Open Access 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

Published: 15 September 2009

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.