Question

I’ve got an array of objects labeled with scipy.ndimage.measurements.label called Labels. I’ve got other array Data containing stuff related to Labels. How can I make a third array Neighbourhoods which could serve to map the nearest label to x,y is L

Given Labels and Data, how can I use python/numpy/scipy to get Neighbourhoods?

Labels = array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
                [0, 1, 1, 1, 1, 0, 0, 0, 0, 0],
                [0, 1, 1, 1, 1, 0, 0, 0, 0, 0],
                [0, 1, 1, 1, 1, 0, 0, 0, 0, 0],
                [0, 1, 1, 1, 1, 0, 0, 0, 0, 0],
                [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
                [0, 0, 0, 0, 0, 0, 2, 2, 2, 0],
                [0, 0, 0, 0, 0, 0, 2, 2, 2, 0],
                [0, 0, 0, 0, 0, 0, 2, 2, 2, 0],
                [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] )

Data = array([[1, 1, 1, 1, 1, 1, 2, 3, 4, 5],
              [1, 0, 0, 0, 0, 1, 2, 3, 4, 5],
              [1, 0, 0, 0, 0, 1, 2, 3, 4, 4],
              [1, 0, 0, 0, 0, 1, 2, 3, 3, 3],
              [1, 0, 0, 0, 0, 1, 2, 2, 2, 2],
              [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
              [2, 2, 2, 2, 2, 1, 0, 0, 0, 1],
              [3, 3, 3, 3, 2, 1, 0, 0, 0, 1],
              [4, 4, 4, 3, 2, 1, 0, 0, 0, 1],
              [5, 5, 4, 3, 2, 1, 1, 1, 1, 1]] )

Neighbourhoods = array([[1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
                        [1, 0, 0, 0, 0, 1, 1, 1, 1, 1],
                        [1, 0, 0, 0, 0, 1, 1, 1, 0, 2],
                        [1, 0, 0, 0, 0, 1, 1, 0, 2, 2],
                        [1, 0, 0, 0, 0, 1, 0, 2, 2, 2],
                        [1, 1, 1, 1, 1, 0, 2, 2, 2, 2],
                        [1, 1, 1, 1, 0, 2, 0, 0, 0, 2],
                        [1, 1, 1, 0, 2, 2, 0, 0, 0, 2],
                        [1, 1, 0, 2, 2, 2, 0, 0, 0, 2],
                        [1, 1, 2, 2, 2, 2, 2, 2, 2, 2]] )

Note: I’m not sure what should happen with ties, so used zeros in the above Neighbourhoods

Answer 1

As suggested by David Zaslavsky, this is the job for a voroni diagram. Here is a numpy implementation: http://blancosilva.wordpress.com/2010/12/15/image-processing-with-numpy-scipy-and-matplotlibs-in-sage/

The relevant function is scipy.ndimage.distance_transform_edt. It has a return_indices option that can be exploited to do what you need (as well as calculate the raw distances (data in your example)).

As an example:

import numpy as np
from scipy.ndimage import distance_transform_edt

labels = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
                  [0, 1, 1, 1, 1, 0, 0, 0, 0, 0],
                  [0, 1, 1, 1, 1, 0, 0, 0, 0, 0],
                  [0, 1, 1, 1, 1, 0, 0, 0, 0, 0],
                  [0, 1, 1, 1, 1, 0, 0, 0, 0, 0],
                  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
                  [0, 0, 0, 0, 0, 0, 2, 2, 2, 0],
                  [0, 0, 0, 0, 0, 0, 2, 2, 2, 0],
                  [0, 0, 0, 0, 0, 0, 2, 2, 2, 0],
                  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] )
i, j = distance_transform_edt(labels == 0, return_distances=False, 
                              return_indices=True) 
neighborhoods = labels[i,j]
print neighborhoods

This yields:

array([[1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
       [1, 1, 1, 1, 1, 1, 1, 1, 1, 2],
       [1, 1, 1, 1, 1, 1, 1, 1, 2, 2],
       [1, 1, 1, 1, 1, 1, 1, 2, 2, 2],
       [1, 1, 1, 1, 1, 1, 2, 2, 2, 2],
       [1, 1, 1, 1, 1, 2, 2, 2, 2, 2],
       [1, 1, 1, 1, 2, 2, 2, 2, 2, 2],
       [1, 1, 1, 2, 2, 2, 2, 2, 2, 2],
       [1, 1, 2, 2, 2, 2, 2, 2, 2, 2]])