Vectorize for loop: corr2(A(:,:,i),B(:,:,i))

Hi, I am trying to accelerate a function and am unable to perform this myself, so I am hoping for your help.

I have a set of 10.000 small images (64x64), and I need to calculate the correlation coefficient for each of these images. This is the code:

clear all
clc
close all

A=rand(64,64,10000);
B=rand(64,64,10000);
corr_result=zeros(1,1,size(A,3));
tic
for i=1:size(A,3)
    corr_result(i)=corr2(A(:,:,i),B(:,:,i));
end
toc

I found this, it results in a 64x64x1 matrix, but I need a 1x1x10000 matrix.... Thanks for your input!!

[Deepak Gupta]

I ran this code and got a matrix of size 64x64x10000 matrix. Don't know what's the problem.

[Ameer Hamza]

but I need a 1x1x10000 matrix

Can you explain how? Shouldn't it be 64x64x10000?

[William Thielicke]

Sorry guys, the code was updated shortly after I posted this question. When you run it like it is posted above, you get a 1x1x10000 matrix. So for each of the 10000 image pairs, I get one correlation coefficient - which is what I want.

[Ameer Hamza]

I think this is already as efficient as it can get in MATLAB. After JIT optimizations, for-loops are not as slow as one might think.

[William Thielicke]

But Matlab is only using 50% of my CPU during this operation. I bet there is a faster way...

Answer 1

[Bruno Luong]

If you have R2020b, you mght try to vectorize with pagemtimes function (or use mtimesx from File exchange)

meanA = mean(A,[1 2]);
meanB = mean(B,[1 2]);
Ac = A-meanA;
Bc = B-meanB;
Ac = reshape(Ac,[],1,size(A,3));
Bc = reshape(Bc,[],1,size(B,3));
% psfun = @(a,b) sum(a.*b,1);
psfun = @(a,b) pagemtimes(a,'transpose',b,'none');
C = psfun(Ac,Bc)./sqrt(psfun(Ac,Ac).*psfun(Bc,Bc))

[William Thielicke]

Thank you, your solution is 3 - 4 times faster, and gives the identical result:

[William Thielicke]

... but beware when you hit the limit of your RAM.... then it suddenly becomes 7 times slower. Is there a way to predict which method is faster BEFORE doing the calculation? I guess it has something to do with the memory used by the variables and the available RAM.

[Bruno Luong]

Divide the calculation into a chunks that do not exeed your PC ram, eg 8e4 images.