This paper is devoted to a numerical implementation of the Francfort–Marigo model of
damage evolution in brittle materials. This quasi-static model is based, at each time step, on …

Image segmentation methods with length regularized edge sets are known to have
segments whose endpoints either terminate perpendicularly to the boundary of the domain …

This chapter is the printed matter of a series of lectures on shape optimization given in Udine
(Italy) in June 2012. It is mainly focused on the optimal design problem in elasticity. It is well …

The level set method [31] is a commonly used framework for image segmentation
algorithms. For edge detection and segmentation models, the standard level set method …

We propose a level set framework for representing triple junctions either with or without free
endpoints. For triple junctions without free endpoints, our method uses two level set …

In two dimensions, the Mumford and Shah functional for image segmentation and
regularization 15 has minimizers (u, K), where u is a piecewise-smooth approximation of the …

Mathematical models in imaging science attempt to understand and analyze the underlying
quantitative structure of images. The most popular mathematical techniques tend to center …

This dissertation is focused on certain variational models of fracture. In engineering, the
design of structures that can resist cracking is an important goal, with implications for …