Most efficient way to calculate radial profile

Question

I need to optimize this part of an image processing application.
It is basically the sum of the pixels binned by their distance from the central spot.

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Answer 1

You can use numpy.histogram to add up all the pixels that appear in a given "ring" (range of values of r from the origin). Each ring is one of the histogram bins. You choose the number of bins depending on how wide you want the rings to be. (Here I found 3 pixel wide rings work well to make the plot not too noisy.)

def radial_profile(data, center):
    y,x = np.indices((data.shape)) # first determine radii of all pixels
    r = np.sqrt((x-center[0])**2+(y-center[1])**2)    

    # radius of the image.
    r_max = np.max(r)  

    ring_brightness, radius = np.histogram(r, weights=data, bins=r_max/3)
    plt.plot(radius[1:], ring_brightness)
    plt.show()

(By the way, if this really needs to be efficient, and there are a lot of images the same size, then everything before the call to np.histogram can be precomputed.)