Average over pixels in python-numpy matrix

Question

Let's say I have a 5x5 matrix:

arr = np.arange(25).reshape((5,5))

array([[ 0,  1,  2,  3,  4],
   [ 5,  6,  7,  8,  9],
   [10, 11, 12, 13, 14],
   [15, 16, 17, 18, 19],
   [20, 21, 22, 23, 24]])

and I want to make a 3x3 matrix out of it by averaging over it.

this should be done in such a way, that the blue pixel should be made out of the included black pixels, the number weighted with the area within the blue pixel.

That means that of the vlaue of the second black pixel (value 1) 3/5(?) should be added to the first blue pixel, 2/5 to the second blue pixel

thanks

Answer 1

It doesn't seem to me like you know what you really want. But what you describe for the top left cornber can be expanded to the whole array with scipy.signal.correlate, although it produces a 4x4 output, and you have the math wrong:

>>> import scipy.signal
>>> scipy.signal.correlate(np.arange(25).reshape(5, 5),
...                        [[1, 3/5], [3/5, 9/25]], 'valid') / 4
array([[  1.44,   2.08,   2.72,   3.36],
       [  4.64,   5.28,   5.92,   6.56],
       [  7.84,   8.48,   9.12,   9.76],
       [ 11.04,  11.68,  12.32,  12.96]])

Answer 2

It seems that you want to resample your image so that it's a different size. If so, then you could use scipy.ndimage.zoom:

import numpy as np
import scipy.ndimage

arr = np.arange(25).reshape((5,5))

resized_arr = scipy.ndimage.zoom(arr, 3. / 5)

print resized_arr.shape
print resized_arr

outputs:

(3, 3)

[[ 0  2  4]
 [10 12 14]
 [20 22 24]]

The idea is that you fit a function to the 2d surface defined by the pixels in your image -- in the case of zoom, the function is a parametric spline fit. Then once you have a function fit to your surface, you can obtain samples at whatever grid points you wish.

You can also use more complex functions to fit the original image. Check out scikits.samplerate for a nice wrapper over the "source rabbit code," a full-featured resampling library.