Double sum of a series
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I am trying to implement the 2D convolution formula in Matlab without using conv2() built-in function. The formula is this:
where z is an [N1xN2] matrix, x is an [M1xM2] matrix and y is a [P1xP2] matrix.
N1=M1+P1-1 and N2=M2+P2-1
I did it with four for-loops but it is really slow for large matrices. Is there an faster way to do it? Here is my code:
[M1,M2] = size(x);
[P1,P2] = size(y);
N1 = M1+P1-1;
N2 = M2+P2-1;
z = zeros([N1 N2]);
y = padarray(y,[N1-P1 N2-P2],'post');
sum1 = 0;
if(n1-k1+1>0 && n2-k2+1>0)
sum1 = sum1 + x(k1,k2)*y(n1-k1+1,n2-k2+1);
z(n1,n2) = sum1;
Andrei Bobrov on 20 Apr 2016
function out = conv2_without_conv2(xinp,yinp)
sx = size(xinp);
sy = size(yinp);
x = xinp(end:-1:1,end:-1:1);
k = sx-1;
so = sy + k*2;
y = zeros(so);
y(sx(1):end-sx(1)+1,sx(2):end-sx(2)+1) = yinp;
i0 = reshape(1:numel(y),size(y));
ii = i0(1:end-k(1),1:end-k(2));
i1 = bsxfun(@plus,(0:sx(1)-1)',(0:sx(2)-1)*so(1));
out = reshape(y(bsxfun(@plus,ii(:),i1(:)'))*x(:),sx+sy-1);
More Answers (1)
Alessandro Masullo on 20 Apr 2016
Edited: Alessandro Masullo on 20 Apr 2016
Why do you want to implement you own convolution when Matlab already has a very fast function for that?
For loops are slow.
Nested for loops are very slow.
Nested for loops in nested for loops are deadly slow.
If you really want to implement your own function for the convolution, and if you really want it to be fast, you need to code it in a mex file. The question is, do you really need your own implementation of conv2?