The Weighted Ambrosio - Tortorelli Approximation Scheme

Abstract

The Ambrosio-Tortorelli approximation scheme with weighted underlying metric is investigated. It is shown that it Γ-converges to a Mumford-Shah image segmentation functional depending on the weight $\omega dx$, where $\omega \in SBV(\Omega )$, and on its value ${\omega }^{-}$.