An approximation for the Mumford-Shah functional
نویسنده
چکیده
Ω |∇u| dx+ cH(Su) where u ∈ SBV (Ω), the space of special functions of bounded variation; Su is the approximate discontinuity set of u and Hn−1 is the (n− 1)-dimensional Hausdorff measure. Several approximation methods are known for the MumfordShah functional and, more in general, for free discontinuity functionals: the Ambrosio & Tortorelli approximation (see [1] and [3]) via elliptic functionals, the Gobbino’s approximation by finite difference methods (see [12]) and many others (see [6], [7], [9], [10]). In [5] Braides & Dal Maso approximate the Mumford-Shah functional by means of a sequence of non-local integral functionals given by
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