summation of a matrix inside circle

Hello,

I have 2D NxN matrix array and I want to get summation of data inside circle from center.

The size of circle is varied from smallest i.e. one pixel at the center to largest i.e. N/2

I want to plot summation w.r.t. circle.

Thanks,

[DGM]

Is N always odd? Is it always even? Could it be either?

Answer 1

[DGM]

This should work regardless of whether N is odd or even.

s = 100;
A = ones(s); % test array

% build distance map
rmax = s/2 - 0.5;
x = linspace(-rmax,rmax,s);
D = sqrt(x.^2 + x.'.^2);

r = 0:ceil(D(1,floor(s/2)));
circint = zeros(1,numel(r));
for rind = 1:numel(r)
    circint(rind) = sum(A(D<=r(rind)));
end
plot(r,circint)

[JK]

any thought on even case?

[DGM]

I modified it. Bear in mind that there is no center pixel in an array with even geometry. The center four pixels are 1/sqrt(2) away from the center. Consequently, the first element of the output is zero.

Similarly, the pixels straddling the midpoints of the edges of a 10x10 array are not at a radius of 5px. They're at a radius of 4.5227px. As the radius vector in this example is integer-valued, you can either choose to stop short at 4px or go a bit too far (5px). I chose to go to 5px. If you want to stop short in the even case, you can remove the ceil() from the definition of r.