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.
Mots-clés : weak solutions, parabolic-elliptic system, image inpainting
@article{COCV_2010__16_4_1040_0,
author = {Jin, Zhengmeng and Yang, Xiaoping},
title = {Weak solutions of a parabolic-elliptic type system for image inpainting},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1040--1052},
publisher = {EDP-Sciences},
volume = {16},
number = {4},
year = {2010},
doi = {10.1051/cocv/2009032},
mrnumber = {2744161},
zbl = {1205.35041},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2009032/}
}
TY - JOUR AU - Jin, Zhengmeng AU - Yang, Xiaoping TI - Weak solutions of a parabolic-elliptic type system for image inpainting JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 1040 EP - 1052 VL - 16 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2009032/ DO - 10.1051/cocv/2009032 LA - en ID - COCV_2010__16_4_1040_0 ER -
%0 Journal Article %A Jin, Zhengmeng %A Yang, Xiaoping %T Weak solutions of a parabolic-elliptic type system for image inpainting %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 1040-1052 %V 16 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2009032/ %R 10.1051/cocv/2009032 %G en %F COCV_2010__16_4_1040_0
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://www.numdam.org/articles/10.1051/cocv/2009032/
[1] , , , and , Filling-in by joint interpolation of vector fields and gray levels. IEEE Trans. Image Process. 10 (2001) 1200-1211. | Zbl
[2] , , and , Image Inpainting. Computer Graphics, SIGGRAPH (2000) 417-424.
[3] , and , Navier-Stokes, fluid-dynamics and image and video inpainting, in Proc. Conf. Comp. Vision Pattern Rec. (2001) 355-362.
[4] , , and , Image selective smoothing and edge detection by nonlinear diffusion. SIAM. J. Num. Anal. 29 (1992) 182-193. | Zbl
[5] and , Variational restoration of nonflat image feature: Models and algorithms. SIAM J. Appl. Math. 61 (2000) 1338-1361. | Zbl
[6] and , Mathematical models for local nontexture inpaintings. SIAM J. Appl. Math. 63 (2002) 1019-1043. | Zbl
[7] , and , Euler's elastica and curvature based inpaintings. SIAM J. Appl. Math. 63 (2002) 564-592. | Zbl
[8] , and , Variational PDE models in image processing. Notices Am. Math. Soc. 50 (2003) 14-26. | Zbl
[9] , Partial differental equations. American Mathematical Society (1998). | Zbl
[10] and , Viscosity analysis on the BSCB models for image inpainting. Chinese Annals of Math. (Ser. A) (to appear).
[11] , Quelques méthodes de résolution des problèmes aux limites non linéaries. Dunod (1969). | Zbl
[12] , Disocclusion: a variational approach using level lines. IEEE Trans. Image Process. 11 (2002) 68-76.
[13] and , Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Machine Intell. 12 (1990) 629-639.
[14] , and , 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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