Skip to main content

Topological Optimization with the -Laplacian Operator and an Application in Image Processing

Abstract

We focus in this paper on the theoretical and numerical aspect os image processing. We consider a non linear boundary value problem (the -Laplacian) from which we will derive the asymptotic expansion of the Mumford-Shah functional. We give a theoretical expression of the topological gradient as well as a numerical confirmation of the result in the restoration and segmentation of images.

Publisher note

To access the full article, please see PDF.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Diaraf Seck.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Sy, A., Seck, D. Topological Optimization with the -Laplacian Operator and an Application in Image Processing. Bound Value Probl 2009, 896813 (2009). https://doi.org/10.1155/2009/896813

Download citation

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Full Article
\