Topological gradient for fourth order PDE and application to the detection of fine structures in 2D images

Gilles Aubert (1) , Audric Drogoul (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

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 to 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 both in the cases of a circular inclusion and a crack. We illustrate our approach by giving two experimental results.

Domaines: Analyse numérique [math.NA]

Gilles Aubert, Audric Drogoul. Topological gradient for fourth order PDE and application to the detection of fine structures in 2D images. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2014, http://www.sciencedirect.com/science/article/pii/S1631073X14001411. ⟨10.1016/j.crma.2014.06.005⟩. ⟨hal-01018207⟩