On the topology of grid continua

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 3454, Issue , 1998, Pages 52-63

  Sloboda, Fridrich ^a   Zaťko, Bedrich ^a   Klette, Reinhard ^b  

^a INSTITUTE OF CHEMISTRY   (Slovakia)

^b UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Digital geometry; Minimal polyhedral Jordan surface in R3; One dimensional grid continua in R2 and R3; Two dimensional grid continua in R3

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; FRACTALS; IMAGE PROCESSING; ONE DIMENSIONAL; SET THEORY; TOPOLOGY; TWO DIMENSIONAL;

DIGITAL GEOMETRY; GRID CONTINUA; MINIMAL POLYHEDRA JORDAN SURFACES; SET THEORETICAL TOPOLOGY;

COMPUTATIONAL GEOMETRY;

EID: 0038636359     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.323274     Document Type: Conference Paper

References (30)

1. E. Artzy, G. Frieder, and G.T. Herman: The theory, design, implementation and evaluation of a three-dimensional surface detection algorithm. CGIP 15 (1981) 1-24.
2. G.T. Herman: Discrete multidimensional Jordan surfaces. CVGIP: Graphical Models Image Processing 54 (1992) 507-515.
3. R. Klette: The m-dimensional grid point space. CVGIP 30 (1985) 1-12.
4. R. Klette: Approximation and representation of 3D objects. Advances in Digital and Computational Geometry (R. Klette, A. Rosenfeld, F. Sloboda, eds.), Springer, Singapore (1998) 161-194.
5. R. Klette: Measurement of object surface area. in: Proceed. Computer Assisted Radiology and Surgery, Tokyo, June 24 - 27, 1998 (to appear).
6. T.Y. Kong and A. Rosenfeld: Digital topology - introduction and survey. CVGIP 48 (1989) 357-393.
7. V.A. Kovalevsky: Discrete topology and contour definition. Pattern Reconit. Lett. 2 (1984) 281-288.
8. W. E. Lorensen and H. E. Cline: Marching cubes - a high resolution 3D surface construction algorithm. Computer Graphics 21 (1987) 163-169.
9. H. v. Mangoldt and K. Knopp: Einführung in die höhere Mathematik, III. Band 12. Auflage, Leipzig, S. Hirzel Verlag (1965).
10. K. Menger: Dimensionstheorie. B.G. Teubner Press, Leipzig (1928).
11. K. Menger: Kurventheorie. B.G. Teubner Press, Leipzig (1932).
12. D.G. Morgenthaler and A. Rosenfeld: Surfaces in three-dimensional digital images. Information and Control 51 (1981) 227-247.
13. A.S. Parchomenko: Was ist eine Kurve? VEB Deutscher Verlag der Wissenschaften, Berlin (1957) (original Moscow (1954)).
14. G. M. Reed and A. Rosenfeld: Recognition of surfaces in three-dimensional digital images. Information and Control 53 (1982) 108-120.
15. A. Rosenfeld: Arcs and curves in digital pictures. J. Assoc. Comput. Mach. 20 (1973) 81-87.
16. A. Rosenfeld: Digital topology. Amer. Math. Monthly 86 (1979) 226-235.
17. A. Rosenfeld, T. Y. Kong and A. Y. Wu: Digital surfaces. CVGIP: Graphical Models Image Processing 53 (1991) 305-312.
18. A. Rosenfeld: Digital geometry - introduction and bibliography. in: Advances in Digital and Computational Geometry, eds. R. Klette, A. Rosenfeld and F. Sloboda, Springer, Singapore (1998) 1-85.
19. W. Scherer: Ein Satz über Gitter und Volumen. Mathematische Annalen 86 (1922) 99-107.
20. 2. Report of the Institute of Control Theory and Robotics, Bratislava (1996).
21. 3. Report of the Institute of Control Theory and Robotics, Bratislava (1996).
22. F. Sloboda: On approximation of Jordan surfaces: a topological approach. Int. Memo, CITR Tamaki, The University of Auckland, (1997).
23. F.Sloboda: On minimal polyhedral Jordan surface and its applications. Report of the Institute of Control Theory and Robotics, Bratislava (1997).
24. F. Sloboda, B. Zaťko and J. Stoer; On approximation of planar one-dimensional continua. in Advances in Digital and Computational Geometry, eds. R. Klette, A. Rosenfeld and F. Sloboda, Springer, Singapore (1998) 113-160.
25. S. Straszewicz: Über die Verallgemeinerung des Jordanschen Kurvensatzes. Fundamenta Math. 4 (1923) 128-135.
26. P. Urysohn: Über die allgemeinen Cantorischen Kurven. Annual meeting of the Deutsche Mathematiker-Vereinigung in Marbourg (1923).
27. P. Urysohn: Mémoire sur les multiplicités Cantoriennes. Fundamenta Math. 6 (1925) 30-130.
28. J. Wilhelms and A. V. Gelder: Topological considerations in isosurface generation. Baskin Center for Computer Engineering and Information Sciences, University of California, Santa Cruz (1994) UCSC-CRL-94-31.
29. G. Wyvill, C. McPheeters, and B. Wyvill: Data structures for soft objects. The Visual Computer 2 (1986) 227-234.
30. D. P. Young, R. G. Melvin, M. B. Bieterman: A locally rectangular grid finite element method-application to computational fluid dynamics and computational physics. J. Comp. Physics 92 (1991) 1-42.