Cycle bases of graphs and sampled manifolds

Authors:
Craig Gotsman;Kanela Kaligosi;Kurt Mehlhorn;Dimitrios Michail;Evangelia Pyrga
Affiliations:
Technion-Israel Institute of Technology, Haifa, Israel;Max-Planck-Institut für Informatik, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany
Venue:
Computer Aided Geometric Design
Year:
2007

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Abstract

Point samples of a surface in R^3 are the dominant output of a multitude of 3D scanning devices. The usefulness of these devices rests on being able to extract properties of the surface from the sample. We show that, under certain sampling conditions, the minimum cycle basis of a nearest neighbor graph of the sample encodes topological information about the surface and yields bases for the trivial and non-trivial loops of the surface. We validate our results by experiments.