no. 7-8
Partial differential equations/Calculus of variations
Topological gradient for fourth-order PDE and application to the detection of fine structures in 2D images
[Gradient topologique pour des EDP du quatrième ordre et application à la détection de structures fines dans des images 2D]

Présenté par : Olivier Pironneau

Aubert, Gilles1 ; Drogoul, Audric1
1 Université Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France
Comptes Rendus. Mathématique, Tome 352 (2014) no. 7-8, pp. 609-613.

Dans cette note, on décrit une nouvelle approche pour la détection de structures fines dans une image. Cette approche est basée sur le calcul du gradient topologique associé à une fonction coût définie à partir des dérivées secondes d'une régularisation des données (éventuellement bruitées). Cette régularisation est obtenue via la résolution d'une EDP du quatrième ordre. L'étude de la sensibilité topologique est faite dans les cas d'une inclusion circulaire et d'un crack. Nous illustrons notre approche en donnant deux résultats expérimentaux.

In this paper we describe a new approach for the detection of fine structures in an image. This approach is based on the computation of the topological gradient associated with a cost function defined from a regularization of the data (possibly noisy). We get this approximation by solving a fourth-order PDE. The study of the topological sensitivity is made in the cases of both a circular inclusion and a crack. We illustrate our approach by giving two experimental results.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.06.005
Aubert, Gilles 1 ; Drogoul, Audric 1

1 Université Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France 
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Aubert, Gilles; Drogoul, Audric. Topological gradient for fourth-order PDE and application to the detection of fine structures in 2D images. Comptes Rendus. Mathématique, Tome 352 (2014) no. 7-8, pp. 609-613. doi : 10.1016/j.crma.2014.06.005. http://www.numdam.org/articles/10.1016/j.crma.2014.06.005/

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