Question

I have 2D numpy arrays and a center with some coordinates (i, j) (coordinates mean row and column). I need to sum
up all array elements at the same distance from the center (simple
euklidean distance) for each possible distance from 0 to the edge of the image, i.e. result is an 1D array where the 0th element gives the sum of pixels in distance 0 from center (i.e. just the center), 1st element is the sum of all pixels at distance 1 pixel and so on.

My feeling is that this should be possible to do without a for loop,
but unfortunately I don’t know enough matrix python tricks to figure
this out.

Thank you very much!

Answer 1

You can use np.bincount…

a = np.random.random((20, 22))

def distance(array, xpos, ypos):
    # probably a gazillion methods to create the actual distances...
    # if you array is large and you are only interested to a certain size
    # you sould probably slice out a smaller one first of course.
    dists = np.sqrt(np.arange(-xpos, array.shape [0]-xpos, dtype=float)[:,None]**2
          + np.arange(-ypos, array.shape [1]-ypos, dtype=float)[None,:]**2)
    return dists

# Prepare which bins to use:
dists = distance(a, 10, 11).astype(int)

# Do a bincount with weights.
result = np.bincount(dists.flat, weights=a.flat)
# and add them up:
result = np.add.accumulate(result)

And result is an array with result[distance] giving sum over all values with smaller or equal distances.