Diffusion filtering without parameter tuning: Models and inference tools

Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

Volumn , Issue , 2010, Pages 2536-2543

  Krajsek, Kai ^a   Scharr, Hanno ^a  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BAYESIAN FRAMEWORKS; BAYESIAN INFERENCE; DERIVATIVE FILTER; DETERMINISTIC APPROACH; DIFFUSION FILTERING; ERROR BOUND; HAND-TUNING; IMAGE CHARACTERISTICS; IMAGE DE-NOISING; IMAGE STATISTICS; INFERENCE TOOLS; INFLUENCE FUNCTIONS; LEARNING SCHEMES; MARKOV RANDOM FIELDS; NOISE LEVELS; PARAMETER-TUNING; PROBABILISTIC ESTIMATION; REGULARIZATION APPROACH; REGULARIZATION SCHEMES; STATE OF THE ART; STILL MISSING;

COMPUTER VISION; DIFFUSION; ERROR ANALYSIS; INFERENCE ENGINES; TUNING;

BAYESIAN NETWORKS;

EID: 77955991437     PISSN: 10636919     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CVPR.2010.5539959     Document Type: Conference Paper

References (37)

1. G. Aubert and P. Kornprobst. Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences). Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2006.
2. Y. Bengio. Gradient-based optimization of hyperparameters. Neural Comput., 12(8):1889-1900, 2000.
3. M. J. Black and G. Sapiro. Edges as outliers: Anisotropic smoothing using local image statistics. In SCALE-SPACE'99: Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision, pages 259-270, London, UK, 1999. Springer-Verlag.
4. M. J. Black, G. Sapiro, D. Marimont, and D. Heeger. Robust anisotropic diffusion. IEEE Transactions on Image Processing, 7(3):421-432, 1998.
5. F. Catte, P. L. Lions, J. M. Morel, and T. Coll. Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal., 29(1):182-193, 1992.
6. P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud. Deterministic edge-preserving regularization in computed imaging. IEEE Transactions on Image Processing, 6(2):298-311, 1997.
7. K. Dabov, R. Foi, V. Katkovnik, and K. Egiazarian. Image denoising with block-matching and 3d filtering. In in Electronic Im aging06, Proc. SPIE 6064, no. 6064A-30, 2006.
8. M. Felsberg. On the relation between anisotropic diffusion and iterated adaptive filtering. In 30. DAGM Symposium Mustererkennung, volume 5096 of LNCS, pages 436-445. Springer, 2008.
9. B. R. Frieden. Restoring with maximum likelihood and maximum entropy. J. Opt. Soc. Am., 62:511-518, 1972.
10. N. P. Galatsanos, V. Z. Mesarovic, R. Molina, and A. K. Katsaggelos. Hierarchical Bayesian image restoration from partially known blurs. IEEE Transactions on Image Processing, 9(10):1784-1797, 2000.
11. D. Geman and G. Reynolds. Constrained restoration and the recovery of discontinuities. IEEE Trans. Pattern Anal. Mach. Intell., 14(3):367-383, 1992.
12. S. Gull. Bayesian inductive inference and maximum entropy. G. J. Erickson and C. R. Smith, editors,Maximum Entropy and Bayesian Methods in Science and Engineering, 1:53-74, 1988.
13. S. Gull. Developments in maximum entropy data analysis. Maximum Entropy and Bayesian Methods, pages 53-71, 1989.
14. P. C. Hansen. The L-curve and its use in the numerical treatment of inverse problems. In Computational Inverse Problems in Electrocardiology, ed. P. Johnston, Advances in Computational Bioengineering, pages 119-142. WIT Press, 2000.
15. C. T. Kelley. Iterative Methods for Linear and Nonlinear Equations. Frontiers in Applied Mathematics 16, SIAM, 1995.
16. D. J. Lee and I. C. F. Ipsen. Zone determinant expansions for nuclear lattice simulations. Phys. Rev. C, 68(6):064003, Dec 2003.
17. A. López, R. Molina, and A. K. Katsaggelos. Bayesian reconstruction for transmission tomography with scale hyperparameter estimation. In IbPRIA (2), pages 455-462, 2005.
18. J. Marroquin, S. Mitter, and T. Poggio. Probabilistic solution of ill-posed problems in computational vision. Journal of the American Statistical Association, 82(397):76-89, 1987.
19. D. Martin, C. Fowlkes, D. Tal, and J. Malik. A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In Proceedings of the 8th IEEE International Conference on Computer Vision (ICCV), pages 416-423, 2001.
20. R. Molina, J. Mateos, and A. K. Katsaggelos. Blind deconvolution using a variational approach to parameter, image, and blur estimation. IEEE Transactions on Image Processing, 15(12):3715-3727, 2006.
21. P. Perona and J. Malik. Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell., 12(7):629-639, 1990.
22. J. Portilla, V. Strela, M. Wainwright, and E. Simoncelli. Adaptive Wiener denoising using a Gaussian scale mixture model in the wavelet domain. In Proceedings of the 8th International Conference on Image Processing (ICIP), volume 2, pages 37-40, 2001.
23. S. Roth and M. J. Black. Fields of Experts: A Framework for Learning Image Priors. In Proc. of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), 2005, pages 860-867, Washington, DC, USA, 2005. IEEE Computer Society.
24. S. Roth and M. J. Black. Steerable random fields. In Proc. of the IEEE International Conference on Computer Vision (ICCV), 2007.
25. H. Rue and L. Held. Gaussian Markov Random Fields: Theory and Applications. Chapman and Hall, 2005.
26. K. G. G. Samuel and M. F. Tappen. Learning optimized map estimates in continuously-valued mrf models. In CVPR, pages 477-484, 2009.
27. H. Scharr. Optimal Operators in Digital Image Processing. PhD thesis, Interdisciplinary Center for Scientific Computing, Univ. of Heidelberg, 2000.
28. H. Scharr, M. J. Black, and H. W. Haussecker. Image statistics and anisotropic diffusion. In Proc. of the IEEE International Conference on Computer Vision (ICCV), pages 840-847, 2003.
29. J. Skilling. On parameter estimation and quantified MaxEnt. Maximum Entropy and Bayesian Methods, pages 267-273, 1991.
30. J. Skilling and R. Bryan. Maximum entropy image reconstruction: general algorithm. In Mon. Notices R. Astron. Soc. 211, pages 111-124, 1984.
31. R. Szeliski. Bayesian Modeling of Uncertainty in Low-level Vision. Kluwer, 1989.
32. A. N. Thikonov and V. Y. Arsenin. Solutions to Ill-posed Problems. Winston and Sons, Washington, D.C., 1977.
33. D. Tschumperle. PDE's Based Regularization of Multivalued Images and Applications. PhD thesis, Universite de Nice-Sophia Antipolis, 2002.
34. G. Wahba. Spline models for observational data. SIAM Series in Applied Mathematics, 59, 1990.
35. J. Weickert. Anisotropic diffusion in image processing. PhD thesis, University of Kaiserslautern, 1996.
36. S. C. Zhu and D. Mumford. Prior learning and gibbs reaction-diffusion. IEEE Trans. Pattern Anal. Mach. Intell., 19(11):1236-1250, 1997.
37. S. C. Zhu, Y. Wu, and D. Mumford. Frame: Filters, random fields, and minimax entropy- towards a unified theory for texture modeling. In Proc. of the Conference on Computer Vision and Pattern Recognition (CVPR), page 686,Washington, DC, USA, 1996. IEEE Computer Society.