Free gradient discontinuity and image inpainting. (English. Russian original) Zbl 1260.49025
J. Math. Sci., New York 181, No. 6, 805-819 (2012); translation from Zap. Nauchn. Semin. POMI 390, 92-116 (2011).
From the authors’ abstract/introduction: “In image restoration, the term ‘inpainting’ denotes the process of filling the missing information in subdomains where a given image is damaged: these domains may correspond to scratches in a camera picture, occlusion by objects, blotches in an old movie film, or aging of the canvas and colors in a painting.
In this paper, we face the inpainting problem for a monochromatic image with a variational approach: solving a Dirichlet-type problem for the main part of the Blake-Zisserman functional. So we introduce and study a formulation of the inpainting problem for two-dimensional images that are locally damaged. This formulation is based on the regularization of the solution of a second-order variational problem with Dirichlet boundary condition. A variational approximation algorithm is proposed.”
In this paper, we face the inpainting problem for a monochromatic image with a variational approach: solving a Dirichlet-type problem for the main part of the Blake-Zisserman functional. So we introduce and study a formulation of the inpainting problem for two-dimensional images that are locally damaged. This formulation is based on the regularization of the solution of a second-order variational problem with Dirichlet boundary condition. A variational approximation algorithm is proposed.”
Reviewer: Hussain A. El-Saify (Beni Suef)
MSC:
| 49K10 | Optimality conditions for free problems in two or more independent variables |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
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