MATLAB implementation of Radon Cumulative Distribution Transform Nearest Subspace (RCDT-NS) classifier

This repository contains the MATLAB implementation of the Radon cumulative distribution transform nearest subspace (RCDT-NS) classifier proposed in the paper titled "Radon cumulative distribution transform subspace models for image classification". A python implementation of the classifier using PyTransKit (Python Transport Based Signal Processing Toolkit) package is also available in: https://github.com/rohdelab/rcdt_ns_classifier.

Walk-through of the RCDT-NS classifier implementation

Organize datasets

Organize an image classification dataset as follows:

1. Download the image dataset, and seperate it into the training and testing sets.
2. For the training set:
   • Save images from different classes into separate .mat files. Dimension of the each .mat file would be M x N x K, where M x N is the size of the images and K is the number of samples per class.
   • Name of the mat file would be dataORG_<class_index>.mat. For example, dataORG_0.mat and dataORG_1.mat would be two mat files for a binary class problem.
   • Save the mat files in the ./data/training directory.
3. For the testing set:
   • The first two steps here are the same as the first two steps for the training set.
   • Save the mat files in the ./data/testing directory.

Read Data

Load the train and test images from the .mat files provided in the dataset directory.

im_train = []; label_train = []; 
im_test = []; label_test = [];
for cls=0:numClass-1
    % train set
    xxO = []; label = [];
    load([datadir 'training/dataORG_' num2str(cls) '.mat']);
    im_train = cat(3,im_train,xxO);
    label_train = cat(2,label_train,label);
    
    % test set
    xxO = []; label = [];
    load([datadir 'testing/dataORG_' num2str(cls) '.mat']);
    im_test = cat(3,im_test,xxO);
    label_test = cat(2,label_test,label);
end

Calculate RCDT

1. Define some basic parameters of RCDT:

I_domain = [0, 1];
Ihat_domain = [0, 1];
theta_seq = 0:4:179;
rm_edge = 1;

2. Calculate RCDT for the train images:

Xtrain = [];
for i = 1:size(im_train,3)
    I = squeeze(im_train(:,:,i));
    Ihat = RCDT(I_domain, I, Ihat_domain, theta_seq, rm_edge);
    Xtrain = cat(2, Xtrain, Ihat(:));
end

3. Calculate RCDT for the test images:

Xtest = [];
for i = 1:size(im_test,3)
    I = squeeze(im_test(:,:,i));
    Ihat = RCDT(I_domain, I, Ihat_domain, theta_seq, rm_edge);
    Xtest = cat(2, Xtest, Ihat(:));
end

Calculate the basis vectors for each class

len_subspace = 0;
for cls=0:numClass-1
    ind = find(label_train==cls);           % find train samples corresponding to class 'cls'
    ind_sub = randsample(ind,trainSamples); % control the number of train samples to fit the model using 
                                            % 'trainSamples' variable; all the samples can also be used
                                            % by setting 'ind_sub = ind'
    classSamples = Xtrain(:,ind_sub);
    
    % calculate basis vectors using SVD
    [uu,su,vu]=svd(classSamples);
    s=diag(su);
    eps= 1e-4;
    indx=find(s>eps);
    V=uu(:,indx);
    
    basis(cls+1).V = V;
    
    % take basis components with atleast 99% variance
    S = cumsum(s);
    S = S/max(S);
    basis_ind = find(S>=0.99);
    if len_subspace < basis_ind(1)
        len_subspace = basis_ind(1);
    end 
end

Test the model

%% PREDICT: classify the test samples
for cls=0:numClass-1
    B = basis(cls+1).V;
    B = B(:,1:len_subspace);
    Xproj = (B*B')*Xtest;               % projection of the test sample on the subspace
    Dproj = Xtest - Xproj;
    D(cls+1,:) = sqrt(sum(Dproj.^2,1)); % distance between test sample and its projection
end
[~,Ytest] = min(D);                     % predict the class label of the test sample
Ytest = Ytest - 1;                      % class labels are defined from 0, but matlab index starts from 1

Accuracy = numel(find(Ytest==label_test))/length(Ytest)

The above steps have also been compiled in a single matlab script RCDT_NS.m which runs the RCDT-NS classifier on MNIST dataset.

Publication for Citation

Please cite the following publication when publishing findings that benefit from the codes provided here.

Shifat-E-Rabbi M, Yin X, Rubaiyat AH, Li S, Kolouri S, Aldroubi A, Nichols JM, Rohde GK. Radon cumulative distribution transform subspace modeling for image classification. Journal of Mathematical Imaging and Vision. 2021 Aug 5:1-9. [Paper]