Discretization in 2D and 3D orders

Graphical Models

Volumn 65, Issue 1-3, 2003, Pages 77-91

  Couprie, Michel ^a   Bertrand, Gilles ^a   Kenmochi, Yukiko ^a  

^a ESIEE PARIS   (France)

Author keywords

Discrete surfaces; Discretization; Orders; Supercover; Topology

Indexed keywords

COMPUTATIONAL GEOMETRY; SET THEORY; THREE DIMENSIONAL; TOPOLOGY; TWO DIMENSIONAL;

DISCRETE SURFACES; DISCRETIZATION; SUPERCOVER;

COMPUTER GRAPHICS;

GRAPHICAL METHOD; TOPOLOGY;

EID: 0038712579     PISSN: 15240703     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1524-0703(03)00003-1     Document Type: Article

References (25)

1. E. Andrès, Modélisation analytique discrète d'objects géométriques, Thèse de HDR, Université de Poitiers (France), 2000.
2. E. Andrès, C. Sibata, R. Acharya, Supercover 3D polygon, in: Conference on Discrete Geometry for Computer Imaging, Lecture Notes in Computer Science, vol. 1176, Springer Verlag, 1996, pp. 237-242.
3. P.S. Alexandroff, Diskrete Räume, Mat. Sbornik 2 (1937) 501-518.
4. P.S. Alexandroff, H. Hopf, Topologie, Springer Verlag, 1937.
5. G. Bertrand, New notions for discrete topology, in: 8th Conference on Discrete Geometry for Computer Imaging, Lecture Notes in Computer Science, vol. 1568, Springer Verlag, 1999, pp. 216-226.
6. G. Bertrand, M. Couprie, A model for digital topology, in: 8th Conference on Discrete Geometry for Computer Imaging, Lecture Notes in Computer Science, vol. 1568, Springer Verlag, 1999, pp. 229-241.
7. J. Bresenham, Algorithm for computer control of digital plotter, IBM Syst. J. 4 (1965) 25-30.
8. V.E. Brimkov, E. Andrès, R.P. Barneva, Object discretization in higher dimensions, in: 9th Conference on Discrete Geometry for Computer Imaging, Lecture Notes in Computer Science, vol. 1953, Springer Verlag, 2000, pp. 210-221.
9. J.M. Chassery, A. Montanvert, Géométrie discrète en imagerie, Hermès, Paris, France, 1991.
10. D. Cohen-Or, A. Kaufman, Fundamentals of surface voxelization, Graphical Models and Image Process 57 (6) (1995) 453-461.
11. M. Couprie, G. Bertrand, Y. Kenmochi, Discretization in 2D and 3D orders, in: 10th Conference on Discrete Geometry for Computer Imaging, Lecture Notes in Computer Science, vol. 2301, Springer Verlag, 2002, pp. 301-312.
12. A.V. Evako, R. Kopperman, Y.V. Mukhin, Dimensional Properties of Graphs and Digital Spaces, J. Math. Imaging and Vision 6 (1996) 109-119.
13. E.D. Khalimsky, On topologies of generalized segments, Soviet Math. Doklady 10 (1969) 1508.
14. E.D. Khalimsky, R. Kopperman, P.R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topology Appl. 36 (1990) 1-17.
15. R. Klette, m-dimensional cellular spaces, internal report, University of Maryland, CAR-TR-6, MCS-82-18408, CS-TR-1281, 1983.
16. R. Klette, The m-dimensional grid point space, Comput. Vis. Graphics Image Process. 30 (1985) 1-12.
17. T.Y. Kong, A. Rosenfeld, Digital topology: introduction and survey, Comput. Vis. Graphics Image Proc. 48 (1989) 357-393.
18. J. Koplowitz, On the performance of chain codes for quantization of line drawings, IEEE Trans. PAMI 3 (1981) 180-185.
19. V.A. Kovalevsky, Topological foundations of shape analysis, in: Shape in Pictures, NATO ASI Series, Series F, vol. 126, 1994, pp. 21-36.
20. J.-P. Reveillès, Géométrie discrète, calcul en nombres entiers et algorithmique, Thèse d'état, Université Louis Pasteur, Strasbourg (France), 1991.
21. C. Ronse, M. Tajine, Hausdorff discretization of algebraic sets and diophantine sets, in: 9th Conference on Discrete Geometry for Computer Imaging, Lecture Notes in Computer Science, vol. 1953, Springer Verlag, 2000, pp. 216-226.
22. C. Ronse, M. Tajine, Hausdorff discretization for cellular distances, and its relation to cover and supercover discretizations, J. Visual Commun. Image Representation 12 (2) (2001) 169-200.
23. A. Rosenfeld, A.C. Kak, Digital picture processing, Academic Press, 1982.
24. J. Serra, Image Analysis and Mathematical Morphology, Academic Press, 1982.
25. J. Webster, Cell complexes and digital convexity, in: Digital and image geometry, Lecture Notes in Computer Science, vol. 2243, Springer Verlag, 2002, pp. 268-278.