Discrete bisector function and euclidean skeleton

Lecture Notes in Computer Science

Volumn 3429, Issue , 2005, Pages 216-227

  Couprie, Michel ^a,b   Zrour, Rita ^a,b  

^a Groupe ESIEE   (France)

^b CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

FILTRATION; MATHEMATICAL TECHNIQUES;

BISECTOR FUNCTION; EUCLIDEAN SKELETON; HOMOTOPY; THINNING METHODS;

ALGORITHMS;

EID: 24344490385     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-31965-8_21     Document Type: Conference Paper

References (26)

1. D. Attali, J.O. Lachaud: "Delaunay Conforming Iso-surface, Skeleton Extraction and Noise Removal", Computational Geometry: Theory and Applications, Vol. 19, pp. 175-189, 2001.
2. D. Attali, A. Montanvert: "Modelling noise for a better simplification of skeletons", Procs. International Conference on Image Processing, Vol. 3, pp. 13-16, 1996.
3. G. Bertrand: "Simple points, topological numbers and geodesic neighborhoods in cubic grids", Pattern Recognition Letters, Vol. 15, pp. 1003-1011, 1994.
4. S.N. Bespamyatnikh, "An efficient algorithm for the three-dimensional diameter problem", Procs. ACM-SIAM symp. on discrete algorithms, pp. 137-146, 1998.
5. H. Blum, "An associative machine for dealing with the visual field and some of its biological implications", Biological prototypes and synthetic systems, Vol. 1, pp. 244-260, 1961.
6. G. Borgefors, I. Ragnemalm, G. Sanniti di Baja, "The Euclidean distance transform: finding the local maxima and reconstructing the shape", Procs. of the 7th Scand. Conf. on image analysis, Vol. 2, pp. 974-981, 1991.
7. P.E. Danielsson: "Euclidean distance mapping", Computer Graphics and Image Processing, 14, pp. 227-248, 1980.
8. J.M. Chassery, A. Montanvert: Géométrie discrète, Hermès, 1991.
9. T.H. Cormen, C.E. Leiserson, R.L. Rivest: Introduction to algorithms, MIT Press, 1990.
10. M. Couprie, R. Zrour: "Discrete bisector function and Euclidean skeleton in 2D and 3D", report IGM2004-12 of the Institut Gaspard Monge (University of Marnela-Vallée), http://www-igm.univ-mlv.fr/LabInfo/rapportsInternes/2004/12.pdf, 2004.
11. X. Daragon, M. Couprie, G. Bertrand: "Discrete frontiers", Springer (Ed.), Discrete Geometry for Computer Imagery, Springer LNCS, Vol. 2886, pp. 236-245, 2003.
12. E.R. Davies, A.P.N. Plummer: "Thinning algorithms: a critique and a new methodology", Pattern Recognition, Vol. 14, pp. 53-63, 1981.
13. Y. Ge, J.M. Fitzpatrick: "On the generation of skeletons from discrete Euclidean distance maps", IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 18, No. 11, pp. 1055-1066, 1996.
14. G.H. Hardy, E.M. Wright: An introduction to the theory of numbers, Oxford University Press, 1938.
15. T. Yung Kong, A. Rosenfeld: "Digital topology: introduction and survey", Computer Vision, Graphics and Image Processing, Vol. 48, pp. 357-393, 1989.
16. L. Lam, S-W. Lee, C.Y. Suen: "Thinning methodologies - a comprehensive survey", IEEE PAMI, Vol. 14, No. 9, pp. 869-885, 1992.
17. M. Luppe, L. da Fontoura Costa, V. Obac Roda: "Parallel implementation of exact dilations and multi-scale skeletonization", Real-Time Imaging, Vol. 9, pp. 163-169, 2003.
18. F. Meyer, Cytologie quantitative et morphologie mathématique, PhD thesis, École des mines de Paris, 1979.
19. G. Malandain, S. Fernández-Vidal, "Euclidean Skeletons", Image and vision computing, Vol. 16, pp. 317-327, 1998.
20. A. Rosenfeld, A.C. Kak: Digital Image processing, Academic Press, 1982.
21. E. Rémy, E. Thiel: "Exact Medial Axis with Euclidean Distance", to appear in Image and Vision Computing, 2004.
22. T. Saito, J.I. Toriwaki: "New algorithms for Euclidean distance transformation of an n-dimensional digitized picture with applications", Pattern Recognition, Vol. 27, pp. 1551-1565, 1994.
23. T. Hirata: "A unified linear-time algorithm for computing distance maps", Information Processing Letters, Vol. 58(3), pp. 129-133, 1996.
24. M.I. Shamos: Computational geometry, PhD thesis, Yale University, 1978.
25. H. Talbot, L. Vincent: "Euclidean skeletons and conditional bisectors", Proceedings of VCIP'92, SPIE, Vol. 1818, pp. 862-876, 1992.
26. L. Vincent: "Efficient Computation of Various Types of Skeletons", Proceedings of Medical Imaging V, SPIE, Vol. 1445, pp. 297-311, 1991.