Scipy ndimage median_filter origin

Question

I have a binary array, say, a = np.random.binomial(n=1, p=1/2, size=(9, 9)). I perform median filtering on it using a 3 x 3 kernel on it, like say, b = nd.median_filter(a, 3). I would expect that this should perform median filter based on the pixel and its eight neighbours. However, I am not sure about the placement of the kernel. The documentation says,

origin : scalar, optional.

The origin parameter controls the placement of the filter. Default 0.0.

If the default were zero, it should be taking the current pixel and the 3 x 3 grid to the right and bottom, no? Shouldn't the default be the center of the footprint? Which in our 3 x 3 example would correspond to (1, 1) as opposed to (0, 0)?

Thanks.

Answer 1

origin says it accepts only a scalar, but for me it also accepts array-like input as also the case for the scipy.ndimage.filters.convolve function. Passing 0 is indeed the center of the footprint. Origin's value is relative to the center. With a 3x3 footprint, you can specify values -1.0 to 1.0. Here are some examples. Notice in the example with origin not specified that the filter is centered as expected.

import numpy as np
import scipy.ndimage

a= np.zeros((5, 5))
a[1:4, 1:4] = np.arange(3*3).reshape((3, 3))

default_out = scipy.ndimage.median_filter(a, size=(3, 3))
shift_pos_x = scipy.ndimage.median_filter(a, size=(3, 3), origin=(0, 1))
shift_neg_x = scipy.ndimage.median_filter(a, size=(3, 3), origin=(0, -1))

print(a)
print(default_out)
print(shift_pos_x)
print(shift_neg_x)

Output:

Input Array:

[[ 0.  0.  0.  0.  0.]
 [ 0.  0.  1.  2.  0.]
 [ 0.  3.  4.  5.  0.]
 [ 0.  6.  7.  8.  0.]
 [ 0.  0.  0.  0.  0.]]

Centered Output:

[[ 0.  0.  0.  0.  0.]
 [ 0.  0.  1.  0.  0.]
 [ 0.  1.  4.  2.  0.]
 [ 0.  0.  4.  0.  0.]
 [ 0.  0.  0.  0.  0.]]

Shifted To Right Output:

[[ 0.  0.  0.  0.  0.]
 [ 0.  0.  0.  1.  0.]
 [ 0.  0.  1.  4.  2.]
 [ 0.  0.  0.  4.  0.]
 [ 0.  0.  0.  0.  0.]]

Shifted To Left Output:

[[ 0.  0.  0.  0.  0.]
 [ 0.  1.  0.  0.  0.]
 [ 1.  4.  2.  0.  0.]
 [ 0.  4.  0.  0.  0.]
 [ 0.  0.  0.  0.  0.]]