect where darker objects are surrounded by spuriously bright border regions The tomographic output files from Unsharp Mask have the letters UM added to the file name suffix of the input files 6 5 Preprocessing Data 6 5 1 Rescale Data IN tomographic data OUT rescaled tomographic data Tomographic data can be compressed towards its mean if scale_factor is less than 1 and can be expanded if scale_factor is greater than 1 The centrum can also be set Expanded data may lead to a better segmentation If the data is very compressed and a small change in the segmentation threshold leads to large changes in porosity expanding the data may prove helpful 6 5 2 Beam Hardening Correction BHC IN tomographic data OUT corrected tomographic data BHC applies a gaussian smoothing kernel on specified regions of the data A Cylindrical Intensity Profile see section above should be plotted to deter mine if BHC is required If so a Radial Beam Hardening Correction can be carried out on the appropriate axis and mid point Enter a maximum radius to determine how far along the rad
43. ted with that voxel The out put file has the extension ai 11 2 2 Subset 11 2 3 Network Construction IN medial axis data OUT pore throat network Generate a pore throat network from medial axis data 12 Pore Throat Network Data 12 1 Processing 12 1 1 Convert File Format 12 1 2 Compare Networks 12 1 3 Connection Matrix IN pore throat network OUT network statistics 40 13 MPE Timings Each log file ends with a MPE log entry This applies only to Mango versions compiled with MPI The master log log_P0 also has combined totals ie summary of all processors Total time taken maximum and average time taken and number of visits are shown These statistics can not be controlled by the user but are useful for finding an optimal number of processors for a particular job For example parallel processing overhead differences be tween two jobs on the same data with different numbers of processors can be calculated with these statistics 14 Algorithms and Optimisations Anisotropic Diffusion Unsharp Mask segmentation methods watershed meth ods medial axis construction homotopic thinning time warp medial axis watershed erosion dilation voronoi tessalation fast marching algorithms burn algorithms marching cubes etc 15 From Tomogram to Network A short Tu torial 16 Conclusion 17 Appendix 17 1 Compilation Libraries needed Compiler directives fast mpi non mpi Al
44. that has the smallest variance The parameter filter_range defines the size of the region used to determine the new value of a voxel No other parameters are taken The performance of the filter for filter range greater than 3 degrades quickly and is not advised In most cases Anisotropic Dif fusion will yield much better results than Kuwahara For 3D the region is divided into 8 blocks 6 4 10 Anisotropic Diffusion IN tomographic data OUT filtered tomographic data Anisotropic Diffusion is an iterative edge enhancing and smoothing filter It is an implementation taken mostly from Frangakis and Hegerl Noise reduc tion in electron tomography J Struct Bio 135 239 250 2001 In practice it has been found to perform very well especially if followed by Unsharp Mask Its only drawback is that it is computationally expensive Usually 20 iterations are sufficient but for noisy data sets 40 iterations can lead to better improvements Set the parameter number_of iterations accordingly time_step contrast The tomographic output files from Anisotropic Diffusion have the letters AD added to the file name suffix of the input files 6 4 11 Unsharp Mask IN tomographic data OUT filtered tomographic data Although there seems to be no theoretical foundation for the Unsharp Mask its results are visually very impressive The filter works in three steps 1 Blur the image with a certain radius Gau
45. the original data is advised Shortcomings of Simple segmentation and how to improve the segmentation 6 6 3 Level Set Segmentation IN tomographic data optional fiducial data file OUT segmented data 22 method may be discarded Level Set segmentation is an implementation of the level set formulation for image processing from Sethian Level Set Methods and Fast Marching Methods p68ff and p219ff It is an iterative method 6 6 4 Metropolis Segmentation IN tomographic data optional fiducial data file OUT segmented data not working yet 6 6 5 Watershed Segmentation IN tomographic data optional fiducial data file OUT segmented data Watershed segmentation is a region growing algorithm which developed from mathematical morphology There are a number of ways to implement the ba sic principle some of which lay claim to work efficiently in parallel One way to imagine the region growing in 2 dimensions is as follows Water starts rising from the lowest level ie the lowest value of the dataset Whenever a new level next higher value is reached a new region starts growing unless this level has a neighbour from a previously labelled flooded region This process continues until all levels have been filled The borders of the regions represent the watershed lines hence the name The various regions are then evaluated in some way average value for example and some are merged according to a criteria
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