Quasi-linear algorithms for the topological watershed

Journal of Mathematical Imaging and Vision

Volumn 22, Issue 2, 2005, Pages 231-249

  Couprie, Michel ^a,b   Najman, Laurent ^a,b   Bertrand, Gilles ^a,b  

^a Groupe ESIEE   (France)

^b CNRS   (France)

Author keywords

Component tree; Discrete topology; Mathematical morphology; Segmentation; Watershed

Indexed keywords

ALGORITHMS; DAMS; IMAGE SEGMENTATION; MATHEMATICAL MORPHOLOGY; TOPOLOGY; TREES (MATHEMATICS); COMPUTER SIMULATION; IMAGE ANALYSIS; IMAGE ENHANCEMENT; IMAGE QUALITY; THEOREM PROVING;

COMPONENT TREES; DISCRETE TOPOLOGY; SEGMENTATION; TOPOLOGICAL WATERSHEDS; BINARY WATERSHEDS; GRAYSCALE IMAGES; WATERSHED TRANSFORMATIONS;

WATERSHEDS; IMAGE SEGMENTATION;

EID: 17444366556     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-005-4892-4     Document Type: Article

References (35)

1. G. Bertrand, "On topological watersheds," Journal of Mathematical Imaging and Vision, Vol. 22, Nos. 2/3, pp. ??-??, 2005.
2. G. Bertrand, J.C. Everat, and M. Couprie, "Image segmentation through operators based upon topology," Journal of Electronic Imaging, Vol. 6, No. 4, pp. 395-405, 1997.
3. S. Beucher and Ch. Lantuéjoul, "Use of watersheds in contour detection," in Proc. Int. Workshop on Image Processing, Real-Time Edge and Motion Detection/Estimation, Rennes, France, 1979.
4. S. Beucher and F. Meyer, "The morphological approach to segmentation: The watershed transformation," in Mathematical Morphology in Image Processing, Dougherty (Ed.), Chap. 12, Marcel Dekker, 1993, pp. 433-481.
5. M.A. Bender and M. Farach-Colton, "The LCA problem revisited," in Proc. 4th Latin American Symposium on Theoretical Informatics, LNCS, Springer, Vol. 1776, 2000, pp. 88-94.
6. U.M. Braga-Neto and J. Goutsias, "A theoretical tour of connectivity in image processing and analysis," Journal of Mathematical Imaging and Vision, Vol. 19, pp. 5-31, 2003.
7. E.J. Breen and R. Jones, "Attribute openings, thinnings and granulometries," Computer Vision and Image Understanding, Vol. 64, No. 3, pp. 377-389, 1996.
8. T. H. Cormen, C. Leiserson, and R. Rivest, Introduction to Algorithms, McGraw-Hill, 1990.
9. M. Couprie and G. Bertrand, "Topological grayscale watershed transformation," in Proc. SPIE Vision Geometry VI, Vol. 3168, 1997, pp. 136-146.
10. M. Couprie, F.N. Bezerra, and G. Bertrand, "Topological operators for grayscale image processing," Journal of Electronic Imaging, Vol. 10, No. 4, pp. 1003-1015, 2001.
11. V. Goetcherian, "From binary to grey tone image processing using fuzzy logic concepts," Pattern Recognition, Vol. 12, No. 12, pp. 7-15, 1980.
12. P. Guillataud, "Contribution á l'analyse dendroniques des images," PhD thesis of Université de Bordeaux I, 1992.
13. P. Hanusse and P. Guillataud, "Sémantique des images par analyse dendronique," in 8th Conf. Reconnaissance des Formes et Intelligence Artificielle, AFCET Ed., Lyon, Vol. 2, 1992, pp. 577-588.
14. J.A. Hartigan, "Statistical theory in clustering," Journal of classification, No. 2, pp. 63-76, 1985.
15. D. Harel and R.E. Tarjan, "Fast algorithms for finding nearest common ancestors," SIAM J. Comput., Vol. 13, No. 2, pp. 338-355, 1984.
16. R. Jones, "Connected filtering and segmentation using component trees," Computer Vision and Image Understanding, Vol. 75, No. 3, pp. 215-228, 1999.
17. T.Y Kong and A. Rosenfeld, "Digital topology: Introduction and survey," Computer Vision, Graphics and Image Processing, Vol. 48, pp. 357-393, 1989.
18. J. Mattes and J. Demongeot, "Tree representation and implicit tree matching for a coarse to fine image matching algorithm," in Proc. MICCAI, LNCS, Springer, Vol. 1679, 1999, pp. 646-655.
19. J. Mattes and J. Demongeot, "Efficient algorithms to implement the confinement tree," in Proc. DGCI, LNCS, Springer, Vol. 1953, 2000, pp. 392-405.
20. J. Mattes, M. Richard, and J. Demongeot, "Tree representation for image matching and object recognition," in Proc. DGCI, LNCS, Springer, Vol. 1568, 1999, pp. 298-309.
21. A. Meijster and M. Wilkinson, "A comparison of algorithms for connected set openings and closings," IEEE PAMI, Vol. 24, pp. 484-494, 2002.
22. F. Meyer, "Un algorithme optimal de ligne de partage des eaux," in Proc. 8th Conf. Reconnaissance des Formes et Intelligence Artificielle, AFCET Ed., Lyon, Vol. 2, 1991, pp. 847-859.
23. L. Najman and M. Couprie, "Watershed algorithms and contrast preservation," in Proc. DGCI, LNCS, Springer, Vol. 2886, 2003, pp. 62-71.
24. L. Najman and M. Couprie, "Quasi-linear algorithm for the component tree," in Proc. SPIE Vision Geometry XII, Vol. 5300, 2004, pp. 98-107.
25. L. Najman, M. Couprie, and G. Bertrand, "Watersheds, mosaics, and the emergence paradigm," to appear in Discrete Applied Mathematics, 2005.
26. L. Najman and M. Schmitt, "Watershed of a continuous function," Signal Processing, Vol. 38, pp. 99-112, 1994.
27. J.B.T.M. Roerdink and A. Meijster, "The watershed transform: Definitions, algorithms and parallelization strategies," Fundamenta Informaticae, Vol. 41, pp. 187-228, 2000.
28. A. Rosenfeld, "On connectivity properties of grayscale pictures," Pattern Recognition, Vol. 16, pp. 47-50, 1983.
29. J. Serra, Image Analysis and Mathematical Morphology, Vol. II: Theoretical Advances, Academic Press, 1988.
30. P. Salembier, A. Oliveras, and L. Garrido, "Antiextensive connected operators for image and sequence processing," IEEE Trans. on Image Processing, Vol. 7, No. 4, pp. 555-570, 1998.
31. R.E. Tarjan, "Disjoint sets," Data Structures and Network Algorithms, Chap. 2, SIAM, 1978, pp. 23-31.
32. M. Thorup, "On RAM priority queues," in 7th ACM-SIAM Symposium on Discrete Algorithms, 1996, pp. 59-67.
33. C. Vachier, "Extraction de caractéristiques, segmentation d'images et Morphologie Mathématique," PhD Thesis, École des Mines, Paris, 1995.
34. L. Vincent and P. Soille, "Watersheds in digital spaces: An efficient algorithm based on immersion simulations," IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 13, No. 6, pp. 583-598, 1991.
35. D. Wishart, "Mode analysis: A generalization of the nearest neighbor which reduces chaining effects," in Numerical Taxonomy, A.J. Cole (Ed.), Academic Press, 1969, pp. 282-319.