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.
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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {607--625},
year = {2007},
publisher = {EDP Sciences},
volume = {41},
number = {3},
doi = {10.1051/m2an:2007027},
mrnumber = {2355713},
zbl = {1138.68622},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2007027/}
}
TY - JOUR AU - Auroux, Didier AU - Belaid, Lamia Jaafar AU - Masmoudi, Mohamed TI - A topological asymptotic analysis for the regularized grey-level image classification problem JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2007 SP - 607 EP - 625 VL - 41 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2007027/ DO - 10.1051/m2an:2007027 LA - en ID - M2AN_2007__41_3_607_0 ER -
%0 Journal Article %A Auroux, Didier %A Belaid, Lamia Jaafar %A Masmoudi, Mohamed %T A topological asymptotic analysis for the regularized grey-level image classification problem %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 607-625 %V 41 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2007027/ %R 10.1051/m2an:2007027 %G en %F 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: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 3, pp. 607-625. doi: 10.1051/m2an:2007027
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