@Article{IJNAM-13-782,
author = {Z. Belhachmi, M. Kallel, M. Moakher and A. Theljani},
title = {Weighted Harmonic and Complex Ginzburg-Landau Equations for Gray Value Image Inpainting},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2016},
volume = {13},
number = {5},
pages = {782--801},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/465.html}
}