[FIXED] Summing each 3x3 window of a M*N matrix, into a M/3*N/3 matrix with numpy

Issue

I'm trying to implement a function that would sum (or eventually average) Each 3x3 window of a given matrix, and create a matrix 9x smaller with the result of each window.

I can't figure out an efficient and concise way to do this with numpy.

Any ideas ?

Thank you!

Solution

The simplest numpy only approach, which does much less work than convolution and will therefore be likely faster than filter based methods, is to resize your original array to one with extra dimensions, then reduce it back to normal by summing over the new dimensions:

>>> arr = np.arange(108).reshape(9, 12)
>>> rows, cols = arr.shape
>>> arr.reshape(rows//3, 3, cols//3, 3).sum(axis=(1, 3))
array([[117, 144, 171, 198],
       [441, 468, 495, 522],
       [765, 792, 819, 846]])

If you wanted the mean, you would simply divide the resulting array by the number of elements:

>>> arr.reshape(rows//3, 3, cols//3, 3).sum(axis=(1, 3)) / 9
array([[ 13.,  16.,  19.,  22.],
       [ 49.,  52.,  55.,  58.],
       [ 85.,  88.,  91.,  94.]])

This method only works if your array has a shape which is itself a multiple of 3.

Answered By - Jaime