Boundary Value Problems
Volume 2009 (2009), Article ID 896813, 20 pages
doi:10.1155/2009/896813
Research Article

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

Alassane Sy1 and Diaraf Seck2

1Université de Bambey, Bambey, Senegal
2Laboratoire 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

Received 14 April 2009; Revised 28 June 2009; Accepted 28 July 2009

Academic Editor: Kanishka Perera

Copyright © 2009 Alassane Sy and Diaraf Seck. 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.

Abstract

We focus in this paper on the theoretical and numerical aspect os image processing. We consider a non linear boundary value problem (the p-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.