Extracting meaningful curves from images

Journal of Mathematical Imaging and Vision

Volumn 22, Issue 2, 2005, Pages 159-181

  Cao, Frédéric ^a   Musé, Pablo ^b   Sur, Frédéric ^b  

^a CAMPUS DE BEAULIEU   (France)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Edge detection; Helmholtz principle; Level lines; Shapes elements; Topographic maps

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; EDGE DETECTION; FEATURE EXTRACTION; MATHEMATICAL MORPHOLOGY; SIGNAL FILTERING AND PREDICTION; MATHEMATICAL MODELS; SPURIOUS SIGNAL NOISE; STATISTICAL METHODS; TOPOLOGY;

HELMHOLTZ PRINCIPLE; LEVEL LINES; SHAPES ELEMENTS; TOPOGRAPHIC MAPS;

IMAGE PROCESSING; IMAGE ANALYSIS;

HELMHOLTZ PRINCIPLE; LEVEL LINES; SHAPE ELEMENTS; TOPOGRAPHIC MAPS;

EID: 17444383487     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-005-4888-0     Document Type: Article

References (44)

1. A. Alexandrov and Y. Reshetnyak, General Theory of Irregular Curves, vol. 29 of Mathematics and Its Applications: Soviet Series. Kluwer Academic Publishers, 1989.
2. E.J. Breen and R. Jones, "Attribute openings, thinnings and granulometries," Computer Vision and Image understanding, Vol. 64, No. 3, pp. 377-389, 1996.
3. J. Canny, "A computational approach to edge detection," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 8, No. 6, pp. 679-698, 1986.
4. F. Cao, "Good continuation in digital images," in Proceeding of ICCV 03, Nice, Vol. 1, 2003, pp. 440-447.
5. V. Caselles, B. Coll, and J.M. Morel, "A kanizsa program," in Progress in Nonlinear Differential Equations and their Applications, Vol. 25, 1996, pp. 35-55.
6. V. Caselles, T. Coll, and J.M. Morel, "Topographic maps and local contrast changes in natural images," International Journal of Computer Vision, Vol. 33, No. 1, pp. 5-27, 1999.
7. V. Caselles, R. Kimmel, and G. Sapiro, "Geodesic active contours," International Journal of Computer Vision, Vol. 22, No. 1, pp. 61-79, 1997.
8. T. Chan and L. Vese, "Active contours without edges," IEEE Transactions on Image Processing, Vol. 10, No. 2, pp. 266-277, 2001.
9. A. Desolneux, L. Moisan, and J.M. Morel, "Meaningful alignments,' International Journal of Computer Vision, Vol. 40, No. 1, pp. 7-23, 2000.
10. A. Desolneux, L. Moisan, and J.M. Morel, "Edge detection by Heimholte principle," Journal of Mathematical Imaging and Vision, Vol. 14, No. 3, pp. 271-284, 2001.
11. A. Desolneux, L. Moisan, and J.M. Morel, "A grouping principle and four applications," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 25, No. 4, pp. 508-513, 2003.
12. A. Desolneux, L. Moisan, and J.M. Morel, "Variational snake theory," in Geometric Level Set Methods in Imaging, Vision, and Graphics, S. Osher and N. Paragios (Eds.), Springer Verlag, 2003.
13. L.C. Evans and R.Gariepy, Measure Theory and Fine Properties of Functions, CRC Press. Ann Harbor, 1992.
14. P. Felzenszwalb and D. Huttenlocher, "Image segmentation using local variation," in Proceedings IEEE Conference on Computer Vision and Pattern Recognition, 1998, pp. 98-104.
15. R. Haralick, "Digital step edges from zero crossing of second directional derivatives," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 6, pp. 58-68, 1984.
16. G. Kanizsa, La Grammaire du Voir. Diderot, 1996. Original title: Grammatica del vedere. French translation from Italian.
17. G. Kanizsa, La Grammaire du Voir. Diderot, 1996. Original title: Grammatica del vedere. French translation from Italian.
18. M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active contour models," International Journal of Computer Vision, Vol. 1, pp. 321-331, 1987.
19. R. Kimmel and A.M. Bruckstein, "On regularized laplacian zero crossings and other optimal edge integrators," International Journal of Computer Vision, Vol. 53, No. 3, pp. 225-243, 2003.
20. J.J. Koenderink, "The structure of images," Biol. Cybern., Vol. 50, pp. 363-370, 1984.
21. T. Lindeberg, "Feature detection with automatic scale selection," International Journal of Computer Vision, Vol. 30, No. 2, pp. 77-116, 1998.
22. J.L. Lisani, L. Moisan, P. Menasse, and J.M. Morel, "On the theory of planar shape," SIAM Multiscale Modeling and Simulation, Vol. 1, No. 1, pp. 1-24, 2003.
23. J.L. Lisani, P. Monasse, and L. Rudin, "Fast shape extraction and application," Preprint 16, CMLA, ENS-Cachan. Available at http://www.cmla.ens-cachan.fr, 2001.
24. S. Mallat, A Wavelet Tour in Signal Processing, 2nd edition. Academic Press, 1999.
25. D. Marr, Vision. W.H. and Co: N.York, 1982.
26. D. Marr and E. Hildreth, "Theory of edge detection," in Proceeding of Royal Society of London, Vol. 207, 1980, pp. 187-207.
27. G. Matheron, Random Sets and Integral Geometry, John Wiley: N.Y., 1975.
28. F. Meyer and P. Maragos, "Nonlinear scale-space representation with morphological levelings," J. of Visual Comm. and Image Representation, Vol. 11, pp. 245-265, 2000.
29. P. Monasse, "Morphological representation of digital images and application to registration," Ph.D. thesis, Université Paris IX Dauphine, 2000.
30. P. Monasse and F. Guichard, "Fast computation of a contrast invariant representation," IEEE Transactions on Image Processing, Vol. 9, No. 5, pp. 860-872, 2000.
31. D. Mumford and J. Shah, "Optimal approximation by piecewise smooth functions and associated variational problems," Communication on Pure and Applied Mathematics, Vol. XLII, No. 4, 1989.
32. P. Musé, F. Sur, and J.M. Morel, "Sur les seuils de reconnaissance de formes," Traitement du Signal, Vol. 19, Nos. 5/6, 2003.
33. P. Musé, F. Sur, F. Cao, and Y. Gousseau, "Unsupervised thresholds for shape matching," in IEEE Int. Conf. on Image Processing, ICIP, 2003.
34. P. Musé, F. Sur, F. Cao, Y. Gousseau, and J.M. Morel, "Accurate estimates of false alarm number in shape recognition," Technical Report 5086, INRIA, 2004. submitted.
35. N. Paragios and R. Deriche, "Geodesic active regions and level set methods for supervised texture segmentation," International Journal of Computer Vision, Vol. 46, No. 3, pp. 223-247, 2002.
36. E. Le Pennec and S. Mallat, "Sparse geometrical image approximation with bandelets," accepted for publication in IEEE Trans. on Image Proc., 2003.
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 and J. Serra, "Flat zones filtering, connected operators, and filters by reconstruction,' IEEE Transactions on Image Processing, Vol. 4, No. 8, pp. 1153-1160, 1995.
39. J. Serra, Image Analysis and Mathematical Morphology, Academic Press, 1982.
40. J. Shi and J. Malik, "Normalized cuts and image segmentation," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 22, No. 8, pp. 888-905, 2000.
41. J.L. Starck, E.J. Candès, and D.L. Donoho, "The Curvelet Transform for Image Denoising," IEEE Transactions on Image Processing, Vol. 11, pp. 670-684, 2000.
42. M. Wertheimer, "Untersuchungen zur Lehre der Gestalt, II," Psychologische Forschung, Vol. 4, No. 301-350, 1923.
43. A.P. Witkin, "Scale space filtering," in Proc. of IJCAI, Karlsruhe, 1983, pp. 1019-1021.
44. S.C. Zhu, "Embedding gestalt laws in markov random fields," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 21, No. 11, pp. 1170-1187, 1999.