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.

Keywords: Topological gradient, fourth order PDE, fine structures, 2D imaging

^{1}; Drogoul, Audric

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@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, Volume 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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