MATLAB: Vectorize a per-pixel classification

classificationimage processingvectorization

Hi, I am using the following code to calculate the likelihood of every pixel x in a RGB image, belonging to a given class;
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= 1/sqrt((2*pi)^2*detZ) * exp(-(x(:,1)-y)'*invZ*(x(:,1)-y)/2);
                ......
The application is classification of video frames and so the current approach using for loops is impractical as it is very slow.
Any suggestions?
thanks, John

Best Answer

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)
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