Euler characteristics of discrete objects and discrete quasi-objects

Computer Vision and Image Understanding

Volumn 75, Issue 3, 1999, Pages 307-318

  Imiya, Atsushi ^a   Eckhardt, Ulrich ^b  

^a CHIBA UNIVERSITY   (Japan)

^b UNIVERSITY OF HAMBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER VISION; GEOMETRY; GRAPH THEORY; TOPOLOGY; TWO DIMENSIONAL;

DISCRETE OBJECTS; DISCRETE QUASI OBJECTS; EULER CHARACTERISTICS; GRAPH REWRITING;

OBJECT RECOGNITION;

EID: 0033350086     PISSN: 10773142     EISSN: None     Source Type: Journal    
DOI: 10.1006/cviu.1999.0791     Document Type: Article

References (20)

1. Imiya A. Geometry of three-dimensional neighborhood and its applications. Trans. Inform. Process. Soc. Jpn. 34:1993;2153-2164.
2. Y. Kenmochi, A. Imiya, and R. Ezuquera, Polyhedra generation from lattice points, in Discrete Geometry for Computer ImageryS. Miguet, A. Montanvert, and S. Ubéda, Eds., pp. 127-138, Lecture Notes in Computer Science, Vol. 1176, Springer-Verlag, Berlin, 1996.
3. Y. Kenmochi and A. Imiya, Deformation of discrete object surfaces, in Computer Analysis of Images and PatternsG. Sommer, K. Daniilidis, and J. Pauli, Eds., pp. 146-153, Lecture Notes in Computer Science, Vol. 1296, Springer-Verlag, Berlin, 1997.
4. Z. Aktouf, G. Bertrand, and L. Perrton, A three-dimensional holes closing algorithm, in Discrete Geometry for Computer ImageryS. Miguet, A. Montanvert, and S. Ubéda, Eds., pp. 36-38, Lecture Notes in Computer Science, Vol. 1176, Springer-Verlag, Berlin, 1996.
5. Grünbaum B. Convex Polytopes. 1967.
6. Okabe A., Boots B., Sugihara K. Spatial Tessellations Concepts and Applications of Voronoi Diagrams. 1992.
7. Hopf H. Differential Geometry in the Large. 1000:1983.
8. Serra J. Image Analysis and Mathematical Morphology. 1982.
9. Toriwaki J.-I. Digital Image Processing for Image Understanding. 1:1988.
10. Yonekura T., Toriwaki J.-I., Fukumura T., Yokoi S. On connectivity and the Euler number of three-dimensional digitized binary picture. Trans. IECE Jpn. E63:1980;815-816.
11. J.-I. Toriwaki, S. Yokoi, T. Yonekura, and T. Fukumura, Topological properties and topological preserving transformation of a three-dimensional binary picture, in Proc. of the 6th ICPR, 1982, pp. 414-419.
12. Lee C.-N., Poston T., Rosenfeld A. Holes and genus of 2D and 3D digital images. CVGIP Graph. Models Image Process. 55:1993;20-47.
13. Françon J. Sur la topologie d'un plan arithmétique. Theoret. Comput. Sci. 156:1996;159-176.
14. Bonnington C. P., Little C. H. C. The Foundation of Toplogical Graph Theory. 1995.
15. Bieri H., Nef W. Algorithms for the Euler characteristic and related additive functionals of digital objects. Comput. Vision Graphics Image Process. 28:1984;166-175.
16. d. Computing. 28:1982;189-198.
17. Bieri H., Nef W. A sweep-plane algorithm for computing the volume of polyhedra represented in Boolean form. Linear Algebra Appl. 52/53:1983;69-97.
18. Bieri H., Nef W. A sweep-plane algorithm for computing the Euler-characteristic of polyhedra represented in Boolean form. Computing. 34:1985;287-304.
19. H. Stark and H. Peng, Shape estimation in computer tomography from minimal data, in Proc. of 9th ICPR, 1998, Vol. 1, pp. 184-186.
20. Ludwing D. The Radon transform on Euclidean space. Comm. Pure Appl. Math. 19:1966;49-81.