Connected operators: A review of region-based morphological image processing techniques

IEEE Signal Processing Magazine

Volumn 26, Issue 6, 2009, Pages 136-157

  Salembier, Philippe ^a   Wilkinson, Michael H F ^b  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

Data mining; Filtering theory; Image processing; Image reconstruction; Lattices; Shape control

Indexed keywords

CRYSTAL LATTICES; DATA MINING; FILTRATION; FORESTRY; IMAGE RECONSTRUCTION; IMAGE SEGMENTATION; LATTICE THEORY; OBJECT RECOGNITION;

ARBITRARY OPERATORS; CLASSICAL FILTERS; CONNECTED OPERATOR; FILTERING THEORY; FILTERING TOOLS; MORPHOLOGICAL IMAGE PROCESSING; RECONSTRUCTION PROCESS; SHAPE CONTROL;

IMAGE PROCESSING;

EID: 85032751427     PISSN: 10535888     EISSN: None     Source Type: Journal    
DOI: 10.1109/MSP.2009.934154     Document Type: Review

References (59)

1. J. Serra and P. Salembier, "Connected operators and pyramids," in Image Algebra and Mathematical Morphology, E. R. Dougherty, P. D. Gader, and J. Serra, Eds., vol. 2030. San Diego, CA: SPIE, July 1993, pp. 65-76.
2. J. Crespo, J. Serra, and R. Schafer, "Theoretical aspects of morphological filters by reconstruction," Signal Process., vol. 47, no. 2, pp. 201-225, 1995.
3. H. J. A. M. Heijmans, "Connected morphological operators for binary images," Comput. Vision Image Understanding, vol. 73, no. 1, pp. 99-120, 1999.
4. J. Crespo and R. Schafer, "Locality and adjacency stability constraints for morphological connected operators," J. Math. Imaging Vision, vol. 7, no. 1, pp. 85-102, 1997.
5. F. Meyer, "From connected operators to levelings," in Proc. 4th Int. Symp. Mathematical Morphology, ISMM'98. Amsterdam, The Netherlands: Kluwer, June 1998, pp. 191-198.
6. F. Meyer, "The levelings," in Proc. 4th Int. Symp. Mathematical Morphology, ISMM'98. Amsterdam, The Netherlands: Kluwer, June 1998, pp. 199-206.
7. J. Serra, "Connectivity on complete lattices," J. Math. Imaging Vision, vol. 9, no. 3, pp. 231-251, 1998.
8. C. Ronse, "Set-theoretical algebraic approaches to connectivity in continuous or digital spaces," J. Math. Imaging Vision, vol. 8, no. 1, pp. 41-58, 1998.
9. U. Braga-Neto and J. Goutsias, "A theoretical tour of connectivity in image processing and analysis," J. Math. Imaging Vision, vol. 19, no. 1, pp. 5-31, 2003.
10. G. K. Ouzounis and M. H. F. Wilkinson, "Mask-based second generation connectivity and attribute filters," IEEE Trans. Pattern Anal. Machine Intell., vol. 29, no. 6, pp. 990-1004, 2007.
11. J. Crespo and V. Maojo, "The strong property of morphological connected alternated filters," J. Math. Imaging Vision, vol. 32, no. 3, pp. 251-263, 2008.
12. L. Vincent, "Morphological area opening and closing for grayscale images," in Proc. NATO Shape in Picture Workshop. Driebergen, The Netherlands: Springer-Verlag, Sept. 1992, pp. 197-208.
13. L. Vincent, "Morphological gray scale reconstruction in image analysis: Applications and efficients algorithms," IEEE Trans. Image Processing, vol. 2, no. 2, pp. 176-201, Apr. 1993.
14. E. Breen and R. Jones, "Attribute openings, thinnings and granulometries," Comput. Vision Image Understanding, vol. 64, no. 3, pp. 377-389, Nov. 1996.
15. P. Salembier, A. Oliveras, and L. Garrido, "Anti-extensive connected operators for image and sequence processing," IEEE Trans. Image Processing, vol. 7, no. 4, pp. 555-570, Apr. 1998.
16. C. Gomila and F. Meyer, "Levelings in vector space," in Proc. IEEE Int. Conf. Image Processing, ICIP'99, vol. 2, Kobe, Japan, Oct. 1999, pp. 929-933.
17. P. Monasse and F. Guichard, "Fast computation of a contrast invariant image representation," IEEE Trans. Image Processing, vol. 9, no. 5, pp. 860-872, May 2000.
18. P. Salembier and L. Garrido, "Binary partition tree as an efficient representation for image processing, segmentation and information retrieval," IEEE Trans. Image Processing, vol. 9, no. 4, pp. 561-576, Apr. 2000.
19. L. Najman and M. Couprie, "Building the component tree in quasi-linear time," IEEE Trans. Image Processing, vol. 15, no. 11, pp. 3531-3539, Nov. 2000.
20. A. Meijster and M. H. F. Wilkinson, "A comparison of algorithms for connected set openings and closings," IEEE Trans. Pattern Anal. Machine Intell., vol. 24, no. 4, pp. 484-494, 2002.
21. F. Cheng and A. N. Venetsanopoulos, "An adaptive morphological filter for image processing," IEEE Trans. Image Processing, vol. 1, no. 4, pp. 533-539, 1992.
22. P. Salembier and M. Kunt, "Size-sensitive multiresolution decomposition of images with rank order based filters," Signal Process., vol. 27, no. 2, pp. 205-241, May 1992.
23. P. Salembier and J. Serra, "Flat zones filtering, connected operators and filters by reconstruction," IEEE Trans. Image Processing, vol. 3, no. 8, pp. 1153-1160, Aug. 1995.
24. J. Crespo, R. Shafer, J. Serra, C. Gratin, and F. Meyer, "A flat zone approach: A general low-level region merging segmentation method," Signal Process., vol. 62, no. 1, pp. 37-60, Oct. 1997.
25. N. Ray and S. Acton, "Inclusion filters: A class of self-dual connected operators," IEEE Trans. Image Processing, vol. 14, no. 11, pp. 1736-1746, Nov. 2005.
26. P. Maragos and G. Evangelopoulos, "Leveling cartoons, texture energy markers, and image decomposition," in Proc. Int. Symp. Mathematical Morphology (INPE), G. J. F. Banon, J. Barrera, U. d. M. Braga-Neto, and N. S. T. Hirata, Eds. Rio de Janeiro, Brazil, Oct. 10-13, 2007, pp. 125-138.
27. E. R. Urbach, J. B. T. M. Roerdink, and M. H. F. Wilkinson, "Connected shapesize pattern spectra for rotation and scale-invariant classification of gray-scale images," IEEE Trans. Pattern Anal. Machine Intell., vol. 29, no. 2, pp. 272-285, 2007.
28. V. Vilaplana, F. Marques, and P. Salembier, "Binary partition trees for object detection," IEEE Trans. Image Processing, vol. 17, no. 11, pp. 1-16, Nov. 2008.
29. J. Serra, Image Analysis and Mathematical Morphology. New York: Academic, 1982.
30. J. Serra, Image Analysis and Mathematical Morphology, Vol. II: Theoretical Advances. New York: Academic, 1988.
31. R. Jones, "Connected filtering and segmentation using component trees," Comput. Vision Image Understanding, vol. 75, no. 3, pp. 215-228, 1999.
32. D. Gatica-Perez, C. Gu, M. T. Sun, and S. Ruiz-Correa, "Extensive partition operators, gray-level connected operators, and region merging/ classification segmentation algorithms: Theoretical links," IEEE Trans. Image Processing, vol. 10, no. 9, pp. 1332-1345, 2001.
33. J. Serra, "A lattice approach to segmentation," J. Math. Imaging Vision, vol. 24, no. 1, pp. 83-130, 2006.
34. C. Ronse, "Partial partitions, partial connections and connective segmentation," J. Math. Imaging Vision, vol. 32, no. 1, pp. 97-125, 2008.
35. J. Klein, "Conception et réalisation d'une unité logique pour l'analyse quantitative d'images," Ph.D. dissertation, Nancy Univ., France, 1976.
36. M. Grimaud, "A new measure of contrast: The dynamics," in Proc. SPIE Visual Communications and Image Processing'92, vol. SPIE 1769, S. Gader and E. R. Dougherty, Eds. San Diego, CA: SPIE, July 1992, pp. 292-305.
37. R. van den Boomgaard and A. Smeulders, "The morphological structure of images, the differential equations of morphological scale-space," IEEE Trans. Pattern Anal. Machine Intell., vol. 16, no. 11, pp. 1101-1113, 1994.
38. P. Maragos, "Differential morphology and image processing," IEEE Trans. Image Processing, vol. 5, no. 6, pp. 922-937, 1996.
39. F. Meyer and P. Maragos, "Nonlinear scale-space representation with levelings," J. Vis. Commun. Image Represent., vol. 11, no. 2, pp. 245-265, Apr. 2000.
40. L. Vincent, "Graphs and mathematical morphology," Signal Process. vol. 16, no. 4, pp. 365-388, Apr. 1989.
41. O. Morris, M. Lee, and A. Constantinidies, "Graph theory for image analysis: An approach based on the shortest spanning tree," IEE Proc. F, vol. 133, no. 2, pp. 146-152, Apr. 1986.
42. L. Garrido, P. Salembier, and D. Garcia, "Extensive operators in partition lattices for image sequence analysis," Signal Process., vol. 66, no. 2, pp. 157-180, Apr. 1998.
43. F. Calderero and F. Marqués, "General region merging approaches based on information theory statistical measures," in Proc. Int. Conf. Image Processing 2008, pp. 3016-3019.
44. Y. Sato, S. Nakajima, N. Shiraga, H. Atsumi, S. Yoshida, T. Koller, G. Gerig, and R. Kinikis, "3D multiscale line filter for segmentation and visualization of curvilinear structures in medical images," Med. Image Anal., vol. 2, no. 2, pp. 143-168, 1998.
45. M. H. F. Wilkinson and M. A. Westenberg, "Shape preserving filament enhancement filtering," in Proc. MICCAI'2001 (Lecture Notes in Computer Science, vol. 2208), W. J. Niessen and M. A. Viergever, Eds. Utrecht, The Netherlands: Springer, 2001, pp. 770-777.
46. M. A. Westenberg, J. B. T. M. Roerdink, and M. H. F. Wilkinson, "Volumetric attribute filtering and interactive visualization using the max-tree representation," IEEE Trans. Image Processing, vol. 16, no. 12, pp. 2943-2952, 2007.
47. A. Viterbi and J. Omura, Principles of Digital Communications and Coding. New York: McGraw-Hill, 1979.
48. Y. Shoham and A. Gersho, "Efficient bit allocation for an arbitrary set of quantizers," IEEE Trans. Acoustics, Speech, and Signal Processing vol. 36, pp. 1445-1453, Sept. 1988.
49. R. E. Tarjan, "Efficiency of a good but not linear set union algorithm," J. ACM, vol. 22, no. 2, pp. 215-225, 1975.
50. T. Géraud, "Ruminations on Tarjan's union-find algorithm and connected operators," in Proc. Int. Symp. Mathematical Morphology (ISMM) 2005, Paris, Apr. 18-20, 2005, pp. 105-116.
51. C. Berger, T. Geraud, R. Levillain, N. Widynski, A. Baillard, and E. Bertin, "Effective component tree computation with application to pattern recognition in astronomical imaging," in Proc. Int. Conf. Image Processing 2007, San Antonio, TX, Sept. 16-19, 2007, pp. IV 40-44.
52. M. H. F. Wilkinson, H. Gao, W. H. Hesselink, J. E. Jonker, and A. Meijster, "Concurrent computation of attribute filters using shared memory parallel machines," IEEE Trans. Pattern Anal. Machine Intell. vol. 30, no. 10, pp. 1800-1813, 2008.
53. J. Serra, "Mathematical morphology for Boolean lattices," in Image Analysis and Mathematical Morphology, II: Theoretical Advances, J. Serra, Ed. London: Academic, 1988, ch. 2, pp. 37-58.
54. U. Braga-Neto and J. Goutsias, "Connectivity on complete lattices: New results," Comput. Vision Image Understanding, vol. 85, no. 1, pp. 22-53, 2002.
55. M. Nagao, T. Matsuyama, and Y. Ikeda, "Region extraction and shape analysis in aerial photographs," Comput. Graph. Image Process., vol. 10, no. 3, pp. 195-223, 1979.
56. G. K. Ouzounis, "Generalized connected morphological operators for robust shape extraction," Ph.D. dissertation, Univ. Groningen, Groningen, The Netherlands, 2009.
57. M. H. F. Wilkinson, "Attribute-space connectivity and connected filters," Image Vision Comput., vol. 25, no. 4, pp. 426-435, 2007.
58. P. Soille, "Constrained connectivity and connected filters," IEEE Trans. Pattern Anal. Machine Intell., vol. 30, no. 7, pp. 1132-1145, July 2008.
59. E. R. Urbach, N. J. Boersma, and M. H. F. Wilkinson, "Vector-attribute filters," in Proc. Int. Symp. Mathematical Morphology (ISMM) 2005 Paris, Apr. 18-20, 2005, pp. 95-104.