Closed curves in n-dimensional discrete space

Graphical Models

Volumn 65, Issue 1-3, 2003, Pages 43-60

  Thürmer, Grit ^a  

^a BAUHAUS UNIVERSITY WEIMAR   (Germany)

Author keywords

Discrete curves; Discrete geometry; Discrete quasi curves; Discrete topology

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; MATHEMATICAL MODELS; OBJECT RECOGNITION;

DISCRETE CURVES; DISCRETE GEOMETRY; DISCRETE SPACE; DISCRETE TOPOLOGY; HAMILTONIAN CYCLE;

COMPUTER GRAPHICS;

CURVATURE; GRAPHICAL METHOD;

EID: 0038825318     PISSN: 15240703     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1524-0703(03)00007-9     Document Type: Article

References (22)

1. D. Cohen-Or, A. Kaufman, Fundamentals of surface voxelization. Graph. Models Image Process. 57 (6) (1995) 453-461.
2. C.A. Wüthrich, A model for curve rasterization in n-dimensional space, Comput. Graph. 22 (2-3) (1998) 153-160.
3. R. Yagel, D. Stredney, G.J. Wiet, P. Schmalbrock, L. Rosenberg, D.J. Sessanna Y. Kurzion, Building a virtual environment for endoscopic sinus surgery simulation. Comput. Graph. 20 (6) (1996) 813-823.
4. S.W. Wang, A.E. Kaufman, Volume-sampled 3D modeling, IEEE Comput. Graph. Appl. 14 (5) (1994) 26-32.
5. N. Shareef, R. Yagel, Rapid previewing via volume-based solid modeling, in Proc. of Solid Modeling '95; 1995. pp. 281-292.
6. 3: a new 3D discrete Jordan theorem. Theor. Comput. Sci. 186 (1997) 1-41.
7. A. Rosenfeld, A converse to the Jordan curve theorem for digital curves. Inf. Control 29 (1975) 292-293.
8. R. Malgouyres, Graphs generalizing closed curves with linear construction of the Hamiltonian cyle-parameterization of discretized curves. Theor. Comput. Sci. 143 (1995) 189-249.
9. J. Lebiedz̀, Discrete arcs and curves, Mach. Graph. Vision 9 (1-2) (2000) 25-30.
10. A. Rosenfeld, Connectivity in digital pictures. J. ACM 17 (1) (1970) 146-160.
11. A. Rosenfeld, Arcs and curves in digital pictures, J. ACM 20 (1) (1973) 81-87.
12. G.T. Herman, Discrete multidimensional Jordan surfaces, Graph. Models Image Process, 54 (6) (1992) 507-515.
13. G.T. Herman, Boundaries in digital space: basic theory, in T.Y. Kong, A. Rosenfeld (Eds). Topological Algorithms for Digital Image Processing, Elsevier, Amsterdam, 1996, pp. 233-261.
14. J.K. Udupa, Connected, oriented, closed boundaries in digital space: theory and algorithms, in: T.Y. Kong, A. Rosenfeld (Eds.), Topological Algorithms for Digital Image Processing, Elsevier, Amsterdam, 1996, pp. 205-231.
15. T.Y. Kong, A. Rosenfeld, Digital topology: a comparison of the graph-based and topological approaches, in: G.M. Reed, A.W. Roscoe, R.F. Wachter (Eds.), Topology and Category Theory in Computer Science, Oxford University Press, Oxford, 1991, pp. 273-289.
16. E.E. Moise, Geometric Topology in Dimensions 2 and 3, Springer, New York, 1977.
17. A. Rosenfeld, Three-dimensional digital topology, Inf. Control 50 (1981) 119-127.
18. 1 Unstetigkeitsstellen in gerasterten Flächen im 3-dimensionalen Raum, Diploma thesis, University of Jena (Germany), Faculty of Mathematics and Informatics; 1998.
19. Malgouyres R. Phd thesis, Université d'Auvergne, Clermont-Ferrand, France; 1994.
20. R.C. Agrawal, S.C. Sahasrabudhe, R.K. Shevgaonkar, Preservation of topological properties of a simple closed curve under digitization, Comput. Vision Image Understanding 67 (2) (1997) 99-111.
21. E. Lawler, J. Lenstra, A. Rinnooy Kan, D. Shmoys, The Traveling Salesman problem: a guided tour of combinatorial optimization, in: Wiley-Interscience Series in Discrete Mathematics, Wiley, New York, 1985.
22. V. Neumann-Lara, R.G. Wilson, Digital Jordan curves-a graph theoretical-approach to a topological theorem, Topol. Appl. 46 (2) (1992) 263-268.