Topological gradient for fourth-order PDE and application to the detection of fine structures in 2D images
Gilles Aubert, Audric Drogoul · Comptes Rendus Mathématique · 2014
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.