Connectivity on Complete Lattices

Journal of Mathematical Imaging and Vision

Volumn 9, Issue 3, 1998, Pages 231-251

  Serra, Jean ^a,b,c,d,e  

^a PSL RESEARCH UNIVERSITY   (France)

^b Campus of Fountainebleau ^*

^c Intl Soc for Math Morphology   (France)

^d Intl Soc for Math Morphology   (France)

^e UNIVERSITY OF BARCELONA   (Spain)

Author keywords

Complete lattices; Connected operators; Connectivity; Filters by reconstruction; Mathematical morphology; Watershed

Indexed keywords

FUNCTIONS; IMAGE RECONSTRUCTION; MATHEMATICAL MORPHOLOGY; MATHEMATICAL OPERATORS; SET THEORY; TOPOLOGY;

SUP GENERATED LATTICES; WATERSHED MAPPINGS;

IMAGE ANALYSIS;

EID: 0032206377     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008324520475     Document Type: Article

References (41)

1. G. Choquet, Topology, Academic Press, 1966.
2. A. Rosenfeld, "Connectivity in digital pictures," J. Assoc. Comp. Mach., Vol. 17, No. 1, pp. 146-160, 1970.
3. H. Digabel and Ch. Lantuejoul, Practical Metallography, Special issue, J.-L. Chermant (Ed.), No. 8, pp. 85-99, 1978.
4. J. Serra, Image Analysis and Mathematical Morphology, Vol. 1, Academic Press: London 1982.
5. J.-C. Klein, "Conception et réalisation d'une unité logique pour l'analyse quantitative d'images," Ph.D. thesis, University of Nancy, 1976.
6. C. Lantuejoul and S. Beucher, "On the use of the geodesic metric in image analysis," J. of Microsc, Vol. 121, pp. 39-49, 1981.
7. G. Matheron, "Remarques sur les fermetures-partitions," Int. Rep. Centre de Géostatistique et de Morphologie Mathématique, Ecole des Mines de Paris, 1985.
8. G. Matheron and J. Serra, "Strong filters and connectivity," in Image Analysis and Mathematical Morphology. J. Serra (Ed.), Academic Press: London, 1988, Vol. 2, pp. 141-157.
9. J. Serra (Ed.), Image Analysis and Mathematical Morphology, Vol. 2, Academic Press: London, 1988.
10. J. Serra and P. Salembier, "Connected operators and pyramids," in SPIE, Nonlinear Algebra and Morphological Image Processing, Vol. 2030, San Diego, July 1993, pp. 65-76.
11. J. Crespo, "Morphological connected filters and intra-region smoothing for image segmentation," Ph.D. thesis, School of Electrical Engineering, Georgia Institute of Technology, 1993.
12. F. Meyer, "Minimum spanning forests for morphological segmentation," in Mathematical Morphology and its Applications to Image and Signal Processing, P. Maragos et al. (Eds.), Kluwer, 1996.
13. J. Crespo and J. Serra, "Morphological pyramids for image coding," in SPIE, Visual Communications and Image Processing, Vol. 2094, Cambridge, Nov. 1993, pp. 159-170.
14. E. Breen and R. Jones, "An attribute-based approach to mathematical morphology," in Mathematical Morphology and its Applications to Image and Signal Processing, P. Maragos et al. (Eds.), Kluwer, 1996.
15. P. Salembier and J. Serra, "Multiscale image segmentation," in SPIE, Visual Communications and Image Processing, Boston, Vol. 1818, Nov. 1992, pp. 620-631.
16. L. Vincent, "Morphological grayscale reconstruction in image analysis: Applications and efficient algorithms," IEEE Transactions in Image Processing, Vol. 2, pp. 176-201, 1993.
17. J. Crespo and J. Serra, "Etude sur la méthode des zones plates (flat zone approach)," Réunion Morpheco-Race (Int. Rep. CT-06/93/MM, Ecole des Mines de Paris), Lausanne, March 1993.
18. H. Pardàs, J. Serra, and L. Torrès, "Connectivity filters for image sequences," in SPIE, Vol. 1769, 1992, pp. 318-329.
19. C. Ronse, "Openings: Main properties, and how to construct them," in Mathematical Morphology: Theory and Hardware, R.M. Haralick (Ed.), Oxford Series on Optical and Imaging Sciences, Vol. 10, Oxford Univ. Press, (1997) to appear.
20. C. Ronse, "Set theoretical algebraic approaches to connectivity in continuous or digital spaces," JMIV, 1998, Vol. 8, pp. 41-58.
21. B. Marcotegui, "Segmentationde séquences d'images en vue du codage," Ph.D. thesis, Ecole des Mines, April 1996.
22. B. Marcotegui and F. Meyer, "Morphological segmentation of image sequences," in Mathematical Morphology and its Applications to Image Processing, J. Serra and P. Soille (Eds.), Kluwer, 1994, pp. 101-108.
23. C. Vachier and F. Meyer, "Extinction value, a new measurement of persistence," IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, June 1995.
24. J. Serra and L. Vincent, "An overview of morphological filtering," Circuit Systems and Signal Processing, Vol. 11, No. 1, 1992.
25. M. Pardas and P. Salembier, "Joint region and motion estimation with morphological tools," in Mathematical Morphology and Its Applications to Image Processing, J. Serra and P. Soille (Eds.), Kluwer, 1994, pp. 93-100.
26. J. Crespo, J. Serra, and R.W. Schafer, "Theoretical aspects of morphological filters by reconstruction," Signal Processing, Vol. 47, No 2, pp. 201-225, 1995.
27. P. Salembier and A. Oliveras, "Practical extensions of connected operators," in Mathematical Morphology and its Applications to Image and Signal Processing, P. Maragos et al. (Eds.), Kluwer, 1996, pp. 97-110.
28. R.M. Haralick and L.G. Shapiro, Computer and Robot Vision. Addison Wesley, 1992, Vol. I, pp. 191-198.
29. G. Birkhoff, Lattice Theory, American Mathematical Society, Providence, 1984.
30. G. Matheron, "Les treillis compacts," Tech. rep. N-23/90/G, Ecole des Mines de Paris, Part 1, 1990, Part 2, 1996.
31. H.J.A.M. Heijmans, "Morphological image operators," Advances in Electronics and Electron Physics, suppl. 24, Vol. 50, P. Hawkes (Ed.), Academic Press: Boston.
32. Gierz et al., A Compendium on Continuous Lattices, Springer, 1980.
33. J. Serra, "Mathematical Morphology for complete lattices," in Image Analysis and Mathematical Morphology, Vol. 2, J. Serra (Ed.), Academic Press, London, 1988, pp. 13-35.
34. H.J.A.M. Heijmans and C. Ronse, "The algebraic basis of Mathematical Morphology," Computer Vision, Graphics and Image Processing, Vol. 50, pp. 245-295, 1990.
35. G. Matheron, "Filters and lattices," in Image Analysis and Mathematical Morphology, Vol. 2, J. Serra (Ed.), Academic Press, London, 1988, pp. 115-140.
36. H.J.A.M. Heijmans and J. Serra, "Convergence, continuity and iteration in Mathematical Morphology," J. of Visual Communication and Image Representation, Vol. 3, No 1, pp. 84-102, 1995.
37. G. Matheron, Random Sets and Integral Geometry, Wiley: New York, 1975.
38. L. Najman and M. Schmitt, "Definition and some properties of the watershed of a continuous function," Signal Processing, Vol. 38, pp. 99-112, 1994.
39. F. Meyer, "Topographic distance and watershed line," Signal Processing, Vol. 38, pp. 113-125, 1994.
40. J. Serra, "Equicontinuous functions, a model for mathematical morphology," in SPIE, Vol. 1769, San Diego, July 1992, pp. 252-263.
41. H. Heijmans, "Introduction to connected operators," Nonlinear Filters in Image Processing, E.R. Dougherty and J. Astola (Eds.), Optical Engineering Press, 1997.