how to Vectorize this for loop?

I am trying to create a full convolution without the conv2 function. For that, i would like to vectorize this nested loop.

 [r,c] = size(A);% size of image A
 [m,n] = size(mask);%size of the mask

 ab=padarray(A,[2 2]); %Padding zeros in the original image
 ab=im2double(ab);

 B = zeros(r+m,c+n);
 for x = 1 : r+m-1
     for y = 1 : n+c-1
         for i = 1 : m
             for j = 1 : n
                 B(x, y) = B(x, y) + (ab(x+i-1, y+j-1) * mask(i, j));
             end
         end
     end
 end

[Jos (10584)]

Why can't you use conv2? (it is rather silly to speed up code that is not optimal)

Another question: why the fixed [2 2] padding?

[Miguel Reina]

Hi Jos, is intended to be for educational purposes. For some students is more difficult to understand some concepts packaged in one function so i want to make it easier for them and also help them with the importance of vectorization in matlab. The padding is for the same reason, to explain what happens with the borders.

Answer 1

[Guillaume]

Well, the vectorised version of your code is to use conv2! Or ifft2 the fft2 product (with suitable padding).

Otherwise, when you're trying to teach the principle of convolutions you use explicit loops as you have.

The only thing you may change would be to replace the two inner loops by a vectorised operation:

for x = 1 : r+m-1
   for y = 1 : n+c-1
      B(x, y) =  sum(ab(x:x+m-1, y:y+m-1) .* mask)
   end
end

I don't understand the fixed size padding. If you're computing a full convolution then you should indeed end up with an array of size size(ab) + size(mask) - 1 but that's because you've padded ab by size(mask).

[Miguel Reina]

There must be a correction, thank you so much !

for x = 1 : r+m-1
 for y = 1 : n+c-1
    B(x, y) =  sum(sum(ab(x:x+m-1, y:y+m-1) .* mask));
 end
end