## Monday, June 25, 2012

### Neighbourhood in a labelled image

Image segmentation can yield labelled images, where the different labels correspond to the objects of interest ( chromosomes, a nuclei ).

It can be necessary to consider particles in the neighbourhood of a given particle.
The following 4x4 labelled image (a numpy array) is made of four particles:
• first particle : light blue (value or label=1)
• second particle : green (value=2)
• third particle : orange (value=3)
• fourth particle : red (value=4)
• background : dark blue (value = 0)

Considering a 3x3 domain (in fact a structuring element), the neighbour particle of the first particle is the 'orange' particle. The 'orange' particle has two neighbours, the 'light blue' and the 'green' particle .

The following python script takes a label image (from the above example) and returns a dictionary, where  in the  key/value pair, the key corresponds to a chosen particle and the value to a set containing the label value of the neighbouring particles:

{1: set([0, 3]), 2: set([0, 3, 4]), 3: set([0, 1, 2]), 4: set([0, 2])}
The calculated dictionary is closed to an adjacency list.

```# -*- coding: utf-8 -*-
"""
Created on Mon Jun 25 10:26:01 2012

@author: Jean-Patrick Pommier
"""

import numpy as np
import mahotas as mh
import pylab as plb

def makelabelarray():
label = np.array([[0,1,0,0],
[1,0,0,2],
[3,0,2,2],
[0,2,0,4]])
return label

def findneighborhoods(label,neighborhood):
''' given a labelled image, should return the adjacency list
of particles, for a given neighborhood:

neighborhood=np.array([1,1,1],[1,1,1],[1,1,1])

The background (0), is kept as a particle neighbor
No fancy indexing
'''
#make the labels list
labmax = label.max()
#print labmax
neighb_dic = {} # a dictionnary containing particle label as key and neighborhood
for i in range(1,labmax+1):
#print neighbor
#==============================================================================
#         #Done without fancy indexing
#==============================================================================
flatlab = np.ndarray.flatten(label)
flatneighborhood = np.ndarray.flatten(neighbor)
flatneighbors = flatlab[flatneighborhood]
flatneighbors.sort()
#set is a trick so that each value of the neighborhoods is present only once
neighb_dic[i] = set(flatneighbors)
#print np.nonzero(flatneighbors)
return neighb_dic

if __name__ == "__main__":
a = makelabelarray()
n = np.array([[1,1,1],[1,1,1],[1,1,1]])
print findneighborhoods(a, n)
plb.imshow(a,interpolation = 'nearest')
plb.show()

```