Weighted Harmonic and Complex Ginzburg-Landau Equations for Gray Value Image Inpainting

Weighted Harmonic and Complex Ginzburg-Landau Equations for Gray Value Image Inpainting

Year:    2016

International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 5 : pp. 782–801

Abstract

We consider two second-order variational models in the image inpainting problems. The aim is to obtain in the restored region some fine features of the initial image, e.g. corners, edges, .... The first model is a linear weighted harmonic method well suited for binary images and the second one is its extension to the complex Ginzburg-Landau equation for the inpainting of multi-gray level images. The approach that we introduce consists of constructing a family of regularized functionals and to select locally and adaptively the regularization parameters in order to capture fine geometric features of the image. The parameters selection is performed, at the discrete level, with a posteriori error indicators in the framework of the finite element method. We perform the mathematical analysis of the proposed models and show that they allow us to reconstruct accurately the edges and the corners. Finally, in order to make some comparisons with well established models, we consider the nonlinear anisotropic diffusion and we present several numerical simulations to test the efficiency of the proposed approach.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2016-IJNAM-465

International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 5 : pp. 782–801

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Image inpainting inverse problems regularization procedures adaptive finite elements.