In this paper, we consider cracks with Dirichlet boundary conditions. We first derive an
asymptotic expansion of the boundary perturbations that are due to the presence of a small …

We give an update on recent techniques which use a level set representation of shapes for
solving inverse scattering problems, completing in that matter the exposition made in (Dorn …

One of the issues for the automotive industry is weight reduction. For this purpose, topology
optimization is used for mechanical parts and usually involves a single part. Its connections …

The aim of this article is to review and extend the applications of the topological gradient to
major image processing problems. We briefly review the topological gradient, and then …

In this paper, we propose new variational model for image registration from tomographic
data. First, we employ the topological gradient approach for a tomographic reconstruction …

Image restoration is a very challenging task in image analysis and plays important roles in
various fields such as medical imaging. In particular, in ultrasound imaging the obtained …

In this paper we propose a new optimal partition algorithm and show applications to
multilabel image classification problems. Possibly noisy and blurred greyscale and color …

We consider a fourth‐order variational model, to solve the image inpainting problem, with
the emphasis on the recovery of low‐dimensional sets (edges and corners) and the …

We combine in this paper the topological gradient, which is a powerful method for edge
detection in image processing, and a variant of the minimal path method in order to find …

In this paper, a general framework based on fractional-order partial differential equations
allows to solve image reconstruction problems. The algorithm presented in this work …