This paper is concerned with the computation of the topological gradient associated to a fourth order Kirchhoff type partial differential equation and to a second order cost function. This computation is motivated by fine structure detection in image analysis. The study of the topological sensitivity is performed both in the cases of a circular inclusion and a crack.
Mots-clés : Topological gradient, fourth order PDE, fine structures, 2D imaging
@article{COCV_2015__21_4_1120_0,
author = {Aubert, Gilles and Drogoul, Audric},
title = {Topological gradient for a fourth order operator used in image analysis},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1120--1149},
publisher = {EDP-Sciences},
volume = {21},
number = {4},
year = {2015},
doi = {10.1051/cocv/2014061},
mrnumber = {3395758},
zbl = {1325.49050},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2014061/}
}
TY - JOUR AU - Aubert, Gilles AU - Drogoul, Audric TI - Topological gradient for a fourth order operator used in image analysis JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 1120 EP - 1149 VL - 21 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2014061/ DO - 10.1051/cocv/2014061 LA - en ID - COCV_2015__21_4_1120_0 ER -
%0 Journal Article %A Aubert, Gilles %A Drogoul, Audric %T Topological gradient for a fourth order operator used in image analysis %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 1120-1149 %V 21 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2014061/ %R 10.1051/cocv/2014061 %G en %F COCV_2015__21_4_1120_0
Aubert, Gilles; Drogoul, Audric. Topological gradient for a fourth order operator used in image analysis. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 1120-1149. doi : 10.1051/cocv/2014061. http://www.numdam.org/articles/10.1051/cocv/2014061/
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