├── README.md ├── example2D.m ├── example3D.m ├── license.txt └── src ├── createMonogenicFilters.m ├── createMonogenicFilters3D.m ├── featureSymmetry.m ├── featureSymmetry3D.m ├── freqgrid2.m ├── freqgrid3.m ├── localEnergy.m ├── localEnergy3D.m ├── localOrientation.m ├── localPhase.m ├── localPhase3D.m ├── monogenicSignal.m ├── monogenicSignal3D.m ├── orientedSymmetry.m ├── orientedSymmetry3D.m ├── phaseCongruency.m └── phaseCongruency3D.m /README.md: -------------------------------------------------------------------------------- 1 | # Monogenic Signal MATLAB (and GNU Octave) Implementation 2 | 3 | This repository contains MATLAB code to calculate the monogenic signal (Felsberg and Sommer) for 2D and 3D images, as well as many quantities that can be derived from the monogenic signal such as Feature Symmetry and Asymmetry, and Phase Congruency. 4 | 5 | The monogenic signal is an alternative way of representing an image, which has a number of advantages for further processing. For an introduction to the monogenic signal and derived features with references to the relevant scientific literature, please see [this document](https://arxiv.org/abs/1703.09199). 6 | 7 | ### Capabilities 8 | 9 | Functions are provided to calculate the following quantities for 2D and 3D images: 10 | 11 | * Monogenic Signal 12 | * Local Energy, Local Phase and Local Orientation to describe the local properties of image. 13 | * Feature Symmetry and Asymmetry, respond to symmetric 'blobs' and boundaries with robustness to variable contrast. 14 | * Oriented Feature Symmetry and Asymmetry, as above but also containing the polarity of the symmetry and the orientation of the boundaries. 15 | * Phase Congruency, responds to edges in the image. 16 | 17 | ### Instructions For Use 18 | 19 | Read through and run the heavily-commented example files (example2D.m and example3D.m) in order to learn how to use the functions (you will need to change the image files used in the examples if you are using Octave). Each function also has a relatively complete description that can be read in the accessed via the help interface. 20 | 21 | ### Compatibility and Dependencies 22 | MATLAB or GNU Octave (all versions on all operating systems should work as far as I am aware). 23 | 24 | ### Installation 25 | You should not need to do anything to install except ensure that the 'src' subdirectory (containing the source files) is added to your MATLAB/Octave path whenever you want to use the functions. 26 | 27 | ### Contributors 28 | This software was written by [Christopher Bridge](https://chrisbridge.science/) (University of Oxford) and was based on previous code by Ana Namburete and Vicente Grau. 29 | 30 | ### Licence 31 | This software is licensed under the GNU Public Licence (GPL). You are free to edit and distribute this code providing certain conditions are met. Read the full licence for further information. 32 | 33 | ### Publications 34 | 35 | This code has been used in the following publication: 36 | 37 | * C.P. Bridge and J.A. Noble, “[Object Localisation in Fetal Ultrasound Images Using Invariant Features](http://ieeexplore.ieee.org/document/7163839/)”. Proceedings of IEEE International Symposium on Biomedical Imaging, New York City, 2015 38 | -------------------------------------------------------------------------------- /example2D.m: -------------------------------------------------------------------------------- 1 | % This is an example script for using the monogenic signal code for 2D 2 | % images 3 | 4 | % Add monogenic_signal source directory to path 5 | addpath('src') 6 | 7 | % Load a matlab test image 8 | % If running under octave, you will need to change this to an image file of 9 | % your choice. 10 | % Note that the monogenic signal is intended to on greyscale images (using it on 11 | % a colour image will result in the three channels being processed independently). 12 | I = imread('coins.png'); 13 | [Y,X] = size(I); 14 | 15 | % First we have to choose a set of centre-wavelengths for our filters, 16 | % typically you will want to play around with this a lot. 17 | % Centre-wavelengths are expressed in pixel units. Here we use a set of 18 | % wavelenths with a constant scaling factor of 1.5 between them, starting 19 | % at 20 pixels 20 | cw = 20*1.5.^(0:4); 21 | 22 | % Now use these wavelengths to create a structure containing 23 | % frequency-domain filters to calculate the mnonogenic signal. We can 24 | % re-use this structure many times if we need for many images of the same 25 | % size and using the same wavelength. We can choose from a number of 26 | % different filter types, with log-Gabor ('lg') being the default. For lg 27 | % filters we can also choose the shape parameter (between 0 and 1), which 28 | % governs the bandwidth (0.41 gives a three-octave filter, 0.55 gives a two 29 | % octave filter) 30 | filtStruct = createMonogenicFilters(Y,X,cw,'lg',0.55); 31 | 32 | % Now we can use this structure to find the monogenic signal for the image 33 | [m1,m2,m3] = monogenicSignal(I,filtStruct); 34 | 35 | % The returned values are the three parts of the monogenic signal: m1 is 36 | % the even part, and m2 and m3 are the odd parts in the vertical and 37 | % horizontal directions respectively. Each array is Y x X x 1 x W, where 38 | % X and Y are the image dimensions and W is the number of wavelengths. 39 | % The filter responses to the filters of each scale are stacked along the 40 | % fourth dimension. 41 | 42 | % (Alternatively one may pass a 3D volume to monogenicSignal, in which case 43 | % the 2D monogenic signal is found for each of the Z 2D planes independently and 44 | % returned as a set of Y x X x Z x W arrays) 45 | 46 | % From here we can straightforwardly find many of the derived measures by 47 | % passing these three arrays 48 | 49 | % Local energy (calculated on a per-scale basis) 50 | LE = localEnergy(m1,m2,m3); 51 | 52 | % Local phase (calculated on a per-scale basis) 53 | LP = localPhase(m1,m2,m3); 54 | 55 | % Local orientation (calculated on a per-scale basis) 56 | % Only need to pass the odd parts (m2,m3) as even part (m1) is irrelevant 57 | LO = localOrientation(m2,m3); 58 | 59 | % Feature symmetry and asymmetry (see Kovesi "Symmetry and Asymmetry from 60 | % Local Phase") pick out 'blob-like' and 'boundary-like' structures 61 | % respectively. This combines all the scales to give a single 2D image. 62 | [FS,FA] = featureSymmetry(m1,m2,m3); 63 | 64 | % Oriented symmetry and asymmetry are like the above but contain more 65 | % information. Symmetric blobs are differentiated into peaks and troughs 66 | % by the sign of the signed feature symmetry (SFS) measure. Oriented 67 | % feature asymmetry (OFA) is a vector quantity (returned below as separate 68 | % components) that describes both the magnitude and orientation of the 69 | % boundary 70 | [OFA_y,OFA_x,SFS] = orientedSymmetry(m1,m2,m3); 71 | 72 | % Display 73 | figure() 74 | imshow(I), axis image, axis off, colormap gray 75 | title('Test Image') 76 | 77 | 78 | figure() 79 | imagesc(reshape(LE,Y,[])), axis image, axis off, colormap gray 80 | title('Local Energy Over Scales') 81 | 82 | figure() 83 | imagesc(reshape(LP,Y,[])), axis image, axis off, colormap gray 84 | title('Local Phase Over Scales') 85 | 86 | figure() 87 | imagesc(reshape(LO,Y,[])), axis image, axis off, colorbar 88 | title('Local Orientation Over Scales (radians)') 89 | 90 | figure() 91 | imagesc([FS,FA]), axis image, axis off, colormap gray 92 | title('Feature Symmetry and Asymmetry') 93 | 94 | figure() 95 | imagesc([FS,OFA_y,OFA_x]), axis image, axis off, colormap gray 96 | title('Signed Feature Symmetry and Oriented Feature Asymmetry') 97 | 98 | %% 99 | 100 | % If you want to visualise the filters to better understand what's going on, 101 | % we can do something like this: 102 | % First the frequency-domain representation (which is how the filter is stored 103 | % and used) for just the third filter in the stack bpFilt(:,:,1,3) 104 | figure() 105 | subplot(1,3,1) 106 | surf(real(fftshift(filtStruct.bpFilt(:,:,1,3))),'edgecolor','none') 107 | title('Even Part of The Frequency Domain Filter') 108 | subplot(1,3,2) 109 | surf(real(fftshift(filtStruct.bpFilt(:,:,1,3).*filtStruct.ReiszFilt)),'edgecolor','none') 110 | title('First Odd Part of The Frequency Domain Filter') 111 | subplot(1,3,3) 112 | surf(imag(fftshift(filtStruct.bpFilt(:,:,1,3).*filtStruct.ReiszFilt)),'edgecolor','none') 113 | title('Second Odd Part of The Frequency Domain Filter') 114 | 115 | % Now the image (spatial) domain filters, which can be found via ifft 116 | figure() 117 | subplot(1,3,1) 118 | surf(real(fftshift(ifft2(filtStruct.bpFilt(:,:,1,3)))),'edgecolor','none') 119 | title('Even Part of The Image Domain Filter') 120 | subplot(1,3,2) 121 | surf(real(fftshift(ifft2(filtStruct.bpFilt(:,:,1,3).*filtStruct.ReiszFilt))),'edgecolor','none') 122 | title('First Odd Part of The Image Domain Filter') 123 | subplot(1,3,3) 124 | surf(imag(fftshift(ifft2(filtStruct.bpFilt(:,:,1,3).*filtStruct.ReiszFilt))),'edgecolor','none') 125 | title('Second Odd Part of The Image Domain Filter') 126 | 127 | 128 | 129 | %% Now for phase congruency 130 | clear 131 | 132 | % Load a matlab test image and convert to greyscale 133 | I = rgb2gray(imread('board.tif')); 134 | [Y,X] = size(I); 135 | 136 | % This time we have to use exactly two scales, as this is required by 137 | % Felsberg's phase congruency method. As he suggests, let's use 138 | % three-ocatave filters and leave a three-octave spacing between them. 139 | % We want small filters to pick out the fine detail in this image. 140 | cw = [3,24]; 141 | 142 | % Construct new filters, as before 143 | filtStruct = createMonogenicFilters(Y,X,cw,'lg',0.41); 144 | 145 | % Find monogenic signal, as before 146 | [m1,m2,m3] = monogenicSignal(I,filtStruct); 147 | 148 | % Now use the phase congruency algorithm. The fourth parameter is a 149 | % threshold between 0 and 1 used for noise supression. You will always need 150 | % to use this to get reasonable results. Somewhere between 0 and 0.1 should 151 | % do in most cases. 152 | PC = phaseCongruency(m1,m2,m3,0.05); 153 | 154 | % Display 155 | figure() 156 | imshow(I), axis image, axis off, colormap gray 157 | title('Test Image') 158 | 159 | figure() 160 | imagesc(PC), axis image, axis off, colormap gray 161 | title('Phase Congruency') 162 | -------------------------------------------------------------------------------- /example3D.m: -------------------------------------------------------------------------------- 1 | % This is an example script for using the monogenic signal code for 3D 2 | % volume images. Most things are the same, with comparable function names 3 | % with '3D' added 4 | 5 | % Add monogenic_signal source directory to path 6 | addpath('src') 7 | 8 | % Load a matlab test volume image, the 'mri' dataset 9 | % If running under Octave, you will need to provide a different volume image 10 | % here 11 | load mri 12 | D = squeeze(D); % get rid of the third singleton dimension 13 | [Y,X,Z] = size(D); 14 | 15 | % First we have to choose a set of centre-wavelengths for our filters, 16 | % For the 3D case you can choose a different set of wavelengths for the Z 17 | % dimension from those used for the X-Y plane. This is because I was 18 | % working with data that were not sampled isotropically. Normally you 19 | % should stick to the same set of wavelengths (in fact the mri dataset is 20 | % not sampled isotropically but we'll pretend it is...) 21 | cw = 5*1.5.^(0:4); 22 | 23 | % Now use these wavelengths to create a structure containing 24 | % frequency-domain filters to calculate the monogenic signal. Same as for 25 | % the 2D case, except now we need to pass three image dimensions and the 26 | % two sets of wavelengths 27 | filtStruct = createMonogenicFilters3D(Y,X,Z,cw,cw,'lg',0.55); 28 | 29 | % Now we can use this structure to find the monogenic signal for the volume 30 | [m1,m2,m3,m4] = monogenicSignal3D(D,filtStruct); 31 | 32 | % Now we have four parts of the monogenic signal as there is another odd 33 | % part for the Z direction. Each is an Y x X x Z x W array where again W is 34 | % the number of scales/wavelengths used, i.e. the responses to each filter 35 | % are again stacked along the fourth dimension 36 | 37 | % From here we can straightforwardly find many of the derived measures by 38 | % passing these four arrays 39 | 40 | % Local energy (calculated on a per-scale basis) 41 | LE = localEnergy3D(m1,m2,m3,m4); 42 | 43 | % Local phase (calculated on a per-scale basis) 44 | LP = localPhase3D(m1,m2,m3,m4); 45 | 46 | % Note that we do not provide a local orientation function for 3D. This is 47 | % because there are various conventions for describing orientation in 3D 48 | % space and people's requirements will vary. It is straightforward to write 49 | % your own for your requirements. 50 | 51 | % Feature symmetry and asymmetry (see Kovesi "Symmetry and Asymmetry from 52 | % Local Phase") pick out 'blob-like' and 'boundary-like' structures 53 | % respectively. Combines all the scales to give a single 3D image. 54 | [FS,FA] = featureSymmetry3D(m1,m2,m3,m4); 55 | 56 | % Display one slice 57 | slice = 13; % near the middle 58 | figure() 59 | imshow(D(:,:,slice)), axis image, axis off, colormap gray 60 | title('Test Volume Slice') 61 | 62 | 63 | figure() 64 | imagesc(reshape(LE(:,:,slice,:),Y,[])), axis image, axis off, colormap gray 65 | title('Local Energy Over Scales') 66 | 67 | figure() 68 | imagesc(reshape(LP(:,:,slice,:),Y,[])), axis image, axis off, colormap gray 69 | title('Local Phase Over Scales') 70 | 71 | figure() 72 | imagesc([FS(:,:,slice),FA(:,:,slice)]), axis image, axis off, colormap gray 73 | title('3D Feature Symmetry and Asymmetry') 74 | 75 | %% Now for phase congruency 76 | % We'll use the same test volume here 77 | 78 | % This time we have to use exactly two scales, as this is required by 79 | % Felsberg's phase congruency method. As he suggests, let's use 80 | % three-ocatave filters and leave a three-octave spacing between them. 81 | cw = [6,48]; 82 | 83 | % Construct new filters, as before 84 | filtStruct = createMonogenicFilters3D(Y,X,Z,cw,cw,'lg',0.55); 85 | 86 | % Find monogenic signal, as before 87 | [m1,m2,m3,m4] = monogenicSignal3D(D,filtStruct); 88 | 89 | % Now use the 3D phase congruency algorithm. Just like the 2D case 90 | PC = phaseCongruency3D(m1,m2,m3,m4,0.05); 91 | 92 | % Display 93 | slice = 13; % near the middle 94 | figure() 95 | imshow(D(:,:,slice)), axis image, axis off, colormap gray 96 | title('Test Volume Slice') 97 | 98 | figure() 99 | imagesc(PC(:,:,slice)), axis image, axis off, colormap gray 100 | title('3D Phase Congruency') 101 | -------------------------------------------------------------------------------- /license.txt: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /src/createMonogenicFilters.m: -------------------------------------------------------------------------------- 1 | function filtStruct = createMonogenicFilters(ysize,xsize,wl,filtType,parameter) 2 | % 3 | % filtStruct = createMonogenicFilters(ysize,xsize,wl, filtType = 'lg', parameter) 4 | % 5 | % Creates a set of frequency domain filters combining bandpass and Reisz 6 | % filters for use in calculating the monogenic signal. 7 | % 8 | % Inputs: 9 | % ysize, xsize - Y and X dimensions of the filters 10 | % wl - Vector of wavelengths to use 11 | % filtType - Filter type to use: 12 | % 'lg' - Log-Gabor radial filter 13 | % 'gabor' - Gabor radial filter 14 | % 'gd' - Gaussian derivative filter 15 | % 'cau' - Cauchy 16 | % 'dop' - Difference of Poisson filter 17 | % parameter - The shape parameters for 'lg' and 'dop' 18 | % type filters 19 | % 20 | % Outputs: 21 | % fltStruct - Output structure containing the filters used 22 | % for use in calculating the mongenic signal. 23 | % 24 | % Fields: 25 | % - bpFilt - A four-dimensional array. Stacked 26 | % along the fourth dimension are the bandpass 27 | % filters for each wavelength. The third 28 | % dimension is singleton. This allows 29 | % intuitive filtering of stacks of images 30 | % (i.e. videos) 31 | % - ReiszFilt - the complex-valued filter for the 32 | % the Reisz transform 33 | % - numFilt - The number of bandpass filters 34 | % 35 | % 36 | % Adapted by Chris Bridge (March 2014) from code by Vicente Grau and Ana 37 | % Namburete 38 | % christopher.bridge@eng.ox.ac.uk 39 | 40 | if nargin < 4 || isempty(filtType) 41 | filtType = 'lg'; 42 | end 43 | 44 | % Frequency grid for the filter 45 | [yGrid,xGrid] = freqgrid2(ysize,xsize); 46 | 47 | % Determine the spatial regions to use 48 | w = sqrt(yGrid.^2 + xGrid.^2); 49 | w(1, 1) = 1; %Trick to avoid division by zero at DC component 50 | 51 | % Determine the number of filters to try from input 52 | numFilt = length(wl); 53 | 54 | % Parameters governing the bandwidth of the bandpass filter for Gabor and 55 | % log-Gabor type filters, and ratio of centre frequencies for difference of 56 | % Poisson filters 57 | 58 | if nargin > 4 && ~isempty(parameter) 59 | if(parameter < 0.0 || parameter > 1.0) 60 | error('Parameter must be between 0.0 and 1.0'); 61 | end 62 | sigmaOnf = parameter; 63 | ratio = parameter; 64 | else 65 | sigmaOnf = 0.5; 66 | ratio = 0.98; 67 | end 68 | 69 | % Output structure 70 | bpFilt = zeros(ysize,xsize,1,numFilt); 71 | 72 | 73 | % Generate band-pass filters (in frequency domain) 74 | for flt = 1:numFilt 75 | % Construct the filter - first calculate the radial filter component. 76 | fo = 1.0/wl(flt); % Centre frequency of filter. 77 | w0 = fo; % Normalised radius from centre of frequency plane 78 | % corresponding to fo. 79 | if strcmp(filtType, 'lg') 80 | bpFilt(:,:,1,flt) = exp((-(log(w/w0)).^2) / (2 * log(sigmaOnf)^2)); % computation of 3D log-gabor filter across the volumetric range 81 | elseif strcmp(filtType, 'gabor') 82 | bpFilt(:,:,1,flt) = exp((-(w/w0).^2) / (2 * sigmaOnf^2)); % gabor filter 83 | elseif strcmp(filtType, 'gd') 84 | bpFilt(:,:,1,flt) = w .* exp(-(w.^2)*(wl(flt)^2)); % isotropic gaussian derivative filter; wl is used for sigma 85 | elseif strcmp(filtType, 'cau') 86 | bpFilt(:,:,1,flt) = w .* exp(-(w)*(wl(flt))); % cauchy filter, wl is used for sigma 87 | elseif strcmp(filtType, 'dop') 88 | s2 = wl(flt)/((ratio-1))*log(ratio); % difference of Poisson filters 89 | s1 = ratio*s2; 90 | bpFilt(:,:,1,flt) = exp(-w*s1) - exp(-w*s2); 91 | end 92 | 93 | % Set the DC value of the filter 94 | bpFilt(1, 1, 1, flt) = 0; 95 | 96 | % Also remove unwanted high frequency components in filters 97 | % with even dimensions 98 | if(mod(ysize,2) == 0) 99 | bpFilt( ysize/2 +1,:, 1, flt) = 0; 100 | end 101 | if(mod(xsize,2) == 0) 102 | bpFilt( :, xsize/2 +1, 1, flt) = 0; 103 | end 104 | end 105 | 106 | % Normalise by the maximum value of the sum of all filters 107 | sumFilt = sum(bpFilt, 4); 108 | filtStruct.bpFilt = bpFilt ./ max(sumFilt(:)); 109 | filtStruct.numFilt = numFilt; 110 | 111 | % Generating the Riesz filter components as a complex filter 112 | filtStruct.ReiszFilt = (1i * yGrid - xGrid)./ w; % (iY) + i(iX) = iY - X 113 | 114 | % Create a frequency-domain differentiation filter (using the 115 | % differentation property of Fourier Transforms) 116 | filtStruct.diffFilt = 2i*pi*yGrid - 2*pi*xGrid; % (iY) + i(iX) = iY - X 117 | 118 | filtStruct.wl = wl; 119 | filtStruct.filtType = filtType; 120 | filtStruct.sigmaOnf = sigmaOnf; 121 | filtStruct.ratio = ratio; 122 | -------------------------------------------------------------------------------- /src/createMonogenicFilters3D.m: -------------------------------------------------------------------------------- 1 | function filtStruct = createMonogenicFilters3D(ysize,xsize,zsize,wl_xy,wl_z,filtType,parameter) 2 | % 3 | % filtStruct = createMonogenicFilters3D(ysize, xsize, zsize , wl_xy, wl_z, filtType = 'lg', parameter) 4 | % 5 | % Creates a set of frequency domain filters combining bandpass and Reisz 6 | % filters for use in calculating the monogenic signal. 7 | % 8 | % Inputs: 9 | % ysize, xsize, zsize - Y and X dimensions of the filters 10 | % wl_xy - vector of spatial wavelengths to use (for 11 | % filtering image dimensions 1 and 2) 12 | % wl_z - vector of temporal wavelengths to use (for 13 | % filtering image dimension 3) 14 | % filtType - Filter type to use: 15 | % 'lg' - Log-Gabor radial filter 16 | % 'gabor' - Gabor radial filter 17 | % 'gd' - Gaussian derivative 18 | % 'cau' - Cauchy 19 | % 'dop' - difference of Poisson filter 20 | % parameter - The shape parameters for 'lg' and 'dop' type 21 | % filters 22 | % 23 | % Outputs: 24 | % fltStruct - Output structure containing the filters used 25 | % for use in calculating the mongenic signal. 26 | % 27 | % Fields: 28 | % - bpFilt - A four-dimensional array. Stacked 29 | % along the fourth dimension are the bandpass 30 | % filters for each wavelength. 31 | % - ReiszFilt03, ReiszFilt12, two complex-valued Reisz 32 | % transform filters that allow the monogenic signal 33 | % to be computed with two IFFTs. The first is for the 34 | % even and third (z) odd part, the second for the 35 | % first and second odd parts (x,y) 36 | % - numFilt - The number of bandpass filters 37 | % 38 | % 39 | % Adapted by Chris Bridge (March 2014) from code by Vicente Grau and Ana 40 | % Namburete 41 | % christopher.bridge@eng.ox.ac.uk 42 | 43 | if nargin < 6 44 | filtType = 'lg'; 45 | end 46 | 47 | % Parameters governing the bandwidth of the bandpass filter for Gabor and 48 | % log-Gabor type filters, and ratio of centre frequencies for difference of 49 | % Poisson filters 50 | if nargin > 6 51 | if(parameter < 0.0 || parameter > 1.0) 52 | error('Parameter must be between 0.0 and 1.0'); 53 | end 54 | sigmaOnf = parameter; 55 | ratio = parameter; 56 | else 57 | sigmaOnf = 0.5; 58 | ratio = 0.98; 59 | end 60 | 61 | % Check that we have the same number of wavelength values for the spatial 62 | % and temporal filters. If one is single valued, extend it to use the same 63 | % value for each 64 | if length(wl_xy) ~= length(wl_z) 65 | if length(wl_xy) == 1 66 | wl_xy = wl_xy*ones(length(wl_z)); 67 | elseif length(wl_z) == 1 68 | wl_z = wl_z*ones(length(wl_xy)); 69 | else 70 | error('The dimensions of the spatial and temporal wavelength vectors must agree, or one must be scalar') 71 | end 72 | end 73 | 74 | % Determine the number of filters to try from input 75 | numFilt = length(wl_xy); 76 | 77 | [yGrid, xGrid, zGrid] = freqgrid3(ysize,xsize,zsize); 78 | 79 | % Output structure 80 | bpFilt = zeros(ysize,xsize,zsize,numFilt); 81 | 82 | % Generate band-pass filters (in frequency domain) 83 | for flt = 1:numFilt 84 | % Construct the filter - first calculate the radial filter component. 85 | fo = 1.0/wl_xy(flt); % Centre frequency of spatial filter. 86 | w0 = fo; % Normalised radius from centre of frequency plane 87 | % corresponding to fo. 88 | 89 | g0 = 1.0/wl_z(flt); % Centre frequency of temporal filter. 90 | u0 = g0/0.5; % Normalised radius from centre of frequency plane 91 | % corresponding to fo. 92 | 93 | % Determine the spatial regions to use 94 | w = sqrt( (yGrid.^2)./(w0^2) + (xGrid.^2)./(w0^2) + (zGrid.^2)./(u0^2) ); 95 | w(1,1,1) = 1; %Trick to avoid division by zero 96 | 97 | if strcmp(filtType, 'lg') 98 | bpFilt(:,:,:,flt) = exp((-(log(w)).^2) / (2 * log(sigmaOnf)^2)); % computation of 3D log-gabor filter across the volumetric range 99 | elseif strcmp(filtType, 'gabor') 100 | bpFilt(:,:,:,flt) = exp((-(w).^2) / (2 * sigmaOnf^2)); % gabor filter 101 | elseif strcmp(filtType, 'gd') 102 | bpFilt(:,:,:,flt) = w .* exp(-4*(w.^2)); % isotropic gaussian derivative filter; wl is used for sigma 103 | elseif strcmp(filtType, 'cau') 104 | bpFilt(:,:,:,flt) = w .* exp(-2*w); % wl is used for sigma 105 | elseif strcmp(filtType, 'dop') 106 | s2 = log(ratio)/(ratio-1); 107 | s1 = ratio*s2; 108 | bpFilt(:,:,:,flt) = exp(-2*w*s1) - exp(-2*w*s2); % difference of Poisson filters 109 | end 110 | 111 | % Set the DC value of the filter 112 | bpFilt(1, 1, 1, flt) = 0; 113 | 114 | % Also remove unwanted high frequency components in filters 115 | % with even dimensions 116 | if(mod(ysize,2) == 0) 117 | bpFilt( ysize/2 +1,:, 1, flt) = 0; 118 | end 119 | if(mod(xsize,2) == 0) 120 | bpFilt( :, xsize/2 +1, 1, flt) = 0; 121 | end 122 | if(mod(zsize,2) == 0) 123 | bpFilt( :, :, zsize/2 +1, flt) = 0; 124 | end 125 | end 126 | 127 | % Normalise by the maximum value of the sum of all filters 128 | sumFilt = sum(bpFilt, 4); 129 | filtStruct.bpFilt = bpFilt ./ max(sumFilt(:)); 130 | 131 | % Generate the Riesz filter components (i.e. the odd filter whose 132 | % components are imaginary) 133 | w = sqrt(yGrid.^2 + xGrid.^2 + zGrid.^2); 134 | w(1, 1, 1) = 1; 135 | filtStruct.ReiszFilt03 = 1 - (zGrid ./ w); % Complex filter for the even and z-dimension odd component 136 | filtStruct.ReiszFilt12 = (1i*yGrid - xGrid)./ w; % Complex filter for the spatial odd components 137 | filtStruct.numFilt = numFilt; 138 | -------------------------------------------------------------------------------- /src/featureSymmetry.m: -------------------------------------------------------------------------------- 1 | function [FS,FA] = featureSymmetry(m1,m2,m3, T) 2 | % 3 | % [FS,FA] = featureSymmetry(m1,m2,m3, T = 0.18) 4 | % 5 | % Calculates the feature symmetry (FS) and feature asymmetry (FA) using 6 | % the components of the monogenic signal (m1,m2,m3). These arrays may be 7 | % four dimensional, with the third dimension corresponding to time and the 8 | % fourth to different wavelengths of the bandpass filter. T is the 9 | % threshold used. 10 | % 11 | % Adapted by Chris Bridge (March 2014) from code by Vicente Grau and Ana 12 | % Namburete 13 | % christopher.bridge@eng.ox.ac.uk 14 | 15 | 16 | % Threshold 17 | if nargin < 4 18 | T = 0.18; 19 | end 20 | 21 | [ysize, xsize, tsize, ssize] = size(m1); 22 | 23 | % Small constant to avoid division by zero 24 | epsilon = 0.001; 25 | 26 | % Combine the odd components 27 | odd = sqrt(m2.^2 + m3.^2); 28 | even = abs(m1); 29 | 30 | % Calculate the denominator (= local energy + epsilon) 31 | denominator = sqrt(even.^2 + odd .^2) + epsilon; 32 | 33 | % Calculate the numerators for FA and FS at all scales 34 | % NB no need to take absolute value of 'odd' as it must be positive due to 35 | % the way it's calculated 36 | FS_numerator = max(even - odd - T, zeros(ysize, xsize, tsize, ssize)); 37 | FA_numerator = max(odd - even - T, zeros(ysize, xsize, tsize, ssize)); 38 | 39 | % Divide numerator by denominator 40 | FS = FS_numerator./denominator; 41 | FA = FA_numerator./denominator; 42 | 43 | % Sum across scales, and divide by nimber of scales to give value between 0 44 | % and 1 (i.e. take mean across the scale dimension) 45 | FS = mean(FS, 4); 46 | FA = mean(FA, 4); 47 | 48 | -------------------------------------------------------------------------------- /src/featureSymmetry3D.m: -------------------------------------------------------------------------------- 1 | function [FS,FA] = featureSymmetry3D(m1,m2,m3,m4,T) 2 | % 3 | % [FS,FA] = featureSymmetry3D(m1,m2,m3, m4, T = 0.18) 4 | % 5 | % Calculates the feature symmetry (FS) and feature asymmetry (FA) using 6 | % the components of the monogenic signal (m1,m2,m3,m4). These arrays may be 7 | % four dimensional, with the fourth dimension corresponding to different 8 | % wavelengths of the bandpass filter. T is the threshold used. 9 | % 10 | % Adapted by Chris Bridge (March 2014) from code by Vicente Grau and Ana 11 | % Namburete 12 | % christopher.bridge@eng.ox.ac.uk 13 | 14 | % Threshold 15 | if nargin < 5 16 | T = 0.18; 17 | end 18 | 19 | [ysize, xsize, zsize, ssize] = size(m1); 20 | 21 | % Small constant to avoid division by zero 22 | epsilon = 0.001; 23 | 24 | % Combine the odd components 25 | odd = sqrt(m2.^2 + m3.^2 + m4.^2); 26 | even = abs(m1); 27 | 28 | % Calculate the denominator (= local energy + epsilon) 29 | denominator = sqrt(even.^2 + odd .^2) + epsilon; 30 | 31 | % Calculate the numerators for FA and FS at all scales 32 | % NB no need to take absolute of 'odd' as it must be positive due to the 33 | % way it's calculated 34 | FS_numerator = max(even - odd - T, zeros(ysize, xsize, zsize, ssize)); 35 | FA_numerator = max(odd - even - T, zeros(ysize, xsize, zsize, ssize)); 36 | 37 | % Divide numerator by denominator 38 | FS = FS_numerator./denominator; 39 | FA = FA_numerator./denominator; 40 | 41 | % Sum across scales, and divide by nimber of scales to give value between 0 42 | % and 1 (i.e. take mean across the scale dimension) 43 | FS = mean(FS, 4); 44 | FA = mean(FA, 4); 45 | 46 | -------------------------------------------------------------------------------- /src/freqgrid2.m: -------------------------------------------------------------------------------- 1 | function [yGrid, xGrid] = freqgrid2(ysize,xsize,gpu) 2 | 3 | % [yGrid, xGrid] = freqgrid2(ysize,xsize) 4 | % [yGrid, xGrid] = freqgrid2(size) 5 | % 6 | % Creates a 2D grid of frequencies of a given size, respecting the MATLAB 7 | % convention for the location of the DC component (top left). This means 8 | % that if a filter is desgined on this grid, ifft2(filter) will behave as 9 | % expected. Use fftshift before visualising. 10 | % 11 | % Chris Bridge, Institute of Biomedical Engineering, University of Oxford 12 | % christopher.bridge@eng.ox.ac.uk 13 | 14 | if nargin < 2 15 | xsize = ysize; 16 | end 17 | 18 | % Dimensions 19 | ymid = floor(ysize/2); 20 | xmid = floor(xsize/2); 21 | 22 | % Work out the maximum frequency in the grid - depends on whether the image 23 | % has odd or even dimensions due to the definition of the FFT 24 | if(mod(ysize,2)) == 0 25 | ymax = ymid-1; 26 | else 27 | ymax = ymid; 28 | end 29 | 30 | if(mod(xsize,2)) == 0 31 | xmax = xmid-1; 32 | else 33 | xmax = xmid; 34 | end 35 | 36 | % Create the grid for the filter 37 | [yGrid, xGrid] = ndgrid( -ymid : ymax, -xmid : xmax); 38 | yGrid = ifftshift(yGrid)/ysize; 39 | xGrid = ifftshift(xGrid)/xsize; -------------------------------------------------------------------------------- /src/freqgrid3.m: -------------------------------------------------------------------------------- 1 | function [yGrid, xGrid, zGrid] = freqgrid3(ysize,xsize, zsize) 2 | 3 | % [yGrid, xGrid, Grid] = freqgrid(ysize,xsizezsize) 4 | % 5 | % Creates a 3d grid of frequencies of a given size, respecting the MATLAB 6 | % convention for the location of the DC component (top left). This means 7 | % that if a filter is desgined on this grid, ifftn(filter) will behave as 8 | % expected. Use fftshift before visualising. 9 | % 10 | % Chris Bridge, Institute of Biomedical Engineering, University of Oxford 11 | % christopher.bridge@eng.ox.ac.uk 12 | 13 | % Dimensions 14 | ymid = floor(ysize/2); 15 | xmid = floor(xsize/2); 16 | zmid = floor(zsize/2); 17 | 18 | % Work out the maximum frequency in the grid - depends on whether the image 19 | % has odd or even dimensions due to the definition of the FFT 20 | if(mod(ysize,2)) == 0 21 | ymax = ymid-1; 22 | else 23 | ymax = ymid; 24 | end 25 | 26 | if(mod(xsize,2)) == 0 27 | xmax = xmid-1; 28 | else 29 | xmax = xmid; 30 | end 31 | 32 | if(mod(zsize,2)) == 0 33 | zmax = zmid-1; 34 | else 35 | zmax = zmid; 36 | end 37 | 38 | % Create the grid for the filter 39 | [yGrid, xGrid, zGrid] = ndgrid( -ymid : ymax, -xmid : xmax, -zmid : zmax); 40 | yGrid = ifftshift(yGrid); 41 | xGrid = ifftshift(xGrid); 42 | zGrid = ifftshift(zGrid); 43 | 44 | yGrid = yGrid ./ ysize; 45 | xGrid = xGrid ./ xsize; 46 | zGrid = zGrid ./ zsize; -------------------------------------------------------------------------------- /src/localEnergy.m: -------------------------------------------------------------------------------- 1 | function LE = localEnergy(m1,m2,m3,wl_ind) 2 | % 3 | % LE = localEnergy(m1,m2,m3,wl_ind) 4 | % 5 | % Calculates the local energy from a monogenic signal (m1,m2,m3) of an 6 | % image or video. The phase is calculated for each scale independently. 7 | % 8 | % Alternatively, wl_ind, a parameter selecting the index of the wavelength 9 | % to use may be passed. 10 | % 11 | % Chris Bridge, Institute of Biomedical Engineering, University of Oxford 12 | % christopher.bridge@eng.ox.ac.uk 13 | 14 | if nargin < 4 15 | LE = m1.^2 + m2.^2 + m3.^2; 16 | else 17 | LE = m1(:,:,:,wl_ind).^2 + m2(:,:,:,wl_ind).^2 + m3(:,:,:,wl_ind).^2; 18 | end -------------------------------------------------------------------------------- /src/localEnergy3D.m: -------------------------------------------------------------------------------- 1 | function LE = localEnergy3D(m1,m2,m3,m4, wl_ind) 2 | % 3 | % LE = localEnergy3D(m1,m2,m3,m4, wl_ind) 4 | % 5 | % Calculates the local energy from a monogenic signal (m1,m2,m3,m4) of a 6 | % volume image. The phase is calculated for each scale independently. 7 | % 8 | % Alternatively, wl_ind, a parameter selecting the index of the wavelength 9 | % to use may be passed. 10 | % 11 | % Chris Bridge, Institute of Biomedical Engineering, University of Oxford 12 | % christopher.bridge@eng.ox.ac.uk 13 | 14 | if nargin < 5 15 | LE = m1.^2 + m2.^2 + m3.^2 + m4.^2; 16 | else 17 | LE = m1(:,:,:,wl_ind).^2 + m2(:,:,:,wl_ind).^2 + m3(:,:,:,wl_ind).^2 + m4(:,:,:,wl_ind).^2; 18 | end 19 | 20 | 21 | -------------------------------------------------------------------------------- /src/localOrientation.m: -------------------------------------------------------------------------------- 1 | function LO = localOrientation(m2,m3,degrees) 2 | % function LO = localOrientation(m2,m3,degrees = false) 3 | % 4 | % This function calculates the local image orientation from the odd parts 5 | % of the monogenic signal. The value returned is in radians unless the 6 | % third argument is set to true. The angle is measured anti-clockwise from 7 | % the increasing x-axis and corresponds to the direction of increasing 8 | % intensity in the image. The value is wrapped to be between -pi and pi 9 | % radians (or -180 to 180 degrees). 10 | % 11 | % Chris Bridge, Institute of Biomedical Engineering, University of Oxford 12 | % christopher.bridge@eng.ox.ac.uk 13 | 14 | if (nargin < 3) 15 | degrees = false; 16 | end 17 | 18 | if (degrees) 19 | LO = atan2d(-m2,m3); 20 | else 21 | LO = atan2(-m2,m3); 22 | end 23 | -------------------------------------------------------------------------------- /src/localPhase.m: -------------------------------------------------------------------------------- 1 | function LP = localPhase(m1,m2,m3, wl_ind) 2 | % 3 | % LP = localPhase(m1,m2,m3,wl_ind) 4 | % 5 | % Calculates the local phase from a monogenic signal (m1,m2,m3) of an image 6 | % or video. The phase is calculated for each scale independently. 7 | % 8 | % Alternatively, wl_ind, a parameter selecting the index of the wavelength 9 | % to use may be passed. 10 | % 11 | % Chris Bridge, Institute of Biomedical Engineering, University of Oxford 12 | % christopher.bridge@eng.ox.ac.uk 13 | 14 | if nargin < 4 15 | LP = atan2( sqrt(m2.^2 + m3.^2), m1); 16 | else 17 | LP = atan2( sqrt(m2(:,:,:,wl_ind).^2 + m3(:,:,:,wl_ind).^2), m1(:,:,:,wl_ind)); 18 | end 19 | 20 | 21 | 22 | 23 | -------------------------------------------------------------------------------- /src/localPhase3D.m: -------------------------------------------------------------------------------- 1 | function LP = localPhase3D(m1,m2,m3,m4,wl_ind) 2 | % 3 | % LP = localPhase3D(m1,m2,m3,m4,wl_ind) 4 | % 5 | % Calculates the local phase from a monogenic signal (m1,m2,m3,m4) of a 6 | % volume image. The phase is calculated for each scale independently. 7 | % 8 | % Alternatively, wl_ind, a parameter selecting the index of the wavelength 9 | % to use may be passed. 10 | % 11 | % Chris Bridge, Institute of Biomedical Engineering, University of Oxford 12 | % christopher.bridge@eng.ox.ac.uk 13 | 14 | if nargin < 5 15 | LP = atan2( sqrt(m2.^2 + m3.^2 + m4.^2), m1); 16 | else 17 | LP = atan2( sqrt(m2(:,:,:,wl_ind).^2 + m3(:,:,:,wl_ind).^2 + m4(:,:,:,wl_ind).^2), m1(:,:,:,wl_ind)); 18 | end 19 | 20 | 21 | 22 | 23 | -------------------------------------------------------------------------------- /src/monogenicSignal.m: -------------------------------------------------------------------------------- 1 | function [Fm1, Fm2, Fm3] = monogenicSignal(im, filtStruct) 2 | % 3 | % [Fm1, Fm2, Fm3] = monogenicSignal(im, filtStruct) 4 | % 5 | % This function computes the monogenic signal using the Riesz transform as 6 | % suggested by Felsberg. This function returns the 2D monogenic signal of 7 | % each frame regardless of the input dimensionality 8 | % 9 | % Inputs: 10 | % im = image for which monogenic signal will be computed. 11 | % May be 2 or 3 dimensional stack of images. 12 | % filtStruct = a structure containing the necessary filters, as 13 | % returned by createMonogenicFilters 14 | % 15 | % Outputs: 16 | % Fm1 = even component of the monogenic signal 17 | % Fm2,Fm3 = odd components of the monogenic signal 18 | % The first three dimensions of the output are the image 19 | % dimensions, the fourth is the bandpass wavelength if 20 | % multiple are used. 21 | % 22 | % 23 | % Adapted by Chris Bridge (March 2014) from code by Vincente Grau and Ana 24 | % Namburete 25 | % christopher.bridge@eng.ox.ac.uk 26 | 27 | % Compute the 2-dimensional fast Fourier transform of the original image or 28 | % stack of images 29 | F = fft2(im); 30 | Ffilt = bsxfun(@times, F, filtStruct.bpFilt); 31 | 32 | % Compute the parts of the monogenic signal (NB applying the ifft2 to a 3D 33 | % image here performs the 2D ifft to each two dimensional slice) 34 | Fm1 = real(ifft2( Ffilt )); %even component 35 | Fmodd = ifft2( bsxfun(@times, Ffilt, filtStruct.ReiszFilt) ); 36 | Fm2 = real(Fmodd); %odd components... 37 | Fm3 = imag(Fmodd); 38 | -------------------------------------------------------------------------------- /src/monogenicSignal3D.m: -------------------------------------------------------------------------------- 1 | function [Fm1, Fm2, Fm3, Fm4] = monogenicSignal3D(vol, filtStruct) 2 | % 3 | % [Fm1, Fm2, Fm3, Fm4] = monogenicSignal3D(vol, filtStruct) 4 | % 5 | % This function computes the monogenic signal using the Riesz transform as 6 | % suggested by Felsberg. 7 | % 8 | % Inputs: 9 | % vol = volume for which monogenic signal will be computed 10 | % filtStruct = a structure containing the necessary filters, as 11 | % returned by createMonogenicFilters3D 12 | % 13 | % Outputs: 14 | % Fm1 = even component of the monogenic signal 15 | % Fm2,Fm3, Fm4 = odd components of the monogenic signal 16 | % 17 | % Adapted by Chris Bridge (March 2014) from code by Vincente Grau and Ana 18 | % Namburete 19 | % christopher.bridge@eng.ox.ac.uk 20 | 21 | % Create output arrays 22 | outputsize = cat(2, size(vol), filtStruct.numFilt); 23 | Fm1 = zeros(outputsize); 24 | Fm2 = zeros(outputsize); 25 | Fm3 = zeros(outputsize); 26 | Fm4 = zeros(outputsize); 27 | 28 | % Compute the 3-dimensional fast Fourier transform of the original image 29 | F = fftn(vol); 30 | 31 | % Filter using the Reisz filter 32 | R_03 = F.*filtStruct.ReiszFilt03; 33 | R_12 = F.*filtStruct.ReiszFilt12; 34 | 35 | % Compute the parts of the monogenic signal 36 | for flt = 1:filtStruct.numFilt 37 | F03 = ifftn(R_03.*filtStruct.bpFilt(:,:,:,flt)); 38 | F12 = ifftn(R_12.*filtStruct.bpFilt(:,:,:,flt)); 39 | Fm1(:,:,:,flt) = real( F03 ); 40 | Fm2(:,:,:,flt) = real( F12 ); 41 | Fm3(:,:,:,flt) = imag( F12 ); 42 | Fm4(:,:,:,flt) = imag( F03 ); 43 | end 44 | -------------------------------------------------------------------------------- /src/orientedSymmetry.m: -------------------------------------------------------------------------------- 1 | function [FA_y, FA_x, FS] = orientedSymmetry(m1,m2,m3,T) 2 | % 3 | % [FA_y, FA_x, FS] = orientedSymmetry(m1,m2,m3,T = 0.18) 4 | % 5 | % Creates an edge map using oriented feature asymmetry calculated from 6 | % the monogenic signal (m1,m2,m3). FA_y contains the vertical edge 7 | % components and FA_x contains the horizontal edge components. The 8 | % direction of the edges is defined to point in the direction of 9 | % increasing intensity, using the standard MATLAB definitions for the 10 | % increasing y and x directions (i.e. down and right). 11 | % 12 | % FS returns the signed feature symmetry map (i.e. feature symmetry 13 | % with a sign to indiciate the polarity of the symmetry) 14 | 15 | % Threshold 16 | if nargin < 4 17 | T = 0.18; 18 | end 19 | 20 | [ysize, xsize, tsize, ssize] = size(m1); 21 | 22 | % Small constant to avoid division by zero 23 | epsilon = 0.001; 24 | 25 | % Take the absolute value of m1 as the even part of the filter 26 | even = abs(m1); 27 | odd = sqrt(m2.*m2 + m3.*m3); 28 | 29 | % Calculate the denominator (= local amplitude + epsilon) 30 | denominator = sqrt(even.*even + m2.*m2 + m3.*m3) + epsilon; 31 | 32 | % Calculate the numerators for FA and FS at all scales 33 | % NB no need to take absolute value of 'odd' as it must be positive due to 34 | % the way it's calculated 35 | FA_numerator = max(odd - even - T, zeros(ysize, xsize, tsize, ssize)); 36 | FS_numerator = max(even - odd - T, zeros(ysize, xsize, tsize, ssize)); 37 | 38 | % Divide numerator by denominator and include orientation 39 | FA_y = (FA_numerator./denominator).*(m2./odd); 40 | FA_x = (FA_numerator./denominator).*(m3./odd); 41 | FS = (FS_numerator./denominator).*sign(m1); 42 | 43 | % Sum across scales, and divide by nimber of scales to give value between 0 44 | % and 1 (i.e. take mean across the scale dimension) 45 | FA_y = mean(FA_y, 4); 46 | FA_x = mean(FA_x, 4); 47 | FS = mean(FS, 4); 48 | 49 | -------------------------------------------------------------------------------- /src/orientedSymmetry3D.m: -------------------------------------------------------------------------------- 1 | function [FA_y, FA_x, FA_z, FS] = orientedSymmetry3D(m1,m2,m3,m4,T) 2 | % 3 | % [FA_y, FA_x, FA_z, FS] = orientedAsymmetry3D(m1,m2,m3,m4,T = 0.18) 4 | % 5 | % Creates an edge map using oriented feature assymetry calculated from 6 | % the monogenic signal (m1,m2,m3,m4). FA_y contains the vertical edge 7 | % components and FA_x contains the horizontal edge components. The 8 | % direction of the edges is defined to point in the direction of 9 | % increasing intensity, using the standard MATLAB definitions for the 10 | % increasing y and x directions (i.e. down and right). 11 | % 12 | % FS returns the oriented feature symmetry map (i.e. feature symmetry 13 | % with a sign to indiciate the polarity of the symmetry) 14 | 15 | % Threshold 16 | if nargin < 5 17 | T = 0.18; 18 | end 19 | 20 | [ysize, xsize, tsize, ssize] = size(m1); 21 | 22 | % Small constant to avoid division by zero 23 | epsilon = 0.001; 24 | 25 | % Take the absolute value of m1 as the even part of the filter 26 | even = abs(m1); 27 | odd = sqrt(m2.*m2 + m3.*m3 + m4.*m4); 28 | 29 | % Calculate the denominator (= local energy + epsilon) 30 | denominator = sqrt(even.*even + m2.*m2 + m3.*m3 + m4.*m4) + epsilon; 31 | 32 | % Calculate the numerators for FA and FS at all scales 33 | % NB no need to take absolute value of 'odd' as it must be positive due to 34 | % the way it's calculated 35 | FA_numerator = max(odd - even - T, zeros(ysize, xsize, tsize, ssize)); 36 | FS_numerator = max(even - odd - T, zeros(ysize, xsize, tsize, ssize)); 37 | 38 | % Divide numerator by denominator and include orientation 39 | FA_y = (FA_numerator./denominator).*(m2./odd); 40 | FA_x = (FA_numerator./denominator).*(m3./odd); 41 | FA_z = (FA_numerator./denominator).*(m4./odd); 42 | FS = (FS_numerator./denominator).*sign(m1); 43 | 44 | % Sum across scales, and divide by nimber of scales to give value between 0 45 | % and 1 (i.e. take mean across the scale dimension) 46 | FA_y = mean(FA_y, 4); 47 | FA_x = mean(FA_x, 4); 48 | FA_z = mean(FA_z, 4); 49 | FS = mean(FS, 4); 50 | 51 | -------------------------------------------------------------------------------- /src/phaseCongruency.m: -------------------------------------------------------------------------------- 1 | function PC = phaseCongruency(m1,m2,m3,T) 2 | % PC = phaseCongruency(m1,m2,m3,T=0.0) 3 | % 4 | % Calculate the phase congruency measure from the monogenic signal 5 | % (m1,m2,m3,m4). This algorithm is from Felsberg and Sommer "A New 6 | % Extension of Linear Signal Processing for Estimating Local Properties and 7 | % Detecting Features" and requires that the monogenic signal is calculated 8 | % at exactly 2 scales. 9 | % 10 | % T is a constant noise threshold used to supress the phase congruency in 11 | % parts of the image with low energy at both scales. It is expressed as a 12 | % value in the range 0-1 where 0 will supress no noise and 1 will suppress 13 | % the entire image. 14 | % 15 | % Chris Bridge, Institute of Biomedical Engineering, University of Oxford 16 | % christopher.bridge@eng.ox.ac.uk 17 | 18 | if (nargin < 4) 19 | T = 0.0; 20 | elseif( T < 0.0 || T > 1.0) 21 | error('T should lie in the range 0-1') 22 | end 23 | 24 | if(any([size(m1,4), size(m2,4), size(m3,4)] ~= 2 )) 25 | error('You must provide a monogenic signal at exactly two wavelengths') 26 | end 27 | 28 | % Stack the parts of the vectors together for scales 1 and 2 29 | f1 = cat(4,m1(:,:,:,1),m2(:,:,:,1),m3(:,:,:,1)); 30 | f2 = cat(4,m1(:,:,:,2),m2(:,:,:,2),m3(:,:,:,2)); 31 | 32 | % Dot product of the two vectors 33 | dotprod = sum(f1.*f2,4); 34 | 35 | % Norm of the two vectors 36 | norm1 = sqrt(sum(f1.^2,4)); 37 | norm2 = sqrt(sum(f2.^2,4)); 38 | 39 | % Cross product of the two vectors amd its norm 40 | xprod = cross(f1,f2,4); 41 | normxprod = sqrt(sum(xprod.^2,4)); 42 | 43 | % Phase congruency 44 | PC = max(dotprod-T*max(dotprod(:)),0)./(normxprod+norm1.*norm2); 45 | -------------------------------------------------------------------------------- /src/phaseCongruency3D.m: -------------------------------------------------------------------------------- 1 | function PC = phaseCongruency3D(m1,m2,m3,m4,T) 2 | % PC = phaseCongruency3D(m1,m2,m3,m4,T=0.0) 3 | % 4 | % Calculate the phase congruency measure from the monogenic signal 5 | % (m1,m2,m3,m4). This algorithm is from Felsberg and Sommer "A New 6 | % Extension of Linear Signal Processing for Estimating Local Properties and 7 | % Detecting Features" and requires that the monogenic signal is calculated 8 | % at exactly 2 scales. This code uses a generalisation of this algorithm to 9 | % three dimensional images. 10 | % 11 | % T is a constant noise threshold used to supress the phase congruency in 12 | % parts of the image with low energy at both scales. It is expressed as a 13 | % value in the range 0-1 where 0 will supress no noise and 1 will suppress 14 | % the entire image. 15 | % 16 | % Chris Bridge, Institute of Biomedical Engineering, University of Oxford 17 | % christopher.bridge@eng.ox.ac.uk 18 | 19 | if (nargin < 5) 20 | T = 0.0; 21 | end 22 | 23 | if(any([size(m1,4), size(m2,4), size(m3,4), size(m4,4)] ~= 2 )) 24 | error('You must provide a monogenic signal at exactly two wavelengths') 25 | end 26 | 27 | % Stack the parts of the vectors together for scales 1 and 2 28 | f1 = cat(4,m1(:,:,:,1),m2(:,:,:,1),m3(:,:,:,1),m4(:,:,:,1)); 29 | f2 = cat(4,m1(:,:,:,2),m2(:,:,:,2),m3(:,:,:,2),m4(:,:,:,2)); 30 | 31 | % Dot product of the two vectors 32 | dotprod = sum(f1.*f2,4); 33 | 34 | % Norms of each monogenic vector 35 | norm1 = sqrt(sum(f1.^2,4)); 36 | norm2 = sqrt(sum(f2.^2,4)); 37 | normproduct = norm1.*norm2; 38 | 39 | % Can't use cross product in 4D to find |sin(x)|, so calculate it from 40 | % cos(x) from the dot product 41 | sinangle = sin(acos(dotprod./normproduct)); 42 | 43 | % Calculate the phase congruency 44 | PC = max(dotprod-T*max(dotprod(:)),0)./(normproduct.*(sinangle + 1.0)); 45 | --------------------------------------------------------------------------------