## Tuesday, June 26, 2012

### Getting the neighborhood of labelled particles in a graph

In the previous post, a labelled image, typically obtained by labelling connected components of a binary image, was used to compute a dictionary representing the neighborhood relationships between the particles.
A dictionary may be not the best data structure to represent such relationship. A graph structure is better suited and networkx provides a python implementation for that.
Starting from the following label image:
 Background Grey level=0, first particle: grey level=1, ...last particle:grey level=5

We get two possible graphs. The first one takes the background (vertex 0) into account so the background is a neighbour of all the particles (there an edge between the vertex 0 and all the other vertex)

In this second graph, the background was removed:

A function  converts the dictionary to a networkx graph:

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

@author: Jean-Patrick Pommier
"""

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

def makelabelarray():
label = np.array([[0,1,4,4],
[1,0,0,2],
[3,0,2,2],
[0,2,0,5]])
return label

def convertToGraph(dic, noBack=True):
G = nx.Graph()
for particle in dic.keys():
list_touching_particles = dic[particle]
# remove background
if noBack:
print 'v(',particle,')=',list_touching_particles
for tp in list_touching_particles:
return G

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

neighborhood=np.array([0,1,0],[1,1,1],[0,1,0])

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):
mask = (label ==i)
neighbor = np.logical_and(dilated, np.logical_not(mask))
#print neighbor
#=======================================================================
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]])
g = findneighborhoods(a, n)
G = convertToGraph(g, noBack=True)

plb.imshow(a,interpolation = 'nearest')
plb.colorbar(ticks=[0,1,2,3,4])
plb.show()

nx.draw(G)
plb.show()

```