How to change Euclidean distance to Mahalanobis distance in my MATLAB code? - matlab

Question

I am trying to segment an image for a given k value using k-means clustering algorithm.
I want to change the distance calculation from Euclidean to Mahalanobis distance But I cannot implement the formula to my existing code because it has three dimensional array.
First I convert RGB image into HSL space. Then I label the pixels after distance calculation. In the last step I convert HSL image back into RGB space.
nC = uint8(input('Enter cluster number: '));
iRGB = double(imread('Bird.png'));
tic
iHSL = rgb2hsl(iRGB/255);
[ro co bd ] = size(iHSL);
% Randomly assign cluster positions
Cs = [randi(ro, nC,1) randi(co, nC,1)];
%create array for labels
Ls = zeros(ro, co);
%create another array for comparison of labels
prev_Ls = ones(ro, co);
distances = zeros( 1, nC );
kcenter = zeros(nC, 3);
for k=1:nC
kcenter(k,:) = iHSL(kcenter(k),kcenter(k,2),:);
end
while (true)
prev_Ls = Ls;
for r = 1:ro
for c = 1:co
for k = 1:nC
distances(k) = sqrt(((iHSL(r,c,1) - kcenter(k,1))^2 +...
(iHSL(r,c,2) - kcenter(k,2))^2 +...
(iHSL(r,c,3) - kcenter(k,3))^2));
end
d = find(distances(:) == min(distances));
Ls(r,c) = d(1);
end
end
H = zeros(1,nC);
S = zeros(1,nC);
L = zeros(1,nC);
cnt = zeros(1,nC);
for r = 1:ro
for c = 1:co
H( Ls(r,c) ) = H( Ls(r,c) ) + iHSL(r,c,1);
S( Ls(r,c) ) = S( Ls(r,c) ) + iHSL(r,c,2);
L( Ls(r,c) ) = L( Ls(r,c) ) + iHSL(r,c,3);
cnt( Ls(r,c) ) = cnt( Ls(r,c) ) + 1;
end
end
for k = 1:nC
kcenter(k,1) = H(k) / cnt(k);
kcenter(k,2) = S(k) / cnt(k);
kcenter(k,3) = L(k) / cnt(k);
end
%if prev_labels are equal to current labels break while loop.
if isequal(prev_Ls, Ls)
break;
end
end
for r = 1:ro
for c = 1:co
iHSL(r,c,1) = kcenter(Ls(r,c), 1);
iHSL(r,c,2) = kcenter(Ls(r,c), 2);
iHSL(r,c,3) = kcenter(Ls(r,c), 3);
end
end
result_img = hsl2rgb(iHSL)*255;
toc
figure(1);
subplot(1,2,1);
imshow(uint8(iRGB));
subplot(1,2,2);
imshow(uint8(result_img));
I want to change this formula with mahalanobis distance calculation formula. I have tried mahal(iHSL(r,c,1),kcenter(k,1)) I got Nan result.
All the examples on the Internet are for two dimensional arrays. But I have 3 dimensional.
I have tried to change this line;
distances(k) = sqrt((iHSL(r,c,1) - kcenter(k,1))^2 +...
(iHSL(r,c,2) - kcenter(k,2))^2 +...
(iHSL(r,c,3) - kcenter(k,3))^2);
to;
distances(k) = mahal(kcenter(k,:), iHSL(:,:,1)) + ...
mahal(kcenter(k,:), iHSL(:,:,2)) + ...
mahal(kcenter(k,:), iHSL(:,:,3));
But it gives me an error saying:
Error using mahal (line 34) Requires the inputs to have the same number of columns.
I do not know how to formulate Mahalanobis distance calculation for my 3d array.