How to Avoid for loops in this Matlab code? - matlab

Question

I am attempting to perform Gaussian smoothing on a 2D object in Matlab. Here is a condensed version of my code
[m,n] = size(object);
area = m*n;
x = [1:m]; y = [1:n]; [x,y] = meshgrid(x,y);
z = zeros(size(x));
for i = 1:m,
for j = 1:n,
z = z + object(i,j)*exp(-((x-i).*(x-i) + (y-j).*(y-j)));
end
end
z = z/area;
This code works quite well, but is very slow for large input matrices. I'm wondering if there is a way to make this faster by avoiding the for loops? I've tried thinking of ways to speed this up but I can't seem to figure out anything useful.

Answer 1

Here you have a vectorized form with no loops. But it uses much more memory and depending on the machine can be slower than the loop. However, most of the computing time is used to compute the variable "kernel" that do not depend on the image. Therefore, if you need to process many images of the same size, you have to compute it only once, and then you might have significant savings in time. I repeat here your code first because I fixed some mixing up of x,y,m,n
[m,n] = size(object);
area = m*n;
x = [1:n]; y = [1:m]; [y,x] = meshgrid(x,y);
z = zeros(size(x));
for i = 1:m,
for j = 1:n,
z = z + object(i,j)*exp(-((x-i).*(x-i) + (y-j).*(y-j)));
end
end
z = z/area;
Here is a first vectorized form
xi=bsxfun(#minus,repmat(x(:),1,area),x(:)');
yj=bsxfun(#minus,repmat(y(:),1,area),y(:)');
kernel=exp(-(xi.^2 + yj.^2));
w=kernel*object(:);
w=reshape(w,[m,n])/area;
And an alternative form not using bsxfun
xx=repmat(x(:),1,area);
yy=repmat(y(:),1,area);
xx=xx-xx';
yy=yy-yy';
kernel=exp(-(xx.^2 + yy.^2));
w=kernel*object(:);
w=reshape(w,[m,n])/area;