The key is recognizing that:
diag(R*A*R') == sum(R*A.*R,2);
Try the following code. It does exactly what your code does, using only one loop, and runs 100 times faster.
clc
I = imread('peppers.png'); I = double(I)/255;
[height,width,~] = size(I);
image = I;
noOfClasses = 5;
pDet = rand(noOfClasses,1);
pInv = rand(3,3,noOfClasses);
pMean = rand(noOfClasses,3);
% ----------------------The original way----------------------
disp('First do it the original way...')
tic
post(height,width,noOfClasses) = 0;
for count=1:height
for count2=1:width
%pixel vector x to be classified
x=[image(count,count2,1);image(count,count2,2);image(count,count2,3)];
%for each class
for count3=1:noOfClasses
detZ = pDet(count3);
invZ = pInv(:,:,count3);
y=(pMean(count3,:)');
%calculate the likelihood
post(count,count2,count3)= 1/sqrt((2*pi)^2*detZ) * exp(-(x(:,1)-y)'*invZ*(x(:,1)-y)/2);
end
end
end
originalway = toc
% ----------------------The fast way----------------------
disp('Now do it the fast way...')
RGB = reshape(I,[],3);
%[colorlist, ~, ind] = unique(RGB,'rows');
colorlist = RGB;
C = 1./sqrt((2*pi)^2*pDet);
ncol = size(colorlist,1);
tic
post2(height,width,noOfClasses) = 0;
for count3=1:noOfClasses
invZ = pInv(:,:,count3);
y=(pMean(count3,:)');
colorlistY = bsxfun(@minus,colorlist,y');
post2(:,:,count3) = reshape(C(count3) * exp(-sum(colorlistY*invZ.*colorlistY,2)/2) , height, width);
end
fasterway = toc
ARETHEYTHESAME = isequal(post,post2)
