Finite Difference Approximation of the Mumford and Shah Functional in a Contact Manifold of the Heisenberg Space
نویسندگان
چکیده
Abstract. The functionality of the visual cortex has been described in [63] and in [50] as a contact manifold of dimension three and in [62] the Mumford and Shah functional has been proposed to segment lifting of an image in the three dimensional cortical space. Hence, we study here this functional and we provide a constructive approach to the problem, extending to the subRiemannian setting an approximation technique proposed by De Giorgi in the Euclidean case.
منابع مشابه
An approximation for the Mumford-Shah functional
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 function...
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