Image Decomposition and Inpainting Based on Besov and Hilbert-Sobolev Space

Article Preview

Abstract:

An image is decomposed into structure and texture adopt Meyer model , In order to more effectively express the characteristics of the image ,a schem is proposed that structure and texture described use Besov space and Hilbert-Sobolev space respectively,and different inpainting methods is adopt for structure and texture .Experimental results show that the algorithm calculated simple, easy to implement ,Smoothness and structure information, such as the basic characteristics of the image portrayed to meet the application requirements and inpaint results in low signal-to-noise ratio, the visual effect is superior to the similar method.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

1857-1862

Citation:

Online since:

August 2014

Authors:

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2014 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

* - Corresponding Author

[1] M. Bertalmío, A. Bertozzi, G. Sapiro, Navier Stokes, fluid-dynamics and image and video inpainting, in: Proc. 2001 IEEE Comput. Soc. Conf. Comput. Vision Pattern Recognion., vol. 1. n. 1, p.355–362, (2001).

DOI: 10.1109/cvpr.2001.990497

Google Scholar

[2] M. Bertalmío, G. Sapiro, V. Caselles, C. Ballester, Image inpainting, SIGGRAPH 34 (2000) 417–424.

Google Scholar

[3] M. Bertalmío, L. Vese, G. Sapiro, S. Osher, Simultaneous structure and texture image inpainting, IEEE Trans. Image Process. Vol. 12, n. 6 p.882–889, (2003).

DOI: 10.1109/tip.2003.815261

Google Scholar

[4] M. Elad, J. -L. Starck, P. Querre and D. Donoho, Simultaneous cartoon and texture image inpainting using morphological component analysis, Appl. Comput. Harmon. Anal. Vol. 19, n. 3, p.340–358, (2005).

DOI: 10.1016/j.acha.2005.03.005

Google Scholar

[5] AN Tikhonov and VA Arsenin. Solution of Ill-posed Problems. (Winston & Sons, Washington, 1977).

Google Scholar

[6] Tony F. Chan and Jianhong Shen. Image processing and analysis: Variational, PDE, wavelet, and stochastic.

Google Scholar

[7] methods. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, (2005).

Google Scholar

[8] Leonid Rudin, Stanley Osher, and Emad Fatemi. Nonlinear total variation based noise removal algorithms. Physica D , (1992).

DOI: 10.1016/0167-2789(92)90242-f

Google Scholar

[9] David Mumford and Jayant Shah. Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math., vol. 42, n. 5, pp.577-685, (1989).

DOI: 10.1002/cpa.3160420503

Google Scholar

[10] A. Criminisi, P. Perez, and K. Toyama. Region Flling and object removal by exemplar-based image inpainting. IEEE Tran. on Image Processing, vol. 13, n. 9, pp.1200-1212, (2004).

DOI: 10.1109/tip.2004.833105

Google Scholar

[11] Meyer Y.Oscillating Patterns in Image Processing and Nonlinear Evolution Equations.Boston University Lecture Series,American M athematical Society,2001.

Google Scholar

[12] Myungjoo Kang and Myeongmin Kang. Compressive Sensing and Applications Asia Pacific Mathematics Newsletter vol. 2, n. 2, pp.1-5, (2012).

Google Scholar

[13] Zuowei Shen, Kim-Chuan Toh, and Sangwoon Yun. An accelerated proximal gradient algorithm for image restoration. preprint, (2009).

Google Scholar

[14] Stanley Osher, Martin Burger, Donald Goldfarb, Jinjun Xu, and Wotao Yin. An iterative regularization method for total variation-based image restoration. SIAM Multiscale Model. Simul., vol. 4, n. 5, pp.460-489, (2005).

DOI: 10.1137/040605412

Google Scholar

[15] Jian-Feng Cai, Stanley Osher, and Zuowei Shen. Split bregman methods and frame based image restoration. Multiscale Model. Simul., vol. 8, n. 14, pp.5057-5071, (2009).

DOI: 10.1137/090753504

Google Scholar

[16] Tom Goldstein and Stanley Osher. The split Bregman method for L1-regularized problems. SIAM J. Imaging Sci., vol. 2, n. 2, pp.323-343, (2009).

DOI: 10.1137/080725891

Google Scholar

[17] Luminita A. Vese and Stanley J. Osher Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing, [J] Journal of Scientific computing , 2003 , 19(1), 553-572.

Google Scholar

[18] Y Meyer Oscillating patterns in image processing and nolinear evolution equations [D] AMS university Lecture Series. (2002).

Google Scholar

[19] Chan T F, Shen J H non-texture inpainting by curature-driven diffusions, [J] Journal of Vision communication and Image Representation, 2001, 12(4): 436-449.

DOI: 10.1006/jvci.2001.0487

Google Scholar

[20] Harsh Potlapalli and Ren C. Luo fractal-based classification of natural textures, IEEE transanctions on industrial electronics, vol. 45. NO. 1 (1998).

DOI: 10.1109/41.661315

Google Scholar

[21] A Cisi, P Perez, K Toyama. Object Removal by Exemplar-based inpainting[C]. Proceedings of Euro, Graph, (2003).

Google Scholar

[22] L. Rudin,S. Osher and E. Fatemi, Nonliner total vartion based noise removal algorithm, physica D., vol. 60, pp.259-268, (1992).

DOI: 10.1016/0167-2789(92)90242-f

Google Scholar

[23] A. Chambolle and P. L. Lions, Image recovery via Total Variational minimization and related problems, Numer. Math. 76, 1997, 167–188.

DOI: 10.1007/s002110050258

Google Scholar

[24] T. Chan and J. Shen, Local inpainting models and TV inpainting, SIAM J. Appl. Math. 62: 3, pp.1019-1043, (2001).

Google Scholar