A topological asymptotic analysis for the regularized grey-level image classification problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 3, p. 607-625

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.

DOI : https://doi.org/10.1051/m2an:2007027
Classification:  35Q80,  49J20,  49K20,  65-04,  68-04,  68U10
Keywords: image classification, topological asymptotic expansion, image restoration
@article{M2AN_2007__41_3_607_0,
     author = {Auroux, Didier and Belaid, Lamia Jaafar and Masmoudi, Mohamed},
     title = {A topological asymptotic analysis for the regularized grey-level image classification problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {3},
     year = {2007},
     pages = {607-625},
     doi = {10.1051/m2an:2007027},
     zbl = {1138.68622},
     mrnumber = {2355713},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2007__41_3_607_0}
}
Auroux, Didier; Belaid, Lamia Jaafar; Masmoudi, Mohamed. A topological asymptotic analysis for the regularized grey-level image classification problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 3, pp. 607-625. doi : 10.1051/m2an:2007027. http://www.numdam.org/item/M2AN_2007__41_3_607_0/

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