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A one-shot inpainting algorithm based on the topological asymptotic analysis. (English) Zbl 1182.94006

Summary: The aim of this article is to propose a new method for the inpainting problem. Inpainting is the problem of filling-in holes in images. We consider in this article the crack localization problem, which can be solved using the Dirichlet to Neumann approach and the topological gradient. In a similar way, we can define a Dirichlet and a Neumann inpainting problem. We then define a cost function measuring the discrepancy between the two corresponding solutions. The minimization is done using the topological asymptotic analysis, and is performed in only one iteration. The optimal solution provides the best localization of the missing edges, and it is then easy to inpaint the holes.

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35R30 Inverse problems for PDEs
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