Open Access

Topological Optimization with the https://static-content.springer.com/image/art%3A10.1155%2F2009%2F896813/MediaObjects/13661_2009_Article_887_IEq1_HTML.gif -Laplacian Operator and an Application in Image Processing

Boundary Value Problems20092009:896813

DOI: 10.1155/2009/896813

Received: 14 April 2009

Accepted: 28 July 2009

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 https://static-content.springer.com/image/art%3A10.1155%2F2009%2F896813/MediaObjects/13661_2009_Article_887_IEq2_HTML.gif -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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Authors’ Affiliations

(1)
Université de Bambey
(2)
Laboratoire de Mathématique de la Décision et d'Analyse Numérique (LMDAN), Ecole Doctorale de Mathématiques et Informatique, Université Cheikh Anta Diop de Dakar

Copyright

© 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.