RGB Image clustering using Mahalanobis distance

The Mahalanobis distance classification is widely used in clustering. The equation has a covariance matrix that works on the variation of the classes to create similarity.

In Matlab, we have the function ‘mahal’ that can calculate the distance between a point and a sample subset.

Let’s use the Mahal() function to cluster a RGB image,

Let’s make four clusters, for the image ‘flower8.jpg’ based on the colors(ie. RGB components).

Take a small subset of the yellow color flower as shown in the picture.

We will use the Red, Green and Blue components of this subset as the sample. The mean and the covariance of this subset is calculated.

Now the distance of each pixels in the image is computed from the sample subset.

The figure below shows the distance of each pixels in the image computed from the subset(yellow color).

Note that the distance is minimal for the yellow color and it is high for other colors.

Likewise, the subset of the blue and pink color is also considered as samples and the computation is done accordingly.

The minimum distance with respect to the subsets is generated and the corresponding pixel position is updated with a unique cluster number.

MATLAB CODE:

clear all

clc

%READ AN RGB IMAGE

A = imread('flower8.jpg');

R = A(:,:,1); %RED COMPONENT

G = A(:,:,2); %GREEN COMPONENT

B = A(:,:,3); %BLUE COMPONENT

%PREALLOCATE THE VECTOR

mahal_dist  = zeros([numel(B),4]);

%CROP THE SMALL SUBSET OF THE YELLOW FLOWER

A1 = imcrop(A,[824.5 203.5 33 22]);

subset_R = A1(:,:,1);

subset_G = A1(:,:,2);

subset_B = A1(:,:,3);

%CALCULATE MAHALANOBIS DISTANCE FOR THE RED, BLUE AND GREEN COMPONENTS OF THE WHOLE IMAGE AND ALSO THE

%RED,GREEN AND BLUE COMPONENTS OF THE SMALL SUBSET

mahal_dist(:,1) = mahal(double([R(:),G(:),B(:)]),double([subset_R(:),subset_G(:),subset_B(:)])); %Yellow

%CROP THE SMALL SUBSET OF THE BLUE FLOWER

A1 = imcrop(A,[449.5 44.5 49 33]);

subset_R = A1(:,:,1);

subset_G = A1(:,:,2);

subset_B = A1(:,:,3);

mahal_dist(:,2) = mahal(double([R(:),G(:),B(:)]),double([subset_R(:),subset_G(:),subset_B(:)])); %Blue

%CROP THE SMALL PORTION OF THE PINK FLOWER

A1 = imcrop(A,[765.5 243.5 60 50]);

subset_R = A1(:,:,1);

subset_G = A1(:,:,2);

subset_B = A1(:,:,3);

%CALCULATE MAHALANOBIS DISTANCE FOR THE RED, BLUE AND GREEN COMPONENTS OF THE WHOLE IMAGE AND ALSO THE

%RED,GREEN AND BLUE COMPONENTS OF THE SMALL SUBSET

mahal_dist(:,3) = mahal(double([R(:),G(:),B(:)]),double([subset_R(:),subset_G(:),subset_B(:)])); %Pink

%CROP THE SMALL SUBSET OF THE OTHER PARTS

A1 = imcrop(A,[505.5 389.5 49 33]);

subset_R = A1(:,:,1);

subset_G = A1(:,:,2);

subset_B = A1(:,:,3);

%CALCULATE MAHALANOBIS DISTANCE FOR THE RED, BLUE AND GREEN COMPONENTS OF THE WHOLE IMAGE AND ALSO THE

%RED,GREEN AND BLUE COMPONENTS OF THE SMALL SUBSET

mahal_dist(:,4) = mahal(double([R(:),G(:),B(:)]),double([subset_R(:),subset_G(:),subset_B(:)]));

%FIND THE MINIMUM VALUE AND GIVE A CLUSTER NUMBER

[val,ind]=min(mahal_dist,[],2);

mask = zeros(size(B));

for k=1:size(mahal_dist,2)

    mask(ind(:)==k)=k;

end

figure, subplot(121),imagesc(A); title('RGB IMAGE'); subplot(122),imagesc(mask);colormap(jet);colorbar;title('CLUSTERS');

figure,

for k=1:size(mahal_dist,2)

    subplot(2,2,k);

    imshow(uint8(double(A).*logical(mask==k)));

   

end

 You can also revisit ‘K_means Clustering for RGB image’ and compare both the methods.