Joint optimization of distortion and cut location for mesh parameterization using an Ambrosio-Tortorelli functional

Second-Order Edge-Penalization in the Ambrosio-Tortorelli functional

Ambrosio-Tortorelli Segmentation of Stochastic Images

We present an extension of the classical Ambrosio-Tortorelli approximation of the Mumford-Shah approach for the segmentation of images with uncertain gray values resulting from measurement errors and noise. Our approach yields a reliable precision estimate for the segmentation result, and it allows to quantify the robustness of edges in noisy images and under gray value uncertainty. We develop ...

Anisotropic Mesh Adaptation for the Minimization of the Ambrosio- Tortorelli Functional with Application to Quasi-static Brittle Frac- ture Propagation

Francfort and Marigo presented in 1998 a model for quasi-static brittle fracture which requires the minimization of the Mumford-Shah functional, representing the energy of the system. The minimization of this functional represents a very challenging issue since it is non-smooth and non-convex. The numerical approximation of this problem can be issued via a Gamma-approximation on the energy func...

An Estimation Theoretical View on Ambrosio-Tortorelli Image Segmentation

In this paper, we examine the Ambrosio-Tortorelli (AT) functional [1] for image segmentation from an estimation theoretical point of view. Instead of considering a single point estimate, i.e. the maximum-a-posteriori (MAP) estimate, we adopt a wider estimation theoretical view-point, meaning we consider images to be random variables and investigate their distribution. We derive an effective blo...

An Adaptive Finite Element Approximation of a Generalised Ambrosio–Tortorelli Functional

The Francfort–Marigo model of brittle fracture is posed in terms of the minimization of a highly irregular energy functional. A successful method for discretizing the model is to work with an approximation of the energy. In this work a generalised Ambrosio–Tortorelli functional is used. This leads to a bound-constrained minimization problem, which can be posed in terms of a variational inequali...