Robust anisotropic diffusion

IEEE Transactions on Image Processing

Volumn 7, Issue 3, 1998, Pages 421-432

  Black, Michael J ^a,d   Sapiro, Guillermo ^b,d   Marimont, David H ^a,d   Heeger, David ^c  

^a PALO ALTO RESEARCH CENTER   (United States)

^b University of Minnesota   (United States)

^c STANFORD UNIVERSITY   (United States)

^d IEEE   (United States)

Author keywords

Anisotropic diffusion; Line processes; Robust statistics

Indexed keywords

ALGORITHMS; FUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS; PIECEWISE LINEAR TECHNIQUES; STATISTICAL METHODS;

ANISOTROPIC DIFFUSION EQUATION; PERONA-MALIK DIFFUSION EQUATION;

IMAGE PROCESSING;

EID: 0032023715     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.661192     Document Type: Article

References (51)

1. Proc. Int. Workshop on Robust Computer Vision, Seattle, WA, Oct. 1990.
2. L. Alvarez, F. Guichard, P. L. Lions, and J. M. Morel, "Axioms and fundamental equations of image processing," Arch. Rational Mechanics, vol. 123, pp. 200-257, 1993.
3. L. Alvarez, P. L. Lions, and J. M. Morel, "Image selective smoothing and edge detection by nonlinear diffusion," SIAM-JNA, vol. 29, pp. 845-866, 1992.
4. G. Aubert and L. Vese, "A variational method for image recovery," SIAM J. Appl Math., to be published.
5. P. J. Besl, J. B. Birch, and L. T. Watson, "Robust window operators," in Proc. Int. Conf. Computer Vision (ICCV-88), pp. 591-600.
6. M. Black and A. Rangarajan, "On the unification of line processes, outlier rejection, and robust statistics with applications in early vision," Int. J. Comput. Vis., vol. 19, pp. 57-92, July 1996.
7. M. J. Black and P. Anandan, "Robust dynamic motion estimation over time," in Proc. Computer Vision and Pattern Recognition, CVPR-91, Maui, HI, June 1991, pp. 296-302.
8. _, "A framework for the robust estimation of optical flow," in Proc. Int. Conf. Computer Vision, (ICCV-93), Berlin, Germany, May 1993, pp. 231-236.
9. A. Blake and A. Zisserman, Visual Reconstruction. Cambridge, MA: MIT Press, 1987.
10. J. Canny, "A computational approach to edge detection," IEEE Trans. Pattern Anal. Machine Intell., vol. 8, pp. 679-698, Nov. 1986.
11. F. Catte, P.-L. Lions, J.-M. Morel, and T. Coll, "Image selective smoothing and edge detection by nonlinear diffusion," SIAM-JNA, vol. 29, pp. 182-193, 1992.
12. P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, "Deterministic edge-preserving regularization in computed imaging," IEEE Trans. Image Processing, vol. 6, pp. 298-311, Feb. 1997.
13. D. S. Chen and B. G. Schunck, "Robust statistical methods for building classification procedures," in Proc. Int. Workshop on Robust Computer Vision, Seattle, WA, Oct. 1990, pp. 72-85.
14. P. B. Chou and C. M. Brown, "The theory and practice of Bayesian image labeling," Int. J. Comput. Vis., vol. 4, pp. 185-210, 1990.
15. D. Gabor, "Information theory in electron microscopy," Lab. Investigation, vol. 14, pp. 801-807, 1965.
16. D. Geiger and A. Yuille, "A common framework for image segmentation," Int. J. Comput. Vis., vol. 6, pp. 227-243, 1991.
17. S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions and Bayesian restoration of images," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 721-741, Nov. 1984.
18. D. Geman and G. Reynolds, "Constrained restoration and the recovery of discontinuities," IEEE Trans. Pattern Anal. Machine Intell., vol. 14, pp. 376-383, Mar. 1992.
19. D. Geman and C. Yang, "Nonlinear image recovery with half-quadratic regularization," IEEE Trans. Image Processing, vol. 4, pp. 932-946, 1995.
20. G. Gerig, O. Kubler, R. Kikinis, and F. A. Jolesz, "Nonlinear anisotropic filtering of MRI data," IEEE Trans. Med. Imag., vol. 11, pp. 221-232, 1992.
21. F. Guichard, "Multiscale analysis of movies: Theory and algorithms," Ph.D. dissertation, CEREMADE, Pans, France, 1993.
22. F. R. Hampel, E. M. Ronchetti, P. J. Rousseeuw, and W. A. Stahel, Robust Statistics: The Approach Based on Influence Functions. New York: Wiley, 1986.
23. J. G. Harris, C. Koch, E. Staats, and J. Luo, "Analog hardware for detecting discontinuities in early vision," Int. J. Comput. Vis., vol. 4, pp. 211-223, 1990.
24. P. J. Huber, Robust Statistics. New York: Wiley, 1981.
25. S. Kichenassamy, "Edge localization via backward parabolic and hyperbolic PDE," preprint, Univ. Minnesota, Minneapolis, 1996.
26. R. Kumar and A. R. Hanson, "Analysis of different robust methods for pose refinement," in Proc. Int. Workshop Robust Computer Vision, Seattle, WA, Oct. 1990, pp. 167-182.
27. Y. G. Leclerc, "Constructing simple stable descriptions for image partitioning," Int. J. Comput. Vis., vol. 3, pp. 73-102, 1989.
28. L. Lui, B. G. Schunck, and C. C. Meyer, "On robust edge detection," in Proc. Int. Workshop on Robust Computer Vision, Seattle, WA, Oct. 1990, pp. 261-286.
29. R. Malladi and J. A. Sethian, "Image processing: Flows under min/max curvature and mean curvature," Graph. Models Image Process., vol. 58, pp. 127-141, Mar. 1996.
30. C. Mead, Analog VLSI and Neural Systems. Reading, MA: Addison-Wesley, 1989.
31. P. Meer, D. Mintz, and A. Rosenfeld, "Robust recovery of piecewise polynomial image structure," in Proc. Int. Workshop Robust Computer Vision, Seattle, WA, Oct. 1990, pp. 109-126.
32. P. Meer, D. Mintz, A. Rosenfeld, and D. Y. Kim, "Robust regression methods for computer vision: A review," Int. J. Comput. Vis., vol. 6, pp. 59-70, 1991.
33. D. W. Murray and B. F. Buxton, "Scene segmentation from visual motion using global optimization," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, pp. 220-228, Mar. 1987.
34. R. Nevatia and K. R. Babu, "Linear feature extraction and description," Comput. Graph. Image Process., vol. 13, pp. 257-269, July 1980.
35. M. Nitzberg and T. Shiota, "Nonlinear image filtering with edge and corner enhancement," IEEE Trans. Pattern Anal. Machine Intell., vol. 14, pp. 826-833, 1992.
36. N. Nordström, "Biased anisotropic diffusion: A unified regularization and diffusion approach to edge detection," Image Vis. Comput., vol. 8, pp. 318-327, 1990.
37. S. Osher and L. I. Rudin, "Feature-oriented image enhancement using shock filters," SIAM-JNA, vol. 27, pp. 919-940, 1990.
38. P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion," IEEE Trans. Pattern Anal. Machine Intell., vol. 12, no. 7 pp. 629-639, July 1990.
39. P. J. Rousseeuw and A. M. Leroy, Robust Regression and Outlier Detection. New York: Wiley, 1987.
40. L. I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D, vol. 60, pp. 259-268, 1992.
41. G. Sapiro, "From active contours to anisotropic diffusion: Relations between basic PDE's in image processing," in Proc. ICIP, Lausanne, Switzerland, Sept. 1996.
42. G. Sapiro and D. Ringach, "Anisotropic diffusion of multivalued images with applications to color filtering," IEEE Trans. Image Processing, vol. 5, pp. 1582-1586, 1996.
43. B. G. Schunck, "Image flow segmentation and estimation by constraint line clustering," IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 1010-1027, Oct. 1989.
44. _, "Robust computational vision," in Proc. Int. Workshop Robust Computer Vision, Seattle, WA, Oct. 1990, pp. 1-18.
45. J. Shah, "A common framework for curve evolution, segmentation, and anisotropic diffusion," in Proc. CVPR, San Francisco, CA, June 1996.
46. D. Shulman and J. Hervé, "Regularization of discontinuous flow fields," in Proc. Workshop Visual Motion. Irvine, CA: IEEE Comput. Soc. Press, Mar. 1989, pp. 81-85.
47. S. S. Sinha and B. G. Schunck, "A two-stage algorithm for discontinuity-preserving surface reconstruction," IEEE Trans. Pattern Anal. Machine Intell., vol. 14, pp. 36-55, Jan. 1992.
48. A. P. Tirumalai, B. G. Schunck, and R. C. Jain, "Robust dynamic stereo for incremental disparity map refinement," in Proc. Int. Workshop Robust Computer Vision, Seattle, WA, Oct. 1990, pp. 412-434.
49. J. Weng and P. Cohen, "Robust motion and structure estimation using stereo vision," in Proc. Int. Workshop on Robust Computer Vision, Seattle, WA, Oct. 1990, pp. 367-388.
50. Y. L. You, W. Xu, A. Tannenbaum, and M. Kaveh, "Behavioral analysis of anisotropic diffusion in image processing," IEEE Trans. Image Processing, vol. 5, pp. 1539-1553, 1996.
51. J. Weickert, "Non-linear diffusion scale-spaces: From the continuous to the discrete setting," in Proc. ICAOS'96, Paris, France, pp. 111-118.