Vectorize calculating a co-variance matrix for every RGB pixel in an image

Hi, I am looking to calculate a variance-covariance matrix for every pixels RGB value in an image for each cluster, k. I then sum the variance-covariance matrices over all pixels and normalize it resulting in k variance-covariance matrices.

I currently have this in a for loop which is very slow, so I was wondering would anyone have any idea as to how to vectorize the 'for count4=1:n...' loop?

image=reshape(image,height*width,3);

%posterior is an n*k matrix where n is the number of pixels and k %is the number of classes holding the probability of pixel n %belonging to cluster k

for count3=1:k
         %calculate new weights
         newWeights(count3)=1/m*n*sum(posterior(:,count3),1);

           %calculate new mu
           postRepMat=repmat(posterior(:,count3),1,3);
           newMu(count3,:)=sum(postRepMat.*image)/sum(posterior(:,count3));

           %calculate new sigma
           %NB Formula is from matlab cov.m file
           %indivdual sigma needed as calculate a covariance matrix for each
           %RGB observation
           individualSigma=zeros(3,3,n);
           %subtract new mu from image
           xc = bsxfun(@minus,image,newMu(count3,:));
           %create cov matrix,

           %create individual covariance matrix for each observation
           for count4=1:n
               individualSigma(:,:,count4)=(xc(count4,:)'*xc(count4,:))*posterior(count4,count3);
           end

           newSigma(:,:,count3)=sum(individualSigma,3)/sum(posterior(:,count3));

    end

regards, John

Answer 1

[Andrei Bobrov]

C = arrayfun(@(i1)xc(i1,:)'*xc(i1,:)*posterior(i1,count3),1:n,'un',0);
individualSigma = cat(3,C{:});

However, one line

individualSigma = reshape(cell2mat(arrayfun(@(i1)xc(i1,:)'*xc(i1,:)*...
                                   posterior(i1,count3),1:n,'un',0)),3,3,[]);

[John]

Hi Andrei, thanks for this response. Unfortunately it is more computationally expensive than the original approach using for loops. For an RGB image with 420360 pixels (n), a for loop takes 21 seconds whilst the methods using arrayfun take 40 and 43 seconds respectively.

regards,

John

[Andrei Bobrov]

Of course with large arrays loop 'for ... end' functions more effective then 'arrayfun' and 'cellfun', ie I showed how not to do...

Answer 2

[Sean de Wolski]

FEX: mtimesx

Reshape your matrix so that it lies along the 3rd dimension both as a column-slice and a row-slice, then multiply directly using mtimesx.