A 3D 6-subiteration curve thinning algorithm based on P-simple points

Discrete Applied Mathematics

Volumn 151, Issue 1-3, 2005, Pages 198-228

  Lohou, Christophe ^a,c   Bertrand, Gilles ^b  

^a UNIVERSITÉ CLERMONT AUVERGNE   (France)

^b Ecole Superieure d'Ingenieurs en Electrotechnique et Electronique   (France)

^c Institut Universitaire de Technologie   (France)

Author keywords

3D thinning algorithm; Digital topology; P simple point; Topology preservation

Indexed keywords

ALGORITHMS; IMAGE ANALYSIS; ITERATIVE METHODS;

DIGITAL TOPOLOGY; P-SIMPLE POINTS; TOPOLOGY PRESERVATION;

MATHEMATICAL TECHNIQUES;

EID: 25144522750     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2005.02.030     Document Type: Conference Paper

References (47)

1. G. Bertrand Simple points, topological numbers and geodesic neighborhoods in cubic grids Pattern Recogn. Lett. 15 1994 1003 1011
2. G. Bertrand, On P-simple points, in: Compte Rendu de l'Académie des Sciences de Paris (Computer Science/Theory of Signals), Série I, vol. 321, 1995, pp. 1077-1084.
3. G. Bertrand, P-simple points: a solution for parallel thinning, in: Actes du 5ème colloque Discrete Geometry for Computer Imagery, DGCI'1995, Clermont-Ferrand, France, 1995, pp. 233-242.
4. G. Bertrand, Sufficient conditions for 3D parallel thinning algorithms, in: Conference on Vision Geometry IV, San Diego, CA, USA, SPIE, vol. 2573, Bellingham, WA, 1995, pp. 52-60.
5. G. Bertrand, Z. Aktouf, A three-dimensional thinning algorithm using subfields, in: Conference on Vision Geometry III, Boston, MA, USA, SPIE, vol. 2356, Bellingham, WA, 1994, pp. 113-124.
6. G. Bertrand, C. Lohou, Three dimensional parallel thinning algorithms based on P-simple points, Congrès à l'occasion du soixantième anniversaire de Denis Richard, Clermont-Ferrand, France, 2002.
7. G. Bertrand, and G. Malandain A new characterization of three-dimensional simple points Pattern Recogn. Lett. 15 1994 169 175
8. 3 J. Math. Imag. Vision 11 1999 207 221
9. G. Borgefors, I. Nyström, and G. Sanniti di Baja Computing skeletons in three dimensions Pattern Recognition 32 7 1999 1225 1236
10. K. Brace, R. Rudell, and R. Bryant Efficient implementation of a bdd package ACM-IEEE 27th Design Automation Conference Orlando, FL, USA 1990 40 45
11. R. Bryant Graph-based algorithms for boolean function manipulation IEEE Trans. Comput. C-35 8 1986 677 691
12. J. Burguet, and R. Malgouyres Polyhedric approximation of the surface of a voxel object Discrete Appl. Math. 125 1 2003 93 114
13. S. Fourey, R. Malgouyres, A concise characterization of 3D simple points, in: International Conference on Discrete Geometry for Computer Imagery, DGCI'2000, Uppsala, Sweden, LNCS, vol. 1953, Springer, Berlin, 2000, pp. 27-36.
14. W. Gong, and G. Bertrand A simple parallel 3D thinning algorithm International Conference on Pattern Recognition Atlantic City, NJ, USA 1990 188 190
15. R. Hall, Connectivity preserving parallel operators in 2D and 3D images, in: Conference on Vision Geometry, Boston, MA, USA, SPIE, vol. 1832, Bellingham, WA, 1992, pp. 172-183.
16. T. Kong A digital fundamental group Comput. and Graphics 13 2 1989 159 166
17. T. Kong, On the problem of determining whether a parallel reduction operator for n-dimensional binary images always preserves topology, in: Conference on Vision Geometry II, Boston, MA, USA, SPIE, vol. 2060, Bellingham, WA, 1993, pp. 69-77.
18. T. Kong On topology preservation in 2-D and 3-D thinning Internat. J. Pattern Recogn. Artif. Intell. 9 5 1995 813 844
19. T. Kong, Topology-preserving deletion of 1's from 2-, 3- and 4-dimensional binary images, in: International Conference on Discrete Geometry for Computer Imagery, DGCI'1997, Montpellier, France, LNCS, vol. 1347, Springer, Berlin, 1997, pp. 3-18.
20. T. Kong, and A. Rosenfeld Digital topology introduction and survey Comput. Vision Graphics Image Process. 48 1989 357 393
21. C. Lohou, G. Bertrand, A new 3D 12-subiteration thinning algorithm based on P-simple points, in: International Workshop on Combinatorial Image Analysis, IWCIA 2001, Philadelphia, PA, USA, ENTCS, vol. 46, 2001, pp. 39-58.
22. C. Lohou, G. Bertrand, A new 3D 6-subiteration thinning algorithm based on P-simple points, in: International Conference on Discrete Geometry for Computer Imagery, DGCI'2002, Bordeaux, France, LNCS, vol. 2301, Springer, Berlin, 2002, pp. 102-113.
23. C. Lohou, G. Bertrand, Two 3D symmetrical thinning algorithms based on P-simple points, International Workshop on Combinatorial Image Analysis, IWCIA 2003, Palermo, Italy, 2003.
24. C. Lohou, and G. Bertrand A 3D 12-subiteration thinning algorithm based on P-simple points Discrete Appl. Math. 139 1-3 2004 171 195
25. C. Ma On topology preservation in 3D thinning Comput. Vision Graphics Image Process. Image Understanding 59 3 1994 328 339
26. C. Ma A 3D fully parallel thinning algorithm for generating medial faces Pattern Recogn. Lett. 16 1995 83 87
27. C. Ma, and M. Sonka A fully parallel 3D thinning algorithm and its applications Comput. Vision Image Understanding 64 3 1996 420 433
28. C. Ma, S.-Y. Wan, and J.-D. Lee Three-dimensional topology preserving reduction on the 4-subfields IEEE Trans. Pattern Anal. Mach. Intell. 24 12 2002 1594 1605
29. G. Malandain, and G. Bertrand Fast characterization of 3D simple points International Conference on Pattern Recognition The Hague, The Netherlands 1992 232 235
30. R. Malgouyres, S. Fourey, Strong surfaces, surface skeletons and image superimposition, in: Conference on Vision Geometry VII, San Diego, CA, USA, SPIE, vol. 3454, Bellingham, WA, 1998, pp. 16-27.
31. A. Manzanera, T. Bernard, F. Prêteux, B. Longuet, A unified mathematical framework for a compact and fully parallel n-D skeletonization procedure, in: Conference on Vision Geometry VIII, Denver, CO, USA, SPIE, vol. 3811, Bellingham, WA, 1999, pp. 57-68.
32. D. Morgenthaler, Three-dimensional simple points: Serial erosion, parallel thinning, and skeletonization, Technical Report TR-1005, Computer Vision Laboratory, University of Maryland, 1981.
33. K. Palágyi, and A. Kuba A 3D 6-subiteration thinning algorithm for extracting medial lines Pattern Recogn. Lett. 19 7 1998 613 627
34. K. Palágyi, and A. Kuba A hybrid thinning algorithm for 3D medical images J. Comput. Inform. Tech. 6 2 1998 149 164
35. K. Palágyi, and A. Kuba A parallel 3D 12-subiteration thinning algorithm Graphical Models Image Process. 61 1999 199 221
36. L. Robert, and G. Malandain Fast binary image processing using binary decision diagrams Comput. Vision Image Understanding 72 1 1998 1 9
37. F. Rolland, J.-M. Chassery, and A. Montanvert 3D medial surfaces and 3D skeletons International Workshop on Visual Form Capri, Italy 1991 443 450
38. C. Ronse A topological characterization of thinning Theoret. Comput. Sci. 43 1986 31 41
39. C. Ronse Minimal test patterns for connectivity preservation in parallel thinning algorithms for binary digital images Discrete Appl. Math. 21 1988 67 79
40. A. Rosenfeld A characterization of parallel thinning algorithms Inform. Control 29 1975 286 291
41. A. Rosenfeld, and A. Kak Digital Picture Processing 1982 Academic Press New York
42. P. Saha, B. Chanda, D. Majumder, Principles and algorithms for 2D and 3D shrinking, Technical Report TR/KBCS/2/91, N.C.K.B.C.S. Library, Indian Statistical Institute, Calcutta, India, 1991.
43. P. Saha, and B. Chaudhuri Detection of 3-D simple points for topology preserving transformations with application to thinning IEEE Trans. Pattern Anal. Mach. Intell. 16 10 1994 1028 1032
44. P. Saha, B. Chaudhuri, B. Chanda, and D.D. Majumder Topology preservation in 3D digital space Pattern Recognition 27 2 1994 295 300
45. P. Saha, B. Chaudhuri, and D.D. Majumder A new shape preserving parallel thinning algorithm for 3D digital images Pattern Recognition 30 12 1997 1939 1955
46. J. Serra Image Analysis and Mathematical Morphology 1982 Academic Press New York
47. Y. Tsao, and K. Fu A parallel thinning algorithm for 3D pictures Comput. Graphics Image Process. 17 1981 315 331