Combinatorial boundary of a 3D lattice point set

Yukiko Kenmochi (1) , Atsushi Imiya (2)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 Chiba University

Boundary extraction and surface generation are important topological topics for three-dimensional digital image analysis. However, there is no adequate theory to establish relations between these different topological procedures in a completely discrete way. In this paper, we present a new boundary extraction algorithm which gives not only a set of border points but also a polyhedral surface whose vertices are border points by using the concepts of combinatorial/algebraic topologies. We show that our boundary can be considered to be a triangulation or polyhedrization of border points in the sense of general topology, that is, we clarify relations between border points and the triangulated surface.

Mots clés: Boundary extraction; Combinatorial surface; Polyhedral complex

Domaines: Mathématique discrète [cs.DM]; Traitement des images [eess.IV]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Yukiko Kenmochi, Atsushi Imiya. Combinatorial boundary of a 3D lattice point set. Journal of Visual Communication and Image Representation, 2006, 17 (4), pp.738-766. ⟨10.1016/j.jvcir.2005.11.001⟩. ⟨hal-00622083⟩