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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Tikhonov, A., Arsenin, V.: Solution of Ill-Posed Problems. Wiley, Winston (1977)
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)
Elder, J.H., Zucker, S.W.: Local scale control for edge detection and blur estimation. IEEE Trans. on PAMI 20, 699–716 (1998)
Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. on PAMI 8, 888–905 (2000)
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)
Geman, S., Reynolds, G.: Constrained restoration and the recovery of discontinuities. IEEE Trans. on PAMI 14, 932–946 (1995)
Charbonnier, P., Blanc-Feraud, L., Aubert, G., Barlaud, M.: Deterministic edge-preserving regularization in computed imaging. IEEE Tr. I.P. 6, 298–311 (1997)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. on PAMI 12, 629–639 (1990)
Rudin, L., Osher, S., Fatemi, E.: Nonlinear total varition based noise removal algorithm. Physica D 60, 259–268 (1992)
Weickert, J.: Coherence-enhancing diffusion filtering. IJCV 31, 111–127 (1999)
Romeny, B.M.: Geometry-Driven Diffusion in Computer Vision. Kluwer Academic Publishers, Dordrecht (1994)
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)
Chen, Y., Levine, S., Rao, M.: Variable exponent, linear growth functionals in image restoration. SIAM Journal of Applied Mathematics 66, 1383–1406 (2006)
Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics 42, 577–684 (1989)
Molina, R., Katsaggelos, A., Mateos, J.: Bayesian and regularization methods for hyperparameters estimate in image restoration. IEEE on S.P. 8, 231–246 (1999)
Bishop, C.M., Tipping, M.E.: Bayesian regression and classification. In: Advances in Learning Theory: Methods, Models and Applications, pp. 267–285 (2003)
Osher, S., Sethian, J.A.: Front propagation with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comp. Phy. 79, 12–49 (1988)
Geman, S., Geman, D.: Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Trans. on PAMI 6, 721–741 (1984)
Zhu, S., Mumford, D.: Prior learning and Gibbs reaction-diffusion. IEEE Trans. on PAMI 19, 1236–1249 (1997)
Roth, S., Black, M.: Fields of experts: A framework for learning image priors. In: CVPR, San Diego, pp. 860–867 (2005)
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)
Pothen, A., Simon, H., Liou, K.: Partitioning sparse matrices with eigenvectors of graphs. SIAM. J. Matrix Anal. App. 11, 435–452 (1990)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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)