Local configurations in discrete combinatorial surfaces

Authors:
Yukiko Kenmochi;Yusuke Nomura
Affiliations:
Institut Gaspard-Monge, Unité Mixte de Recherche CNRS-UMLV-ESIEE, Laboratoire A2SI, Groupe ESIEE, Cité Descartes, BP99, 93162 Noisy-le-Grand Cedex, France;Department of Information Technology, Okayama University, 3-1-1 Tsushimanaka, 700-8530 Okayama, Japan
Venue:
Image and Vision Computing
Year:
2007

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Abstract

Representing discrete objects by polyhedral complexes, we can define all conceivable topological characteristics of points in discrete objects, namely those of vertices of polyhedral complexes. Such a topological characteristic is determined for each point by observing a configuration of object points in the 3x3x3 local point set of its neighbors. We study a topological characteristic such that the point is in the boundary of a 3D polyhedral complex and the boundary forms a 2D combinatorial surface. By using the topological characteristic, we present an algorithm which examines whether the central point of a local point set is in a combinatorial surface, and show how many local point configurations exist in combinatorial surfaces in a 3D discrete space.