Topological gradient for a fourth order operator used in image analysis

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.

Mots clés: image segmentation.; Calculus of variations; topological gradient

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Gilles Aubert, Audric Drogoul. Topological gradient for a fourth order operator used in image analysis. ESAIM: Control, Optimisation and Calculus of Variations, 2015, 21 (4), pp.1120-1149. ⟨hal-01016415v2⟩