Matlab: How to vectorize a nested loop over a 2D set of vectors

Question

I have a function in the following form:

function Out = DecideIfAPixelIsWithinAnEllipsoidalClass(pixel,means,VarianceCovarianceMatrix)  
   ellipsoid = (pi         


        

Answer 1

No need for loops!

pMinusMean = bsxfun( @minus, reshape( image, [], 7 ), means' ); %//' subtract means from all pixes
iCv = inv( arianceCovarianceMatrix );
ell = sum( (pMinusMean * iCv ) .* pminusMean, 2 ); % note the .* the second time!
Out = reshape( ell <= 1, size(image(:,:,1)) ); % out is 2048-by-2048 logical image

Update:

After a (somewhat heated) debate in the comments below I add a correction made by Rody Oldenhuis:

pMinusMean = bsxfun( @minus, reshape( image, [], 7 ), means' ); %//' subtract means from all pixes
ell = sum( (pMinusMean / varianceCovarianceMatrix ) .* pminusMean, 2 ); % note the .* the second time!
Out = reshape( ell <= 1, size(image(:,:,1)) );

The key issue in this change is that Matlab's inv() is poorly implemented and it is best to use mldivide and mrdivide (operators / and \) instead.