The Locality Property in Topological Irregular Graph Hierarchies
Graph contraction is applied in many areas of computer science, for instance, as a subprocess in parallel graph partitioning. Parallel graph partitioning is usually implemented as a poly-algorithm intended to speed up the solving of systems of linear equations. Image analysis is another field of application for graph contraction. There regular and irregular image hierarchies are built by coarsening images.
In this paper a general structure of (multilevel) graph contraction is given. The graphs of these coarsening processes are given a topological structure which allows to use concepts like the neighborhood, the interior and the boundary of sets in a well-defined manner. It is shown in this paper that the various coarsenings used in practice are continuous and therefore local processes. This fact enables the efficient parallelization of these algorithms. This paper also demonstrates that the efficient parallel implementations which already exist for multilevel partitioning algorithms can easily be applied to general image hierarchies.
KeywordsTopological Structure Dual Graph Graph Partitioning Random Match Image Pyramid
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