Geodesic
Topological gradient for a fourth order operator used in image analysis
Aubert, Gilles1  ; Drogoul, Audric1 
1 UniversitéNice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 1120-1149

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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.

DOI : 10.1051/cocv/2014061
Classification : 35J30, 49Q10, 49Q12, 94A08, 94A13
Keywords: Topological gradient, fourth order PDE, fine structures, 2D imaging

Aubert, Gilles 1 ; Drogoul, Audric 1

1 UniversitéNice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France 
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     title = {Topological gradient for a fourth order operator used in image analysis},
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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

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