Volume 13, Issue 5
Weighted Harmonic and Complex Ginzburg-Landau Equations for Gray Value Image Inpainting

Z. Belhachmi, M. Kallel, M. Moakher & A. Theljani

Int. J. Numer. Anal. Mod., 13 (2016), pp. 782-801

Published online: 2016-09

Preview Purchase PDF 83 2144
Export citation
  • 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 allows 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.

  • Keywords

Image inpainting inverse problems regularization procedures adaptive finite elements

  • AMS Subject Headings

65M32 65M50 65M22 94A08

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@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 = {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 allows 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.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/465.html} }
TY - JOUR T1 - Weighted Harmonic and Complex Ginzburg-Landau Equations for Gray Value Image Inpainting AU - Z. Belhachmi, M. Kallel, M. Moakher & A. Theljani JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 782 EP - 801 PY - 2016 DA - 2016/09 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/465.html KW - Image inpainting KW - inverse problems KW - regularization procedures KW - adaptive finite elements AB - 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 allows 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.
Z. Belhachmi, M. Kallel, M. Moakher & A. Theljani. (1970). Weighted Harmonic and Complex Ginzburg-Landau Equations for Gray Value Image Inpainting. International Journal of Numerical Analysis and Modeling. 13 (5). 782-801. doi:
Copy to clipboard
The citation has been copied to your clipboard