DEEPAK SAINI DEEPAK SAINI - 29 days ago 10
Python Question

Weighted array of neighbors for each element in a numpy array

I have a numpy array(A) and a weights matrix(say m, which is sort of filter). I want to apply this filter at each element of A and get an array of neighbors multiplied by m for each element of A.

For example, if m is a 3x3 kernel, then we get:

for each (i,j), A[i,j] --> array([A[i-1,j-1]*m[0,0], A[i-1,j]*m[0,1],...,A[i+1,j+1]*m[2,2]])

So, output will have one dimension more than A.
Preferably for border cases, I need to consider partial filter(equivalent to padding with zeros). Is there any way to do this efficiently?

Answer

Here's an approach using skimage's view_as_windows that gives us sliding windows of required kernel shape -

from skimage.util import view_as_windows as viewW

# Pad with one layer of zeros around input array 
a1 = np.lib.pad(a, (1,1), 'constant', constant_values=0)

# Create 3x3 sliding windows for each elem and multiply with m.
# Reshape each window as a 9 elem list as per requirement.
out = (viewW(a1,[3,3])*m).reshape(a.shape + (9,))

Sample run :

1] Input array -

In [64]: a            
Out[64]: 
array([[75, 46, 74, 72, 96],
       [44, 72, 41, 81, 50],
       [16, 70, 22, 19, 49],
       [87, 74, 78, 66, 49]])

2] Input array padded -

In [65]: a1  
Out[65]: 
array([[ 0,  0,  0,  0,  0,  0,  0],
       [ 0, 75, 46, 74, 72, 96,  0],
       [ 0, 44, 72, 41, 81, 50,  0],
       [ 0, 16, 70, 22, 19, 49,  0],
       [ 0, 87, 74, 78, 66, 49,  0],
       [ 0,  0,  0,  0,  0,  0,  0]])

3] 3D Output array -

In [66]: out       
Out[66]: 
array([[[  0,   0,   0,   0, 450, 276,   0, 220, 504],
        [  0,   0,   0, 450, 276, 444, 352, 360, 287],
        [  0,   0,   0, 276, 444, 432, 576, 205, 567],
        [  0,   0,   0, 444, 432, 576, 328, 405, 350],
        [  0,   0,   0, 432, 576,   0, 648, 250,   0]],

       [[  0, 300, 276,   0, 264, 432,   0,  80, 490],
        [375, 184, 444, 264, 432, 246, 128, 350, 154],
        [230, 296, 432, 432, 246, 486, 560, 110, 133],
        [370, 288, 576, 246, 486, 300, 176,  95, 343],
        [360, 384,   0, 486, 300,   0, 152, 245,   0]],

       [[  0, 176, 432,   0,  96, 420,   0, 435, 518],
        [220, 288, 246,  96, 420, 132, 696, 370, 546],
        [360, 164, 486, 420, 132, 114, 592, 390, 462],
        [205, 324, 300, 132, 114, 294, 624, 330, 343],
        [405, 200,   0, 114, 294,   0, 528, 245,   0]],

       [[  0,  64, 420,   0, 522, 444,   0,   0,   0],
        [ 80, 280, 132, 522, 444, 468,   0,   0,   0],
        [350,  88, 114, 444, 468, 396,   0,   0,   0],
        [110,  76, 294, 468, 396, 294,   0,   0,   0],
        [ 95, 196,   0, 396, 294,   0,   0,   0,   0]]])

4] Let's verify results. The first sliding window on un-padded region would be a[:3,:3]. Let's multiply that against m. After multiplication, it should be same as out[1,1,:] -

In [67]: a[:3,:3]*m
Out[67]: 
array([[375, 184, 444],
       [264, 432, 246],
       [128, 350, 154]])

In [68]: out[1,1,:]
Out[68]: array([375, 184, 444, 264, 432, 246, 128, 350, 154])

It's worth mentioning here that the 3D array of sliding windows are simply views into the array and as such are really efficient on further operations involving those -

In [75]: np.may_share_memory(a1,viewW(a1,[3,3]))
Out[75]: True