Is it possible to convolve a stack of 'images' with a stack equal in amount of different kernels, without a for loop?

The only solutions I found so far is when one uses the same kernel. However, I have a different kernel for each image. Does someone know a smart way to omit a for loop here?

This is how my (super slow) script currently works:

images = randn(5,5,2) % 2 images in z dimension, each 5x5.
kernels = randn(3,3,2) % 2 kernels in z dimension, each 3x3.

% slow for loop method
for ii = size(images,3) % ii loops over images
    images(:,:,ii) = conv2(images(:,:,ii),kernels(:,:,ii),'same')
end

Perhaps a fourier transform could do the job? But I am not so experienced with this.

Thanks in advance!

Answer 1

[Vijeta]

Hi Kevin,

It is possible to convolve a stack of images with a stack of kernels without using a for loop. One way to do this is by using the convn function in MATLAB, which performs N-dimensional convolution.

Here are some links you can refer to:https://www.mathworks.com/help/matlab/ref/conv.html

Thanks.

[Kevin Jansen]

Hi Vijeta,

Thanks for your answer. However, I don't think that is what I am looking for. As far as I know, convn convolves 3D array A with 3D array B, in one go. It does not convolve every slice of array A with every slice of array B, what I would like.

e.g.:

images = randn(5,5,2); % 2 images in z dimension, each 5x5.
kernels = randn(3,3,2); % 2 kernels in z dimension, each 3x3.
imagesCopy = images; % copy for second method (convn)

% --- first method, slow for loop
for ii = size(images,3) % ii loops over images
    images(:,:,ii) = conv2(images(:,:,ii),kernels(:,:,ii),'same');
end

% --- second method, convn
imagesCopy = convn(imagesCopy,kernels,'same');

% --- images and imagesCopy are not the same
isequal(images,imagesCopy)

Thanks for answering though!