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Local configurations in discrete combinatorial surfaces

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 3 × 3 × 3 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.
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Yukiko Kenmochi, Yusuke Nomura. Local configurations in discrete combinatorial surfaces. Image and Vision Computing, Elsevier, 2007, 25 (10), pp.1657-1670. ⟨10.1016/j.imavis.2006.06.018⟩. ⟨hal-00622234⟩



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