A model for digital topology

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1568, Issue , 1999, Pages 229-241

  Bertrand, Gilles ^a   Couprie, Michel ^a  

^a ESIEE PARIS   (France)

Author keywords

Digital topology; Discrete topology; Simple point; Surface

Indexed keywords

GEOMETRY; SURFACES;

3-DIMENSIONAL; ADJACENCY RELATIONS; DIGITAL TOPOLOGY; DISCRETE SPACES; DISCRETE TOPOLOGY; SIMPLE POINT;

TOPOLOGY;

EID: 84958747434     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-49126-0_18     Document Type: Conference Paper

References (23)

1. P. Alexandroff, “Diskrete Räume”, Mat. Sbornik, 2, pp. 501-518, 1937.
2. R. Ayala, E. Domínguez, A.R. Francés, A. Quintero, J. Rubio, “On surfaces in digital topology”, 5th Colloquium Discrete Geometry for Comp. Imagery, pp. 271-276, 1995.
3. n, Discrete Geometry for Computer Imagery, Vol. 1176, Lect. Notes in Comp. Science, Springer Verlag, pp. 163-176, 1996.
4. R. Ayala, E. Domínguez, A.R. Francés, A. Quintero, “Digital lighting functions”, Discrete Geometry for Computer Imagery, Vol. 1347, Lect. Notes in Comp. Science, Springer Verlag, pp. 139-150, 1997.
5. G. Bertrand, “Simple points, topological numbers and geodesic neighborhoods in cubic grids”, Pattern Rec. Letters, Vol. 15, pp. 1003-1011, 1994.
6. G. Bertrand, “New notions for discrete topology”, 8th Conf. on Discrete Geom. for Comp. Imag., Vol. 1568, Lect. Notes in Comp. Science, Springer Verlag, pp. 216-226, 1999.
7. A.V. Evako, R. Kopperman, Y.V. Mukhin, “Dimensional Properties of Graphs and Digital Spaces”, Jour. of Math. Imaging and Vision, 6, pp. 109-119, 1996.
8. J. Françon, “Discrete combinatorial surfaces”, CVGIP: Graphical Models and Image Processing, Vol. 57, pp. 20-26, 1995.
9. J. Françon, “On recent trends in discrete geometry in computer science”, Conf. on Discrete Geometry for Comp. Imag., pp. 3-16, 1996.
10. E. Khalimsky, R. Kopperman, P. R. Meyer, “Computer Graphics and Connected Topologies on Finite Ordered Sets”, Topology and its Applications, 36, pp. 1-17, 1990.
11. T. Y. Kong, A. W. Roscoe, “Continuous Analogs of Axiomatized Digital Surfaces”, Computer Vision, Graphics, and Image Processing, 29, pp. 60-86, 1985.
12. T.Y. Kong and A. Rosenfeld, “Digital Topology: introduction and survey”, Comp. Vision, Graphics and Image Proc., 48, pp. 357-393, 1989.
13. T.Y. Kong, “Topology-Preserving Deletion of 1’s from 2-, 3-and 4-Dimensional Binary Images”, Conf. on Discrete Geometry for Comp. Imag., Lect. Notes in Comp. Science, Vol. 1347, Springer Verlag, pp. 3-18, 1997.
14. T. Y. Kong, R. Kopperman, P. R. Meyer, “A Topological Approach to Digital Topology”, American Mathematical Monthly, 38, pp. 901-917, 1991.
15. R. Kopperman, P.R. Meyer and R.G. Wilson, “A Jordan surface theorem for threedimensional digital spaces”, Discrete Comput. Geom., 6, pp. 155-161, 1991.
16. V. A. Kovalevsky, “Finite Topology as Applied to Image Analysis”, Computer Vision, Graphics, and Image Processing, 46, pp. 141-161, 1989.
17. V.A. Kovalevsky, “Topological foundations of shape analysis”, in Shape in Pictures, NATO ASI Series, Series F, Vol. 126, pp. 21-36, 1994.
18. R. Malgouyres, “A definition of surfaces of Z3”, Conf. on Discrete Geometry for Comp. Imag., pp. 23-34, 1993. See also Doctoral dissertation, Université d’Auvergne, France, 1994.
19. D.G. Morgenthaler and A. Rosenfeld, “Surfaces in three-dimensional images”, Information and Control, 51, 227-247, 1981.
20. G.M. Reed and A. Rosenfeld, “Recognition of surfaces in three-dimensional digital images”, Information and Control, Vol. 53, pp. 108-120, 1982.
21. G.M. Reed, “On the characterization of simple closed surfaces in three-dimensional digital images”, Computer Vision, Graphics and Image Proc., Vol. 25, pp. 226-235, 1984.
22. A. Rosenfeld, “Digital Topology”, Amer. Math. Monthly, 86, pp. 621-630, 1979.
23. J. Serra, Image Analysis and Mathematical Morphology, Academic Press, 1982.