Matlab 3D矩阵通过2D矩阵矢量化对三维进行转换

Question

I have 3D matrix A of size N, M, 3 and 2D transformation T of size 3, 3 that I apply to the 3rd dimension of matrix A . In case it's relevant, this 3D matrix is an RGB image.

My current solution looks like this:

for i = 1:N
    for j = 1:M
        A(i, j, :) = T * [A(i, j, r); A(i, j, g); A(i, j, b)];
    end
end

But I'm curious if there is a way to vectorize it?

Answer 1

You can try this. First switch the dimensions so the channel will be the first:

B = permute(A,[3,1,2])

Then reshape B to be a matrix of size 3xN*M:

C = reshape(B,3,[])

And now compute a matrix multiplication:

D = T*C;

You then need to reshape and permute back:

E = permute(reshape(D,3,M,N),[2,3,1])

I didn't test it so there may be something missing, but generally this should work (and fast!)