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Random Walks, Constrained Multiple Hypothesis Testing and Image Enhancement

  • Noura Azzabou
  • Nikos Paragios
  • Frederic Guichard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3951)

Abstract

Image restoration is a keen problem of low level vision. In this paper, we propose a novel – assumption-free on the noise model – technique based on random walks for image enhancement. Our method explores multiple neighbors sets (or hypotheses) that can be used for pixel denoising, through a particle filtering approach. This technique associates weights for each hypotheses according to its relevance and its contribution in the denoising process. Towards accounting for the image structure, we introduce perturbations based on local statistical properties of the image. In other words, particle evolution are controlled by the image structure leading to a filtering window adapted to the image content. Promising experimental results demonstrate the potential of such an approach.

References

  1. 1.
    Alvarez, L., Guichard, F., Lions, P.-L., Morel, J.-M.: Axioms and fundamental equations of image processing. Archive for Rational Mechanics 123, 199–257 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  3. 3.
    Black, M., Sapiro, G., Marimont, D., Heeger, D.: Robust anisotropic diffusion. IEEE Transactions on Image Processing 7, 421–432 (1998)CrossRefGoogle Scholar
  4. 4.
    Buades, A., Coll, B., Morel, J.-M.: A non-local algorithm for image denoising. In: CVPR, pp. 60–65 (2005)Google Scholar
  5. 5.
    Cheng, Y.: Mean Shift, Mode Seeking, and Clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 17, 790–799 (1995)CrossRefGoogle Scholar
  6. 6.
    Do, M., Vetterli, M.: Pyramidal directional filter banks and curvelets. In: ICIP 2001, pp. III:158–161 (2001)Google Scholar
  7. 7.
    Doucet, A., de Freitas, J., Gordon, N.: Sequential Monte Carlo Methods in Practice. Springer, New York (2001)CrossRefzbMATHGoogle Scholar
  8. 8.
    Doucet, A.: On sequential simulation-based methods for bayesian filtering. Technical Report CUED/F-INFENG/TR. 310, Cambridge University Department of Engineering (1998)Google Scholar
  9. 9.
    Gordon, N.: Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation. IEE Proceedings 140, 107–113 (1993)Google Scholar
  10. 10.
    Gordon, N.: A Tutorial on Particle Filters for On-line Non-linear/Non-Gaussian Bayesian Tracking. IEEE Transactions on Signal Processing 50, 174–188 (2002)CrossRefGoogle Scholar
  11. 11.
    Haralick, R.M., Shanmugam, K., Dinstein, I.: Textural features for image classification. In: SMC, pp. 610–621 (1973)Google Scholar
  12. 12.
    Kimmel, R., Malladi, R., Sochen, N.: Image processing via the beltrami operator. In: ACCV, pp. 574–581 (1998)Google Scholar
  13. 13.
    Le Pennec, E., Mallat, S.: Sparse geometric image representations with bandelets. IEEE Transactions on Image Processing, 423–438 (2005)Google Scholar
  14. 14.
    Lee, A., Pedersen, K., Mumford, D.: The nonlinear statistics of high-contrast patches in natural images. International Journal of Computer Vision, 83–103 (2003)Google Scholar
  15. 15.
    Lee, S.: Digital image smoothing and the sigma filter. CVGIP 24(2), 255–269 (1983)Google Scholar
  16. 16.
    Levin, A., Zomet, A., Weiss, Y.: Learning to perceive transparency from the statistics of natural scenes. In: NIPS (2002)Google Scholar
  17. 17.
    Mallat, S.: A theory for multiscale signal decomposition: The wavelet representation. IEEE Transactions on Pattern and Machine Intelligence, 674–693 (1989)Google Scholar
  18. 18.
    Monasse, P., Guichard: Fast computation of a contrast invariant image representation. IEEE Transactions on Image Processing 9, 860–872 (2000)CrossRefGoogle Scholar
  19. 19.
    Mumford, D., Shah, J.: Optimal Approximation by Piecewise Smooth Functions and Associated Variational Problems. Communications on Pure and Applied Mathematics 42, 577–685 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern and Machine Intelligence 12, 629–639 (1990)CrossRefGoogle Scholar
  21. 21.
    Rudin, L., Osher, S., Fatemi, E.: Nonlinear Total Variation Based Noise Removal. Physica D 60, 259–268 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: ICCV, pp. 839–846 (1998)Google Scholar
  23. 23.
    Tschumperle, D., Deriche, R.: Vector-valued image regularization with pde’s: A common framework for different applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, 506–517 (2005)Google Scholar
  24. 24.
    Vese, L., Osher, S.: Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing. Journal of Scientific Computing, 553–572Google Scholar
  25. 25.
    Vincent, L.: Morphological grayscale reconstruction in image analysis: Applications and efficient algorithms. IEEE Transactions on Image Processing 2, 176–201 (1993)CrossRefGoogle Scholar
  26. 26.
    Wand, M., Jones, M.: Kernel Smoothing. Chapman and Hall, Boca Raton (1995)CrossRefzbMATHGoogle Scholar
  27. 27.
    West, W.: Modelling with mixtures. In: Bernardo, J., Berger, J., Dawid, A., Smith, A. (eds.) Bayesian Statistics, Clarendon Press (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Noura Azzabou
    • 1
    • 2
  • Nikos Paragios
    • 1
  • Frederic Guichard
    • 2
  1. 1.MAS, Ecole Centrale de ParisChatenay-MalabryFrance
  2. 2.DxOLabsBoulogneFrance

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