Derived neighborhoods and frontier orders

Discrete Applied Mathematics

Volumn 147, Issue 2-3, 2005, Pages 227-243

  Daragon, Xavier ^a   Couprie, Michel ^a   Bertrand, Gilles ^a  

^a ESIEE PARIS   (France)

Author keywords

Derived neighborhoods; Discrete surfaces; Frontier orders; Partially ordered sets; Simplicial complexes

Indexed keywords

DERIVED NEIGHBORHOODS; DISCRETE SURFACES; FRONTIER ORDERS; PARTIALLY ORDERED SETS; SIMPLICIAL COMPLEXES;

COMBINATORIAL MATHEMATICS; COMPUTER GRAPHICS; IMAGE PROCESSING; MATHEMATICAL OPERATORS; PIECEWISE LINEAR TECHNIQUES; SET THEORY;

TOPOLOGY;

EID: 14744292892     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2004.09.013     Document Type: Conference Paper

References (21)

1. J.W. Alexander The combinatorial theory of complexes Ann. Math. 31 1930 294 322
2. P. Alexandroff Diskrete Räume Mat. Sbornik 2 1937 501 518
3. P. Alexandroff Combinatorial Topology 1998 Dover New York
4. R. Ayala, E. Domínguez, A.R. Francés, A. Quintero, Digital lighting functions, in: Proceedings of the Discrete Geometry for Computer Imagery, Lecture Notes in Computer Science, vol. 1347, Springer, 1997, pp. 139-150.
5. G. Bertrand, New notions for discrete topology, in: G. Bertrand, M. Couprie, L. Perroton (Eds.), Discrete Geometry for Computer Imagery, Lecture Notes in Computer Science, vol. 1568, 1999, pp. 218-228.
6. G. Bertrand, M. Couprie, A model for digital topology, in: G. Bertrand, M. Couprie, L. Perroton (Eds.), Discrete Geometry for Computer Imagery, Lecture Notes in Computer Science, vol. 1568, 1999, pp. 229-241.
7. E. Brisson Representing geometric structures in d dimensions topology and order Discrete Comput. Geom. 9 4 1993 387 426
8. X. Daragon, M. Couprie, and G. Bertrand Marching chains algorithm for Alexandroff-Khalimsky spaces L.J. Latecki D.M. Mount A.Y. Wu Vision Geometry XI 2002 51 62
9. X. Daragon, M. Couprie, G. Bertrand, Discrete frontiers, in: I. Nystrom, G. Sanniti di Baja, S. Svensson (Eds.), Discrete Geometry for Computer Imagery, Lecture Notes in Computer Science, vol. 2886, 2003, pp. 236-245.
10. X. Daragon, M. Couprie, G. Bertrand, Discrete surfaces and frontier orders, Tech. Rep. IGM2004-05, Université de Marne-la-Vallée, 2004. J. Math. Imaging and Vision, to appear.
11. A.V. Evako Dimension on discrete spaces Internat. J. Theoret. Phys. 33 1996 1553 1568
12. A.V. Evako, R. Kopperman, and Y.V. Mukhin Dimensional properties of graphs and digital spaces J. Math. Imaging and Vision 6 1996 109 119
13. J.F.P. Hudson Piecewise Linear Topology 1969 W. A. Benjamin Inc.
14. A.V. Ivashchenko Representation of smooth surfaces by graphs transformations of graphs which do not change the Euler characteristic of graphs Discrete Math. 122 1993 133 219
15. E.D. Khalimsky On topologies of generalized segments Soviet Mat. Doklady 10 1969 1508 1511
16. E.D. Khalimsky, R. Kopperman, and P.R. Meyer Computer graphics and connected topologies on finite ordered sets Topology Appl. 36 1990 1 17
17. T.Y. Kong, and A. Rosenfeld Digital topology introduction and survey Computer Vision Graphics and Image Process. 48 1989 357 393
18. R. Kopperman, P.R. Meyer, and R.G. Wilson A Jordan surface theorem for three-dimensional digital spaces Discrete Comput. Geom. 6 1991 155 161
19. V.A. Kovalevsky, A new concept for digital geometry, in: Shape in Pictures, NATO ASI Series F., vol. 126, 1994, pp. 37-51.
20. W.B.R. Lickorish, Simplicial moves on complexes and manifolds, Geometry And Topology Monograph, Proceedings of the KirbyFest, vol. 2, 1998, pp. 229-320.
21. P. Lienhardt N-dimensional generalized combinatorial maps and cellular quasi-manifolds Internat. J. Comput. Geom. Appl. 4 3 1994 275 324