Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Fast and effective algorithms for graph partitioning and sparse-matrix ordering
IBM Journal of Research and Development - Special issue: optical lithography I
Numerical Computation, Volume I
Numerical Computation, Volume I
The Topological Consistence of Path Connectedness in Regular and Irregular Structures
SSPR '98/SPR '98 Proceedings of the Joint IAPR International Workshops on Advances in Pattern Recognition
Digital Topologies Revisited: An Approach Based on the Topological Point-Neighbourhood
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
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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.