Topological gradient for a fourth order PDE and application to the detection of fine structures in 2D and 3D images

Audric Drogoul (1) , Gilles Aubert (1) , Didier Auroux (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

In this paper we describe a new variational approach for the detection of fine structures in an image (like filaments in 2D). This approach is based on the computation of the topological gradient associated to a cost function defined from a regu- larized version of the data (possibly noisy and / or blurred). We get this approximation by solving a fourth order PDE. The study of the topological sensitivity is made in the case of a crack. We give the numerical algorithm to compute this topological gradient and we illustrate our approach by giving several experimental results in 2D and 3D images.

Domaines: Analyse numérique [math.NA]

Audric Drogoul, Gilles Aubert, Didier Auroux. Topological gradient for a fourth order PDE and application to the detection of fine structures in 2D and 3D images. IEEE International Conference on Image Processing 2014 (ICIP 2014), Oct 2014, Paris, France. 5 p. ⟨hal-01018623⟩