Perform Local Mean with circular neighboorhod

Hi! I would like to perform a local mean to an image. I am using conv2 function. I know that to compute the local mean of each pixel i may do, for example, something like this:

C = conv2(A, ones(3)/9, 'same')

Where A is the image. This should perform a local mean of a pixel and its 9 surrounding pixels ina 3x3 box.

So, what if I would like to do this local mean calculation but with the surrounding pixels placed in a circle of a certain radius?

I have tried doing the following:

 r = 15;
 x = -r:r;
 y = -r:r;
 [X,Y] = meshgrid(x,y);
 circ = power(X,2) + power(Y,2) < power(r,2);
 kernelMean = double(circ)/(r*2)^2;

So r is the radius and kernelMean would replace ones(3)/9 in the previous example.

Is that correct? I have tried but I am not getting the expected results... May am I doing something wrong?

Thanks!

[Adam]

kernelMean = double(circ)/nnz( circ );

looks like it would be what is needed. You don't have a perfect circle, of course, with pixels so you should get the count of the number of non-zero pixels in your mask rather than trying to use analytical circle geometry.

I haven't tried applying this to an image, but it does at least provide a kernel whose elements sum to 1.