The Weighted Ambrosio--Tortorelli Approximation Scheme
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 $\omega^-$.