Level lines selection with variational models for segmentation and encoding

Journal of Mathematical Imaging and Vision

Volumn 27, Issue 1, 2007, Pages 5-27

  Ballester, Coloma ^a   Caselles, Vicent ^a   Igual, Laura ^a   Garrido, Luis ^a  

^a UNIVERSITAT POMPEU FABRA   (Spain)

Author keywords

Mathematical morphology; Minimal description length; Morphological encoding; Rate distortion; Segmentation; Tree structure

Indexed keywords

COSTS; IMAGE CODING; IMAGE RECONSTRUCTION; MATHEMATICAL MODELS; MATHEMATICAL MORPHOLOGY; OPTIMIZATION; SIGNAL FILTERING AND PREDICTION;

MINIMAL DESCRIPTION LENGTH; MORPHOLOGICAL ENCODING; RATE DISTORTION; TREE OF SHAPES; TREE STRUCTURE; VARIATIONAL MODELS;

IMAGE SEGMENTATION;

EID: 33846301073     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-006-7252-0     Document Type: Article

References (49)

1. M.D. Adams, "The jpeg-2000 still image compression standard." Available at http://www.ece.ubc.ca/mdadams, 2001.
2. C. Ballester, E. Cubero-Castan, M. Gonzalez, and J.M. Morel, "Image intersection and applications to satellite imaging," Preprint, C.M.L.A., Ecole Normale Supérieure de Cachan, 1998.
3. C. Ballester, V. Caselles, and P. Menasse, "The tree of shapes of an image," ESAIM: Control, Opt. and Calc/ of Variations, Vol. 9, pp. 1-18, 2003.
4. T. Berger, Rate Distortion Theory: A Mathematical Basis for Data Compression. Prentice Hall, 1971.
5. L. Breiman, J.H. Friedman, R.A. Olsen, and C. J. Stone, Classification and Regression Trees. Wadsworth, Belmont, California, 1984.
6. F. Cao, P. Musé, and F. Sur, "Extracting meaningful curves in images," To appear in Journal of Mathematical Imaging and Vision, 2005.
7. F. Cao, Y. Gousseau, J.M. Morel, P. Musé, and F. Sur, "An a contrario decision method for shape element recognition," Preprint CMLA, No. 16, 2004.
8. V. Caselles, B. Coll, and J.M. Morel, "Topographic maps and local contrast changes in natural images," Int. J. Comp. Vision, Vol. 33, pp. 5-27, 1999.
9. V. Caselles, J.L. Lisani, J.M. Morel, and G. Sapiro, "Shape preserving histogram modification," IEEE Transactions on Image Processing, Vol. 8, No. 2, pp. 220-230, 1999.
10. V. Caselles, J.M. Morel, and C. Sbert, "An axiomatic approach to image interpolation," IEEE Transactions on Image Processing, Vol. 7, pp. 376-386, 1998.
11. V. Caselles, and P. Monasse, "Morse theories of the Topographic map," In preparation.
12. V. Caselles, G. Sapiro, A. Sole, and C. Ballester, "Morse description and morphological encoding of continuous data," SIAM Journal on Multiscale Modeling and Simulation, Vol. 2, pp. 179-209, 2004.
13. R. Chiariglioni, "MPEG and multimedia communitations," IEEE Transactions on Circuits and Systems for Video Technology, Vol. 7, pp. 5-18, 1997.
14. P.A. Chou, T. Lookabaugh, and R.M. Gray, "Optimal pruning with applications to tree-structured source coding and modeling," IEEE Trans. Inform. Theory, Vol. 35, pp. 299-315, 1989.
15. A. Desolneux, L. Moisan, and J.M. Morel, "Edge detection by Helmholtz principle," Journal of Mathematical Imaging and Vision, Vol. 14, pp. 271-284, 2001.
16. M. Eden and M. Kocher, "On the performance of a contour coding algorithm in the context of image coding. Part I: Contour segment coding," Signal Processing, Vol. 8, pp. 381-386, 1985.
17. J. Froment, "A functional analysis model for natural images permitting structured compression," ESAIM: Control, Optimization and Calculus of Variation, Vol. 4, pp. 473-495, 1999.
18. L. Garrido, "Hierarchical region based processing of images and video sequences: Application to filtering, sementation and information retrieval," PhD thesis, Universitat Politécnica de Catalunya, 2002.
19. F. Guichard and J.M. Morel, Image Iterative Smoothing and P.D.E.'s'. Book in preparation, 2000.
20. L. Guigues, "Modèles Multi-Échelles pour la Segmentation d'Images," PhD thesis, Université de Cergy-Pontoise, 2003.
21. A. Gersho and R.M. Gray, Vector Quantization and Signal Compression, Kluwer Academic Publishers, 1992.
22. J.M. Hyman, "Accurate monotonicity preserving cubic interpolation." SIAM J. Sci. Stat. Comp, Vol. 4, pp. 645-654, 1983.
23. L. Igual, L. Garrido, and V. Caselles, "A contrast invariant approach to motion estimation, validation and motion segmentation,"
24. G. Koepfler, C. Lopez, and J.M. Morel, "A multiscale algorithm for image segmentation by variational method," SIAM J. Numer. Anal, Vol. 31, pp. 282-299, 1994.
25. C. Kuratowski, Topologie I, II. Editions J. Gabay: Paris, 1992.
26. Y. G. Leclerc, "Constructing simple stable descriptions for image partitioning," International Journal of Computer Vision, Vol. 3, pp. 73-102, 1989.
27. F. Meyer, "The dynamics of minima and contours," in Methematical Morphology and Its Applications to Image Processing, Atlanta (GA), USA, pp. 329-336, 1996.
28. F. Meyer and S. Beucher, "Morphological segmentation," J. of Visual Communication and Image Representation, Vol. 1, pp. 21-46, 1990.
29. P. Menasse, "Représentation morphologique d'images numériques et application au recalage," PhD thesis, Université de Paris-Dauphine, 2000.
30. P. Monasse, "Contrast invariant image registration," in: Proc. of International Conference on Acoustics, Speech and Signal Processing, Vol. 6, pp. 3221-3224, 1999.
31. P. Monasse and F. Guichard, "Fast computation of a contrast invariant image representation," IEEE Transactions on Image Processing, Vol. 9, pp. 860-872, 2000.
32. J.M. Morel and S. Solimini, Variational Methods in Image Processing. Birkhäuser Verlag: Basel, 1994.
33. D. Mumford and J. Shah, "Optimal approximations by piecewise smooth functions and variational problems," Communications on Pure and Applied Mathematics, Vol. 42, No. 5, pp. 577-685, 1988.
34. J. Rissanen, "Minimum-Description-Length principle," in Encyclopedia of Statistical Sciences. John Wiley: New York, 1987, Vol. 5, pp. 523-527.
35. P. Salembier, "Morphological multiscale segmentation for image coding," IEEE Transactions on Signal Processing, Vol. 38, No. 3, pp. 359-386, 1994.
36. P. Salembier, P. Brigger, J. R. Casas, and M. Pardàs, "Morphological operators for image and video compression," IEEE Transactions on Image Processing, Vol. 5, pp. 881-897, 1996.
37. P. Salembier and L. Garrido, "Binary partition tree as an efficient representation for image processing, segmentation, and information retrieval," IEEE Transactions on Image Processing, Vol. 9, No. 4, pp. 561-576, 2000.
38. P. Salembier, F. Marqués, M. Pardás, R. Morros, I. Corset, S. Jeannin, L. Bouchard, F. Meyer, and B. Marcotegui, "Segmentation-based video coding system allowing the manipulation of objects," IEEE Transactions on Circuits and Systems for Video Technology, Vol. 7, pp. 60-73, 1997.
39. P. Salembier and J. Serra, "Flat zones filtering, connected operators and filters by reconstruction," IEEE Transactions Image Processing, Vol. 4, No. 8, pp. 1153-1160, 1995.
40. G.M. Schuster and A.K. Katsaggelos, Rate-Distortion Based Video Compression. Kluwer Academic Publishers, 1997.
41. Y. Shoham and A. Gersho, "Efficient bit allocation for an arbitrary set of quantizers." IEEE Trans. on Acoust., Speech, Signal Processing, Vol. 36, No. 9, pp. 1445-1453, 1988.
42. J. Serra, Image Analysis and Mathematical Morphology, Academic Press: New York, 1982.
43. T. Sikora, "The MPEG-7 visual standard for content description - an overview." IEEE Transactions on Circuits and Systems for Video Technology, Vol. 11, pp. 696-702, 2001.
44. P. Soille, Morphological Image Analysis. Springer Verlag, 2003.
45. A. Solé, "Geometric image coding, filtering and restoration," PhD thesis, Universitat Pompeu Fabra, 2002.
46. L. Vincent, "Morphological area openings and closings for greyscale images," in Proceedings of the Workshop Shape in Picture: Mathematical Description of Shape in Gray-Level Images. Driebergen, The Netherlands, pp. 197-208, 1994.
47. L. Vincent and P. Soille, "Watersheds in digital spaces: An efficient algorithm based on Immersion simulations," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 13, No. 6, pp. 583-598, 1991.
48. M.J. Weinberger, G. Seroussi, and G. Sapiro, "The LOCO-I lossless image compression algorithm: Principles and standardization into JPEG-LS," IEEE Transactions on Image Processing Vol. 9, No. 8, pp. 1309-1324, 2000.
49. M. Wertheimer, "Untersuchungen zur Lehre der Gestalt, II," Psychologische Forschung, Vol. 4, pp. 301-350, 1923.