Opened Access On surfaces in digital topology
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Author: Ayala Gómez, Rafael
Domínguez Murillo, Eladio
Francés Román, Ángel Ramón
Quintero Toscano, Antonio Rafael
Rubio Sender, Julio
Department: Universidad de Sevilla. Departamento de Geometría y Topología
Date: 1995
Published in: 5th International Workshop on Discrete Geometry for Computer Imagery (1995),
Document type: Presentation
Abstract: In R. Ayala, E. Domínguez, A.R. Francés, A. Quintero, J. Rubio. A Polyhedral Approach to Digital Topology a new framework for digital topology has been proposed. This framework offers the possibility of transfering, in an easy way, definitions, statements and proofs from continuous topology to digital topology. In particular, it provides a straightforward definition of n-dimensional digital manifold. In this paper we prove that the class of digital 2-manifolds without boundary in the grid Z3 agrees with the class of (26, 6)-surfaces defined by Kong-Roscoe and other authors. As a consequence, the separation theorem for digital surfaces stated in D.G. Morgenthaler, A. Rosenfeld. Surfaces in threedimensional digital images. Information and Control, 51 (1981), 227-247] and G.M. Reed. On the Characterization of Simple Closed Surfaces in Three-dimensional Digital Images. Computer Graphics and Image Processing, 25 (1984), 226-235 is obtained.
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