numpy: 1d histogram based on 2d-pixel euclidean distance from center - numpy

Question

I am using python, with scipy, numpy, etc.
I want to compute the histogram of intensity values of a grayscale image, based on the distance of the pixels to the center of mass of the image. The following solution works, but is very slow:
import matplotlib.pyplot as plt
from scipy import ndimage
import numpy as np
import math
# img is a 2-dimensionsl numpy array
img = np.random.rand(300, 300)
# center of mass of the pixels is easy to get
centerOfMass = np.array(list(ndimage.measurements.center_of_mass(img)))
# declare histogram buckets
histogram = np.zeros(100)
# declare histogram range, which is half the diagonal length of the image, enough in this case.
maxDist = len(img)/math.sqrt(2.0)
# size of the bucket might be less than the width of a pixel, which is fine.
bucketSize = maxDist/len(histogram)
# fill the histogram buckets
for i in range(len(img)):
for j in range(len(img[i])):
dist = np.linalg.norm(centerOfMass - np.array([i,j]))
if(dist/bucketSize < len(histogram)):
histogram[int(dist/bucketSize)] += img[i, j]
# plot the img array
plt.subplot(121)
imgplot = plt.imshow(img)
imgplot.set_cmap('hot')
plt.colorbar()
plt.draw()
# plot the histogram
plt.subplot(122)
plt.plot(histogram)
plt.draw()
plt.show()
As I said before, this works, but is very slow because you are not supposed to double-loop arrays in this manner in numpy. Is there a more efficient way of doing the same thing? I assume I need to apply some function on all the array elements, but I need the index coordinates as well. How can I do that? Currently it takes several seconds for a 1kx1k image, which is ridiculously slow.

Answer 1

All numpy binning functions (bincount, histogram, histogram2d... have a weights keyword argument you can use to do really weird things, such as yours. This is how I would do it:
rows, cols = 300, 300
img = np.random.rand(rows, cols)
# calculate center of mass position
row_com = np.sum(np.arange(rows)[:, None] * img) / np.sum(img)
col_com = np.sum(np.arange(cols) * img) / np.sum(img)
# create array of distances to center of mass
dist = np.sqrt(((np.arange(rows) - row_com)**2)[:, None] +
(np.arange(cols) - col_com)**2)
# build histogram, with intensities as weights
bins = 100
hist, edges = np.histogram(dist, bins=bins, weights=img)
# to reproduce your exact results, you must specify the bin edges
bins = np.linspace(0, len(img)/math.sqrt(2.0), 101)
hist2, edges2 = np.histogram(dist, bins=bins, weights=img)
Haven't timed both approaches, but judging from the delay when running both from the terminal, this is noticeably faster.