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Introducing Dynamic Prior Knowledge to Partially-Blurred Image Restoration

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Pattern Recognition (DAGM 2006)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4174))

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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.

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References

  1. Tikhonov, A., Arsenin, V.: Solution of Ill-Posed Problems. Wiley, Winston (1977)

    Google Scholar 

  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. 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. Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. on PAMI 8, 888–905 (2000)

    Google Scholar 

  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. Geman, S., Reynolds, G.: Constrained restoration and the recovery of discontinuities. IEEE Trans. on PAMI 14, 932–946 (1995)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  8. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. on PAMI 12, 629–639 (1990)

    Google Scholar 

  9. Rudin, L., Osher, S., Fatemi, E.: Nonlinear total varition based noise removal algorithm. Physica D 60, 259–268 (1992)

    Article  MATH  Google Scholar 

  10. Weickert, J.: Coherence-enhancing diffusion filtering. IJCV 31, 111–127 (1999)

    Article  Google Scholar 

  11. Romeny, B.M.: Geometry-Driven Diffusion in Computer Vision. Kluwer Academic Publishers, Dordrecht (1994)

    MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  13. Chen, Y., Levine, S., Rao, M.: Variable exponent, linear growth functionals in image restoration. SIAM Journal of Applied Mathematics 66, 1383–1406 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    MATH  MathSciNet  Google Scholar 

  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. Osher, S., Sethian, J.A.: Front propagation with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comp. Phy. 79, 12–49 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  18. Geman, S., Geman, D.: Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Trans. on PAMI 6, 721–741 (1984)

    MATH  Google Scholar 

  19. Zhu, S., Mumford, D.: Prior learning and Gibbs reaction-diffusion. IEEE Trans. on PAMI 19, 1236–1249 (1997)

    Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  22. Pothen, A., Simon, H., Liou, K.: Partitioning sparse matrices with eigenvectors of graphs. SIAM. J. Matrix Anal. App. 11, 435–452 (1990)

    MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

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Zheng, H., Hellwich, O. (2006). Introducing Dynamic Prior Knowledge to Partially-Blurred Image Restoration. In: Franke, K., Müller, KR., Nickolay, B., Schäfer, R. (eds) Pattern Recognition. DAGM 2006. Lecture Notes in Computer Science, vol 4174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11861898_12

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  • DOI: https://doi.org/10.1007/11861898_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44412-1

  • Online ISBN: 978-3-540-44414-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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