Homology Group Generator Analysis in Irregular Graph Pyramids

Computation of homology generators using an irregular graph pyramid can significantly increase performance compared to the classical methods. First results in 2D exist and show the advantages of the method. The generators are computed in upper levels of pyramid where it is known that the graphs contains a number of self loops and multiple edges product of the contraction processes. Using a straight lines strategy to draw this edges would not be useful to analyze the graphs on those levels. This paper presents a novel algorithm for nicely visualize irregular graph pyramids, including multiple edges and self loops which preserves the geometry and the topology of the original image. This new algorithm is used to give new insights about the top-down delineation of homology generators in irregular graph pyramids.