by Brimkov, VE and Klette, R
Abstract:
In this paper we propose several equivalent definitions of digital curves and hypersurfaces in arbitrary dimension. The definitions involve properties such as one-dimensionality of curves and (n -1)dimensionality of hypersurfaces that make them discrete analogs of corresponding notions in topology. Thus this work appears to be the first one on digital manifolds where the definitions involve the notion of dimension. In particular, a digital hypersurface in nD is an (n -l)-dimensional object, as it is in the case of continuous hypersurfaces. Relying on the obtained properties of digital hypersurfaces, we propose a uniform approach for studying good pairs defined by separations and obtain a classification of good pairs in arbitrary dimension. © Springer-Verlag 2004.
Reference:
Curves, Hypersurfaces, and Good Pairs of Adjacency Relations (Brimkov, VE and Klette, R), In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), volume 3322, 2004.
Bibtex Entry:
@article{brimkov2004curvesrelations,
author = "Brimkov, VE and Klette, R",
journal = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "276--290",
title = "Curves, Hypersurfaces, and Good Pairs of Adjacency Relations",
volume = "3322",
year = "2004",
abstract = "In this paper we propose several equivalent definitions of digital curves and hypersurfaces in arbitrary dimension. The definitions involve properties such as one-dimensionality of curves and (n -1)dimensionality of hypersurfaces that make them discrete analogs of corresponding notions in topology. Thus this work appears to be the first one on digital manifolds where the definitions involve the notion of dimension. In particular, a digital hypersurface in nD is an (n -l)-dimensional object, as it is in the case of continuous hypersurfaces. Relying on the obtained properties of digital hypersurfaces, we propose a uniform approach for studying good pairs defined by separations and obtain a classification of good pairs in arbitrary dimension. © Springer-Verlag 2004.",
issn = "0302-9743",
eissn = "1611-3349",
keyword = "Digital curve",
keyword = "Digital geometry",
keyword = "Digital hypersurface",
keyword = "Digital topology",
keyword = "Good pair",
language = "eng",
}