Scipy label dilation

Question

Similar to my question about eroding a scipy label array, I'm trying to dilate label regions.

The tricky part is keeping the different regions from "invading each other."

Starting with A, how can I get something like B?

A = array([[0, 0, 0, 0, 0, 0, 0, 0],
           [0, 1, 1, 2, 2, 0, 0, 0],
           [0, 1, 1, 2, 2, 0, 3, 3],
           [0, 0, 0, 0, 0, 0, 3, 3],
           [0, 0, 0, 0, 0, 0, 3, 3],
           [0, 0, 0, 0, 0, 0, 0, 0],
           [0, 0, 0, 0, 0, 0, 0, 0],
           [0, 0, 0, 0, 0, 0, 0, 0]])

B = array([[1, 1, 1, 2, 2, 2, 0, 0],
           [1, 1, 1, 2, 2, 2, 3, 3],
           [1, 1, 1, 2, 2, 2, 3, 3],
           [1, 1, 1, 2, 2, 3, 3, 3],
           [0, 0, 0, 0, 0, 3, 3, 3],
           [0, 0, 0, 0, 0, 3, 3, 3],
           [0, 0, 0, 0, 0, 0, 0, 0],
           [0, 0, 0, 0, 0, 0, 0, 0]])

There are some cases that are ambiguous, and I'm not quite sure how it should behave, but I think what I'm after is clear.

Answer 1

One option is to just use a maximum filter and then reset any regions that were "invaded".

As an example:

import numpy as np
import scipy.ndimage as ndimage

A = np.array([[0, 0, 0, 0, 0, 0, 0, 0],
              [0, 1, 1, 2, 2, 0, 0, 0],
              [0, 1, 1, 2, 2, 0, 3, 3],
              [0, 0, 0, 0, 0, 0, 3, 3],
              [0, 0, 0, 0, 0, 0, 3, 3],
              [0, 0, 0, 0, 0, 0, 0, 0],
              [0, 0, 0, 0, 0, 0, 0, 0],
              [0, 0, 0, 0, 0, 0, 0, 0]])

B = ndimage.maximum_filter(A, 3)
B[A != 0] = A[A != 0]

print B

This yields:

[[1 1 2 2 2 2 0 0]
 [1 1 1 2 2 3 3 3]
 [1 1 1 2 2 3 3 3]
 [1 1 2 2 2 3 3 3]
 [0 0 0 0 0 3 3 3]
 [0 0 0 0 0 3 3 3]
 [0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0]]

In the dilated areas, the biggest number always "wins". It's one approach, at any rate.