Journal of Mathematical Imaging and Vision, volume 11, issue 3, pages 207-221
Some Topological Properties of Surfaces in Z3
1
Laboratoire PSI, ESIEE, Cité Descartes, Noisy-Le-Grand Cedex, France. bertrang@esiee.fr
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2
GREYC, ISMRA 6, Bd Maréchal Juin, Caen Cedex, France. malgouyres@greyc.ismra.fr
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Publication type: Journal Article
Publication date: 1999-01-01
Q2
Q2
SJR: 0.684
CiteScore: 4.3
Impact factor: 1.3
ISSN: 09249907, 15737683
Condensed Matter Physics
Statistics and Probability
Applied Mathematics
Computer Vision and Pattern Recognition
Modeling and Simulation
Geometry and Topology
Abstract
A basic property of a simple closed surface is the Jordan property: the complement of the surface has two connected components. We call back-component any such component, and the union of a back-component and the surface is called the closure of this back-component. We introduce the notion of strong surface as a surface which satisfies a strong homotopy property: the closure of a back-component is strongly homotopic to that back-component. This means that we can homotopically remove any subset of a strong surface from the closure of a back-component. On the basis of some results on homotopy, and strong homotopy, we have proved that the simple closed 26-surfaces defined by Morgenthaler and Rosenfeld, and the simple closed 18-surfaces defined by one of the authors are both strong surfaces. Thus, strong surfaces appear as an interesting generalization of these two notions of a surface.
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Bertrand G., MALGOUYRES R. Some Topological Properties of Surfaces in Z3 // Journal of Mathematical Imaging and Vision. 1999. Vol. 11. No. 3. pp. 207-221.
GOST all authors (up to 50)
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Bertrand G., MALGOUYRES R. Some Topological Properties of Surfaces in Z3 // Journal of Mathematical Imaging and Vision. 1999. Vol. 11. No. 3. pp. 207-221.
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RIS
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TY - JOUR
DO - 10.1023/a:1008348318797
UR - https://doi.org/10.1023/a:1008348318797
TI - Some Topological Properties of Surfaces in Z3
T2 - Journal of Mathematical Imaging and Vision
AU - Bertrand, Gilles
AU - MALGOUYRES, RÉMY
PY - 1999
DA - 1999/01/01
PB - Springer Nature
SP - 207-221
IS - 3
VL - 11
SN - 0924-9907
SN - 1573-7683
ER -
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BibTex (up to 50 authors)
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@article{1999_Bertrand,
author = {Gilles Bertrand and RÉMY MALGOUYRES},
title = {Some Topological Properties of Surfaces in Z3},
journal = {Journal of Mathematical Imaging and Vision},
year = {1999},
volume = {11},
publisher = {Springer Nature},
month = {jan},
url = {https://doi.org/10.1023/a:1008348318797},
number = {3},
pages = {207--221},
doi = {10.1023/a:1008348318797}
}
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Bertrand, Gilles, and RÉMY MALGOUYRES. “Some Topological Properties of Surfaces in Z3.” Journal of Mathematical Imaging and Vision, vol. 11, no. 3, Jan. 1999, pp. 207-221. https://doi.org/10.1023/a:1008348318797.