The fact that applying of a median filter with the window size 1 will not change the array gives us a freedom to apply the median filter row-wise or column-wise.

For example, this code

from scipy.ndimage import median_filter
import numpy as np

arr = np.array([[1., 2., 3.], [4., 5., 6.], [7., 8., 9.]])
median_filter(arr, size=3, cval=0, mode='constant')
#with cval=0, mode='constant' we set that input array is extended with zeros 
#when window overlaps edges, just for visibility and ease of calculation

outputs an expected filtered with window (3, 3) array

array([[0., 2., 0.],
       [2., 5., 3.],
       [0., 5., 0.]])

because median_filter automatically extends the size to all dimensions, so the same effect we can get with:

median_filter(arr, size=(3, 3), cval=0, mode='constant')

Now, we can also apply median_filter row-wise with setting 1 to the first element of size

median_filter(arr, size=(1, 3), cval=0, mode='constant')

Output:

array([[1., 2., 2.],
       [4., 5., 5.],
       [7., 8., 8.]])

And column-wise with the same logic

median_filter(arr, size=(3, 1), cval=0, mode='constant')

Output:

array([[1., 2., 3.],
       [4., 5., 6.],
       [4., 5., 6.]])