Issue M2AN Volume 41, Number 3, May-June 2007 Page(s) 607 - 625 DOI 10.1051/m2an:2007027 Published online 02 August 2007

M2AN, Vol. 41, N°3, pp. 607-625
DOI: 10.1051/m2an:2007027

A topological asymptotic analysis for the regularized grey-level image classification problem

Didier Auroux¹, Lamia Jaafar Belaid² and Mohamed Masmoudi<sup>1

1</sup>  Institut de Mathématiques de Toulouse, UMR 5219, Université Paul Sabatier Toulouse 3, 31062 Toulouse cedex 9, France
²  ENIT-LAMSIN, BP37, 1002 Tunis Belvédère, Tunisia

(Received October 28, 2005. Revised January 15, 2007. Published online 2 August 2007.)

Abstract
The aim of this article is to propose a new method for the grey-level image classification problem. We first present the classical variational approach without and with a regularization term in order to smooth the contours of the classified image. Then we present the general topological asymptotic analysis, and we finally introduce its application to the grey-level image classification problem.

Mathematics Subject Classification. 35Q80, 49J20, 49K20, 65-04, 68-04, 68U10.

Key words: Image classification, topological asymptotic expansion, image restoration.


© EDP Sciences, SMAI 2007

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