Proximal Based Strategies for Solving Discrete Mumford-Shah With Ambrosio-Tortorelli Penalization on Edges

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

An approximation of Mumford-Shah energy by a family of discrete edge-preserving functionals

We show the Γ-convergence of a family of discrete functionals to the Mumford and Shah image segmentation functional. The functionals of the family are constructed by modifying the elliptic approximating functionals proposed by Ambrosio and Tortorelli. The quadratic term of the energy related to the edges of the segmentation is replaced by a nonconvex 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 ...

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...

Discrete Optimization of the Multiphase Piecewise Constant Mumford-Shah Functional

The Mumford-Shah model has been one of the most powerful models in image segmentation and denoising. The optimization of the multiphase Mumford-Shah energy functional has been performed using level sets methods that optimize the Mumford-Shah energy by evolving the level sets via the gradient descent. These methods are very slow and prone to getting stuck in local optima due to the use of the gr...