I have a function in the following form:
function Out = DecideIfAPixelIsWithinAnEllipsoidalClass(pixel,means,VarianceCovarianceMatrix)
ellipsoid = (pixel-means)'*(VarianceCovarianceMatrix^(-1))*(pixel-means);
if ellipsoid <= 1
Out = 1;
else
Out = 0;
end
end
I am doing remote-sensing processes with matlab and I want to classify a LandSatTM images.This picture has 7 bands and is 2048*2048.So I stored them in 3 dimentinal 2048*2048*7 matrix.in this function means is a 7*1 matrix calculated earlier using the sample of the class in a function named ExtractStatisticalParameters and VarianceCovarianceMatrix is a 7*7 matrix in fact you see that:
ellipsoid = (pixel-means)'*(VarianceCovarianceMatrix^(-1))*(pixel-means);
is the equation of an ellipsoid.My problem is that each time you can pass a single pixel(it is a 7*1 vector where each row is the value of the pixel in a seperated band) to this function so I need to write a loop like this:
for k1=1:2048
for k2=1:2048
pixel(:,1)=image(k1,k2,:);
Out = DecideIfAPixelIsWithinAnEllipsoidalClass(pixel,means,VarianceCovarianceMatrix);
end
end
and you know it will take alot of time and energy of the system.Can you suggest me a way to reduce the pressure applied on the systam?
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
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.
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