Delineating Homology Generators in Graph Pyramids

Abstract

Abstract. Computation of homology generators using a graph pyramid can significantly increase performance, compared to the classical methods. First results in 2D exist and show the advantages of the method. Generators are computed on the upper level of a graph pyramid. Toplevel graphs may contain self loops and multiple edges, as a side product of the contraction process. Using straight lines to draw these edges would not show the full information: self loops disappear, parallel edges collapse. This paper presents a novel algorithm for correctly visualizing graph pyramids, including multiple edges and self loops which preserves the geometry and the topology of the original image. New insights about the top-down delineation of homology generators in graph pyramids are given.

Invariant representative cocycles of cohomology generators using irregular graph pyramids

“…A method for efficiently computing representative cycles of homology generators using an irregular graph pyramid is given in [12]. In [13] a novel algorithm for correctly visualizing graph pyramids, including multiple edges and self-loops is given. This algorithm preserves the geometry and the topology of the original image and has been used to produce the images throughout the paper (see Fig.…”

Irregular Graph Pyramids and Representative Cocycles of Cohomology Generators

“…A method for efficiently computing representative cycles of homology generators using an irregular graph pyramid is given in [7]. In [8] a novel algorithm for correctly visualizing graph pyramids, including multiple edges and self-loops is given. This algorithm preserves the geometry and the topology of the original image.…”