Friday, June 6, 2014

Graph again


Update 06 /11 /2014


The ipython notebook from the previous post was rewritten . A python  function building a graph from a skeleton was modified to generate a multigraph (networkx). This function (available in an ipython notebook) is used as follow:

    Graph= nx.MultiGraph()
    C8_Skeleton_To_Graph_01(Graph, skeleton)


With:
  • Graph : a networkx multigraph object.
  • skeleton : the binary image of skeleton obtained by morphological thining with mahotas.
In the following example (from the previous ipython notebook), the skeleton of the letter 'a' was converted into a networkx multigraph: 

image_test= makeLetterImage('a', 75)
skeleton_test = mh.thin(image_test)
_,_,Bp_test,Ep= SkeletonDecomposition(skeleton_test)
Ep_Ep = skeleton_test*np.logical_not(Ep)
Ep_Ep,_ = mh.label(Ep,Ep)
l_Ep, _ = mh.label(Ep)


Graph_test = nx.MultiGraph()
C8_Skeleton_To_Graph_01(Graph_test, skeleton_test)
print Graph_test.edges(data=True)

figsize(16,8)
subplot(131)
imshow(skeleton_test+l_Ep+3*Bp_test,interpolation='nearest')
subplot(132, xticks=[],yticks=[])
nx.write_dot(Graph_test,'multi.dot')
!neato -T png multi.dot > multi.png
imshow(mh.imread('multi.png'), interpolation='nearest')
subplot(133)
nx.draw(Graph_test)



The skeleton has two edges, linking the same branched points (yellow and red pixels). The graph was exported to build an image of the multigraph (middle), networkx doesn't seem to be capable to dispolay correctly such multigraph (right)




When applied to a lowercase alphabet:



The function produced the corresponding graphs (the letter 'o' excepted):
However,it is possible to find case where the function failed to buil a graph as:

   imTest = makeLetterImage('b', 70)
   skelTest = mh.thin(imTest)
   Ep_Bp, Bp_Bp, Bp, Ep = SkeletonDecomposition(skelTest)


where:
  • skeltest: the image skeleton obtained by thining with mahotas.
  • Bp : image of branched-point(s)
  • Ep: image of end-point(s)
  • Bp_Bp :edge(s) between branched-points
  • Ep_Bp:edge(s) between end-point(s) and branched-point(s)
If the skeleton of the letter 'b' is decomposed as follow:
The function fails to produce a graph due to the presence of a closed edge (right) which should be processed as a self loop for the corresponding branched-point (middle image).

An other graph library: Graph-tool


The graphic representation of a multigraph produced by graphtool is so nice that it may worth to learn the graphtool syntax to make a graph:
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