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Proceedings Paper

Simplicity surfaces: a new definition of surfaces in Z3
Author(s): Michel Couprie; Gilles Bertrand
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Paper Abstract

In this paper, we introduce a new motion of surfaces in Z3, called simplicity surfaces. In the continuous space, a surface is characterized by the fast that the neighborhood of each point of the surface is homomorphic to an Euclidean disc. The chosen approach consists in characterizing a surface in Z3 by the condition that the neighborhood of any point constitutes a simple closed curve. The major problem is than, if we consider only the usual adjacency relations, this condition is not satisfied even for the simplest surfaces, e.g. digital planes. We thus have to consider another relation. We use a relation for points in Z3 which is based on the notion of homotopy. This allows to define a surface as a connected set of points in which the neighborhood of each point constitutes a simples closed curve for this relation; such a surface is called a simplicity surface. We give two different local characterizations of simplicity surfaces. We then show that a simplicity surface may also be seen as a combinatorial manifold, that is, a set of faces which are linked by an adjacency relation. Furthermore, we show that the main existing notions of surfaces, for the 6- and the 26- adjacency, are also simplicity surfaces.

Paper Details

Date Published: 2 October 1998
PDF: 12 pages
Proc. SPIE 3454, Vision Geometry VII, (2 October 1998); doi: 10.1117/12.323265
Show Author Affiliations
Michel Couprie, Groupe ESIEE (France)
Gilles Bertrand, Groupe ESIEE (France)

Published in SPIE Proceedings Vol. 3454:
Vision Geometry VII
Robert A. Melter; Angela Y. Wu; Longin Jan Latecki, Editor(s)

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