Image intensity histogram - radial

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I have an image with (reasonable) radial symmetry. I would like to generate an intensity histogram as a function of distance from the origin, i.e. average the intensity over small "rings" and display the mean intensity of each ring.

I wrote the following code, but obviously it's very inefficient due to loop usage. Is there a more elegant solution for this problem, perhaps a built-in one? I haven't found on the web. Thanks.

x = 609; y = 513; % captured from snapshot
distmat = zeros(size(getsnapshot(vid1)));
[r,c] = size(distmat);
for i = 1:r
    for j = 1:c
        distmat(i,j) = sqrt((i-y)^2+(j-x)^2);
    end
end
uni = unique(distmat);
rad = zeros(size(uni));
for i = 1:length(uni);
    rad(i) = sum(avgim(distmat == uni(i))) / length(avgim(distmat == uni(i)));
end
bar(rad)