How do I dissolve a pattern in a numpy array?

Question

Excuse the strange title, I couldn't really think of a suitable wording.

Say I have an array like:

arr = [[0 1 1 1 1 1 1 1 0],
       [0 0 1 1 1 1 1 0 0],
       [0 0 0 1 1 1 0 0 0],
       [0 0 0 0 1 0 0 0 0],
       [0 0 0 0 0 0 0 0 0]]

I'm looking to "etch" away the 1s that touch 0s, which would result in:

arr = [[0 0 1 1 1 1 1 0 0],
       [0 0 0 1 1 1 0 0 0],
       [0 0 0 0 1 0 0 0 0],
       [0 0 0 0 0 0 0 0 0],
       [0 0 0 0 0 0 0 0 0]] .

I've tried a few things with the likes of np.roll but it seems inefficient (and has edge effects). Is there a nice short way of doing this?

Answer 1

Morpholocial erosion can be used here.

Morphological erosion sets a pixel at (i, j) to the minimum over all pixels in the neighborhood centered at (i, j). source

data
Out[39]: 
array([[0, 1, 1, 1, 1, 1, 1, 1, 0],
       [0, 0, 1, 1, 1, 1, 1, 0, 0],
       [0, 0, 0, 1, 1, 1, 0, 0, 0],
       [0, 0, 0, 0, 1, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0]])

structure
Out[40]: 
array([[0, 1, 0],
       [1, 1, 1],
       [0, 1, 0]])

eroded = binary_erosion(data, structure, border_value=1).astype(int)

eroded
Out[42]: 
array([[0, 0, 1, 1, 1, 1, 1, 0, 0],
       [0, 0, 0, 1, 1, 1, 0, 0, 0],
       [0, 0, 0, 0, 1, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0]])

Answer 2

Consider convolving with a cross-shaped kernel.

import numpy as np
from scipy.signal import convolve2d
kernel = np.array([[0,1,0], [1,1,1], [0,1,0]])
mask = convolve2d(arr, kernel, boundary='symm', mode='same')
arr[mask!=5] = 0

This method works correctly for all inputs:

In [143]: D = np.random.random_integers(0,1, (5,5))

In [144]: D2 = D.copy()

In [145]: mask = convolve2d(D, kernel, boundary='symm', mode='same')

In [146]: D2[mask!=5] = 0

In [147]: binary_erosion(D, kernel2, border_value=1).astype(int)
Out[147]: 
array([[0, 1, 0, 1, 0],
       [0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0]])

In [148]: D2
Out[148]: 
array([[0, 0, 0, 1, 0],
       [0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0]])

In [149]: D
Out[149]: 
array([[1, 0, 1, 1, 1],
       [0, 1, 0, 1, 0],
       [0, 1, 0, 1, 0],
       [0, 0, 1, 1, 0],
       [1, 0, 1, 0, 0]])
In [150]: kernel
Out[150]: 
array([[0, 1, 0],
       [1, 1, 1],
       [0, 1, 0]])

In [151]: kernel2
Out[151]: 
array([[0, 1, 0],
       [1, 0, 1],
       [0, 1, 0]])

Look into the corners to see the differences.