Vectorization of the forward mapping loop- affine transformation

Hi! I want to vectorize this fragment of code. So basically I want to transform the input image ( input ). The matrix is 3x3 matrix of affine 2D transformation (for example scaling [2 0 0; 0 2 0; 0 0 1]). After forward mapping I got indices of output image ( output ) and I put pixels of input image into output image.

for u=1:size(input,2)
    for v=1:size(input,1)
        indices=ceil((matrix)'*[u;v;1]);
        output(indices(2),indices(1),:)=input(v,u,:);
    end
end

The problem is probably simple, but I don't have any idea how to use vectorization here. This loop is working fine in my program, just want to optimize it.