Higher order Ambrosio–Tortorelli scheme with non-negative spatially dependent parameters.

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 ω ⁢ d ⁢ x , where ω is a special function of bounded variation, and on its values at the jumps. [ABSTRACT FROM AUTHOR]