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Open Access Open Badges Research Article

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

Alassane Sy1 and Diaraf Seck2*

Author Affiliations

1 Université de Bambey, Bambey, Senegal

2 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

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Boundary Value Problems 2009, 2009:896813  doi:10.1155/2009/896813

The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2009/1/896813

Received:14 April 2009
Revisions received:28 June 2009
Accepted:28 July 2009
Published:15 September 2009

© 2009 The Author(s).

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.


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.

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