Weak solutions of a parabolic-elliptic type system for image inpainting
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 1040-1052.

In this paper we consider the initial boundary value problem of a parabolic-elliptic system for image inpainting, and establish the existence and uniqueness of weak solutions to the system in dimension two.

DOI : 10.1051/cocv/2009032
Classification : 35D05, 68U10
Mots-clés : weak solutions, parabolic-elliptic system, image inpainting 
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     title = {Weak solutions of a parabolic-elliptic type system for image inpainting},
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Jin, Zhengmeng; Yang, Xiaoping. Weak solutions of a parabolic-elliptic type system for image inpainting. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 1040-1052. doi : 10.1051/cocv/2009032. http://archive.numdam.org/articles/10.1051/cocv/2009032/

[1] C. Ballester, M. Bertalmio, V. Caselles, G. Sapiro and J. Verdera, Filling-in by joint interpolation of vector fields and gray levels. IEEE Trans. Image Process. 10 (2001) 1200-1211. | Zbl

[2] M. Bertalmio, G. Sapiro, V. Caselles and C. Ballsester, Image Inpainting. Computer Graphics, SIGGRAPH (2000) 417-424.

[3] M. Bertalmio, A. Bertozzi and G. Sapiro, Navier-Stokes, fluid-dynamics and image and video inpainting, in Proc. Conf. Comp. Vision Pattern Rec. (2001) 355-362.

[4] F. Catte, P.L. Lions, J.M. Morel and T. Coll, Image selective smoothing and edge detection by nonlinear diffusion. SIAM. J. Num. Anal. 29 (1992) 182-193. | Zbl

[5] T. Chan and J. Shen, Variational restoration of nonflat image feature: Models and algorithms. SIAM J. Appl. Math. 61 (2000) 1338-1361. | Zbl

[6] T. Chan and J. Shen, Mathematical models for local nontexture inpaintings. SIAM J. Appl. Math. 63 (2002) 1019-1043. | Zbl

[7] T. Chan, S. Kang and J. Shen, Euler's elastica and curvature based inpaintings. SIAM J. Appl. Math. 63 (2002) 564-592. | Zbl

[8] T. Chan, J. Shen and L. Vese, Variational PDE models in image processing. Notices Am. Math. Soc. 50 (2003) 14-26. | Zbl

[9] L.C. Evans, Partial differental equations. American Mathematical Society (1998). | Zbl

[10] Z.M. Jin and X.P. Yang, Viscosity analysis on the BSCB models for image inpainting. Chinese Annals of Math. (Ser. A) (to appear).

[11] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaries. Dunod (1969). | Zbl

[12] S. Masnou, Disocclusion: a variational approach using level lines. IEEE Trans. Image Process. 11 (2002) 68-76.

[13] P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Machine Intell. 12 (1990) 629-639.

[14] X.C. Tai, S. Osher and R. Holm, Image inpainting using a TV-Stokes equation, in Image Processing based on partial differential equations, X.C. Tai, K.-A. Lie, T.F. Chan and S. Osher Eds., Springer, Heidelberg (2007) 3-22. | Zbl

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