Matlab image filtering with vector coefficients

Question

I'm trying to create a filter that uses vectors as coefficients.

A typical kernel used in imfilter looks like:

0  1  0
1 -4  1
0  1  0

Where each element is a scalar, and the filtering basically takes all windows of 3x3 of the image (MxN), multiplies the pixel values by the matching coefficients and sums all products to place the output pixel.

I would like to extend this, so that each element in the kernel is not a scalar, but actually a vector (Px1). This makes the kernel something like 3x3xP. The rest of the functionality should be the same: Multiply the coefficient (vector) by the image pixel (scalar * vector), sum all products (sum of vectors of same dimensions), and the output matrix should have the dimensions of (MxNxP).

I know that imfilter doesn't support that and produces a result of (MxN).

Is there another Matlab function that does this, or do I need to implement from scratch?

Some comments: The image is usually logical (0 or 1), and some of the filter elements can be zero, and not contribute to the sum.

Answer 1

Without another solution, I would brute-force it. If each vector in your 3x3 filter has P elements, I'd apply each element independently and sum the result.

%load my image
im = imread(fname);

%define my kernel
h = zeros(3,3,P);  % P elements deep
h(:,:,1) = [0  1  0; 1 -4  1; 0  1  0];  %first element my kernel
h(:,:,2) = [0.2  1.5  0.2; 1.5 -6  1.5; 0.2  1.5  0.2]; %second element
%keep adding elements until you get your P elements

%loop over each element in your kernel
output = zeros(size(im))
for I=1:size(h,3)
    output = output + imfilter(im,h(:,:,I));  %apply filter and accumulate
end