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Introducing Dynamic Prior Knowledge to Partially-Blurred Image Restoration

  • Hongwei Zheng
  • Olaf Hellwich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4174)

Abstract

The paper presents an unsupervised method for partially-blurred image restoration without influencing unblurred regions or objects. Maximum a posteriori estimation of parameters in Bayesian regularization is equal to minimizing energy of a dataset for a given number of classes. To estimate the point spread function (PSF), a parametric model space is introduced to reduce the searching uncertainty for PSF model selection. Simultaneously, PSF self-initializing does not rely on supervision or thresholds. In the image domain, a gradient map as a priori knowledge is derived not only for dynamically choosing nonlinear diffusion operators but also for segregating blurred and unblurred regions via an extended graph-theoretic method. The cost functions with respect to the image and the PSF are alternately minimized in a convex manner. The algorithm is robust in that it can handle images that are formed in variational environments with different blur and stronger noise.

Keywords

Point Spread Function Image Restoration Variable Exponent Blind Deconvolution Blur Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Tikhonov, A., Arsenin, V.: Solution of Ill-Posed Problems. Wiley, Winston (1977)Google Scholar
  2. 2.
    Luxen, M., Förstner, W.: Characterizing image quality: Blind estimation of the point spread function from a single image. In: PCV 2002, pp. 205–211 (2002)Google Scholar
  3. 3.
    Elder, J.H., Zucker, S.W.: Local scale control for edge detection and blur estimation. IEEE Trans. on PAMI 20, 699–716 (1998)Google Scholar
  4. 4.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. on PAMI 8, 888–905 (2000)Google Scholar
  5. 5.
    Keuchel, J., Schnörr, C., Schellewald, C., Cremers, D.: Binary partitioning, perceptual grouping, and restoration with semidefinite programming. IEEE Trans. on PAMI 25, 1364–1379 (2003)Google Scholar
  6. 6.
    Geman, S., Reynolds, G.: Constrained restoration and the recovery of discontinuities. IEEE Trans. on PAMI 14, 932–946 (1995)CrossRefGoogle Scholar
  7. 7.
    Charbonnier, P., Blanc-Feraud, L., Aubert, G., Barlaud, M.: Deterministic edge-preserving regularization in computed imaging. IEEE Tr. I.P. 6, 298–311 (1997)CrossRefGoogle Scholar
  8. 8.
    Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. on PAMI 12, 629–639 (1990)Google Scholar
  9. 9.
    Rudin, L., Osher, S., Fatemi, E.: Nonlinear total varition based noise removal algorithm. Physica D 60, 259–268 (1992)MATHCrossRefGoogle Scholar
  10. 10.
    Weickert, J.: Coherence-enhancing diffusion filtering. IJCV 31, 111–127 (1999)CrossRefGoogle Scholar
  11. 11.
    Romeny, B.M.: Geometry-Driven Diffusion in Computer Vision. Kluwer Academic Publishers, Dordrecht (1994)MATHGoogle Scholar
  12. 12.
    Bar, L., Sochen, N.A., Kiryati, N.: Variational Pairing of Image Segmentation and Blind Restoration. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3022, pp. 166–177. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Chen, Y., Levine, S., Rao, M.: Variable exponent, linear growth functionals in image restoration. SIAM Journal of Applied Mathematics 66, 1383–1406 (2006)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics 42, 577–684 (1989)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Molina, R., Katsaggelos, A., Mateos, J.: Bayesian and regularization methods for hyperparameters estimate in image restoration. IEEE on S.P. 8, 231–246 (1999)MATHMathSciNetGoogle Scholar
  16. 16.
    Bishop, C.M., Tipping, M.E.: Bayesian regression and classification. In: Advances in Learning Theory: Methods, Models and Applications, pp. 267–285 (2003)Google Scholar
  17. 17.
    Osher, S., Sethian, J.A.: Front propagation with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comp. Phy. 79, 12–49 (1988)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Geman, S., Geman, D.: Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Trans. on PAMI 6, 721–741 (1984)MATHGoogle Scholar
  19. 19.
    Zhu, S., Mumford, D.: Prior learning and Gibbs reaction-diffusion. IEEE Trans. on PAMI 19, 1236–1249 (1997)Google Scholar
  20. 20.
    Roth, S., Black, M.: Fields of experts: A framework for learning image priors. In: CVPR, San Diego, pp. 860–867 (2005)Google Scholar
  21. 21.
    Zheng, H., Hellwich, O.: Double Regularized Bayesian Estimation for Blur Identification in Video Sequences. In: Narayanan, P.J., Nayar, S.K., Shum, H.-Y. (eds.) ACCV 2006. LNCS, vol. 3852, pp. 943–952. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  22. 22.
    Pothen, A., Simon, H., Liou, K.: Partitioning sparse matrices with eigenvectors of graphs. SIAM. J. Matrix Anal. App. 11, 435–452 (1990)MathSciNetGoogle Scholar
  23. 23.
    Hansen, P., O’Leary, D.: The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comput. 14, 1487–1503 (1993)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Portilla, J., Strela, V., Wainwright, M., Simoncelli, E.: Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Trans. on Image Processing 12, 1338–1351 (2003)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hongwei Zheng
    • 1
  • Olaf Hellwich
    • 1
  1. 1.Computer Vision & Remote Sensing, Berlin University of TechnologyBerlin

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