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