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