Analysis of a Variational Framework for Exemplar-Based Image Inpainting.
Pré-print du CMLA 2011-05 - version du 19 septembre 2011
Auteurs : Pablo Arias, Vicent Caselles, Gabriele Facciolo
Abstract :
In this paper we study some variational models for exemplar-based image inpainting. We propose a general variational framework for non-local inpainting and we single out two particular methods that we study in depth in this paper: the patch non-local means method and the non-local Poisson method.
In both cases, the unknowns are the image u to be reconstructed and a weight function w expressing the similarity of patches. As a limit case of the proposed framework, the weight function reduces to a correspondence map from the inpainting domain to the know part of the image.
We prove the existence and regularity of minima for both functionals. In particular, we prove the existence of optimal correspondence maps which are uniform limits of maps of bounded variation with finitely many values. Then we prove the convergence of an alternating optimization scheme for the variables (u,w).
We also prove the convergence in probability of the PatchMatch method, a recently introduced and efficient algorithm to compute optimal correspondence maps. Finally, we display some numerical experiments illustrating the performance and properties of the methods.
In this paper we study some variational models for exemplar-based image inpainting. We propose a general variational framework for non-local inpainting and we single out two particular methods that we study in depth in this paper: the patch non-local means method and the non-local Poisson method.
In both cases, the unknowns are the image u to be reconstructed and a weight function w expressing the similarity of patches. As a limit case of the proposed framework, the weight function reduces to a correspondence map from the inpainting domain to the know part of the image.
We prove the existence and regularity of minima for both functionals. In particular, we prove the existence of optimal correspondence maps which are uniform limits of maps of bounded variation with finitely many values. Then we prove the convergence of an alternating optimization scheme for the variables (u,w).
We also prove the convergence in probability of the PatchMatch method, a recently introduced and efficient algorithm to compute optimal correspondence maps. Finally, we display some numerical experiments illustrating the performance and properties of the methods.
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