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  • Research Article
  • Open Access

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

Boundary Value Problems20092009:896813

  • Received: 14 April 2009
  • Accepted: 28 July 2009
  • Published:


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.


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

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Authors’ Affiliations

Université de Bambey, Bambey, Senegal
Laboratoire de Mathématique de la Décision et d'Analyse Numérique (LMDAN), Ecole Doctorale de Mathématiques et Informatique, Université Cheikh Anta Diop de Dakar, B.p. 16 889, Dakar-Fann, Senegal


© A. Sy and D. Seck. 2009

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.