Finitary 1-Simply Connected Digital Spaces

Graphical Models and Image Processing

Volumn 60, Issue 1, 1998, Pages 46-56

  Herman, Gabor T ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; GRAPH THEORY; IMAGE PROCESSING; IMAGE QUALITY; THEOREM PROVING;

DIGITAL TOPOLOGY; SIMPLY CONNECTED SPACES;

DIGITAL SIGNAL PROCESSING;

EID: 0031601032     PISSN: 10773169     EISSN: None     Source Type: Journal    
DOI: 10.1006/gmip.1997.0456     Document Type: Article

References (31)

1. R. Aharoni, G. T. Herman, and M. Loebl, Jordan graphs, Graphical Models Image Process. 58, 1996, 345-359.
2. E. Artzy, G Frieder, and G. T. Herman, The theory, design, implementation, and evaluation of a three-dimensional surface detection algorithm, Comput. Graphical Image Process. 15, 1981, 1-24.
3. L.-S. Chen, G. T. Herman, R. A. Reynolds, and J. K. Udupa, Surface shading in the cuberille environment, IEEE Comput. Graphics Appl. 5(12), 33-43, 1985. [Erratum appeared in 6(2), 1986, 67-69]
4. H. M. S. Coxeter, Introduction to Geometry, Wiley, New York, 1961.
5. M. Farber, Bridged graphs and geodesic convexity, Discrete Math. 66, 1987, 249-257.
6. D. Gordon and J. K. Udupa, Fast surface tracking in three-dimensional binary images, Comput. Vision Graphics Image Process. 45, 1989, 196-241.
7. F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969.
8. G. T. Herman, On topology as applied to image analysis, Comput. Vision Graphics Image Process. 52, 1990, 409-415.
9. G. T. Herman, Oriented surfaces in digital spaces, CVGIP: Graphical Models Image Process. 55, 1993, 381-396.
10. G. T. Herman, Boundaries in digital spaces: Basic theory, in Topological Algorithms in Digital Image Processing (T. Y. Kong and A. Rosenfeld, Eds.), pp. 233-261, Elsevier, Amsterdam, 1996.
11. G.T. Herman and D. Webster, A topological proof of a surface tracking algorithm, Comput. Vision Graphics Image Process. 23, 1983, 162-177.
12. G. T. Herman and E. Zhao, Jordan surfaces in simply connected digital spaces, J. Math. Imaging Vision 6, 1996, 121-138.
13. S. W. Hughes, T. J. D'Arcy, D.J. Maxwell, J. E. Saunders, C. F. Ruff, W. S. C. Chiu, and R. J. Sheppard, Application of a new discreet form of Gauss' theorem for measuring volumes, Phys. Med. Biol. 41, 1996, 1809-1821.
14. L. Ibáñez, C. Hamitouche, and C. Roux, Determination of discrete sampling grids with optimal topological and spectral properties, in Discrete Geometry for Computer Imagery (S. Miguet, A. Montanvert, and S. Ubéda, Eds.), pp.181-192, Springer-Verlag, Berlin, 1996.
15. E. Khalimsky, Pattern analysis of n-dimensional digital images, in IEEE Int. Conf. Syst. Man Cyber., Atlanta, 1983, pp. 1559-1562.
16. C. Kittel, Introduction to Solid State Physics, 7th ed., Wiley, New York, 1996.
17. T. Y. Kong, A digital fundamental group, Comput. Graphics 13, 1989, 159-166.
18. T. Y. Kong, R. Kopperman, and P. R. Meyer, A topological approach to digital topology, Amer. Math. Monthly 98, 1991, 901-917.
19. T. Y. Kong, A. W. Roscoe, and A. Rosenfeld, Concepts of digital topology. Topology Appl. 46, 1992, 219-262.
20. T. Y. Kong and A. Rosenfeld, Digital topology: Introduction and survey, Comput. Vision Graphics Image Process. 48, 1989, 357-393.
21. T. Y. Kong and J. K. Udupa, A justification of a fast surface tracking algorithm, CVGIP: Graphical Models Image Process. 54, 1992, 162-170.
22. R. D. Kopperman, The Khalimsky line as a foundation for digital topology, in Shape in Picture: Mathematical Description of Shape in Grey-Level Images (Y. L. O, A. Toet, D Foster, H. J. A. M. Heijmans, and P. Meer, Eds.), pp. 3-20, Springer-Verlag, Berlin, 1994.
23. R. D. Kopperman, P. R. Meyer, and R. G. Wilson, A Jordan surface theorem for three-dimensional digital spaces, Discrete Comput. Geom. 6, 1991, 155-162.
24. V. A. Kovalevsky, Discrete topology and countour definition, Pattern Recognition Lett. 2, 1984, 281-288.
25. V. A. Kovalevsky, Finite topology as applied to image analysis, Comput. Vision Graphics Image Process. 46, 1989, 141-161.
26. S. Matej and R. M. Lewitt, Efficient 3D grids for image reconstruction using spherically-symmetric volume elements, IEEE Trans. Nucl. Sci. 42, 1995, 1361-1370.
27. J. R. Munkres, Topology: A First Course, Prentice Hall, Englewood Cliffs, NJ, 1975.
28. D. P. Petersen and D. Middleton, Sampling and reconstruction of wave-number-limited functions in n-dimensional Euclidean spaces, Inform. and Control 5, 1962, 279-323.
29. K. Preston, Jr., Multidimensional logical transforms, IEEE Trans. Pattern Anal. Machine Intell. 5, 1983, 539-554.
30. A. Rosenfeld, Fuzzy digital topology, Inform. and Control 40, 1979, 76-87.
31. J. K. Udupa and S. Samarasekera Fuzzy connectedness and object definition: Theory, algorithms and applications in image segmentation, Graphical Models Image Process. 58, 1996, 246-261.