Numerical study of a new global minimizer for the Mumford-Shah functional in R3
نویسندگان
چکیده
منابع مشابه
Numerical study of a new global minimizer for the Mumford-Shah functional in 3
In [8], G. David suggested a new type of global minimizer for the Mumford-Shah functional in R, for which the singular sets belong to a three parameters family of sets (0 < δ1, δ2, δ3 < π). We first derive necessary conditions satisfied by global minimizers of this family. Then we are led to study the first eigenvectors of the Laplace-Beltrami operator with Neumann boundary conditions on subdom...
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Using a calibration method we prove that, if Γ ⊂ Ω is a closed regular hypersurface and if the function g is discontinuous along Γ and regular outside, then the function uβ which solves { ∆uβ = β(uβ − g) in Ω \ Γ ∂νuβ = 0 on ∂Ω ∪ Γ is in turn discontinuous along Γ and it is the unique absolute minimizer of the nonhomogeneous Mumford-Shah functional
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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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A Second Order Minimality Condition for the Mumford-shah Functional
A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on H1 0 (Γ) , Γ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact ...
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ژورنال
عنوان ژورنال: ESAIM: Control, Optimisation and Calculus of Variations
سال: 2007
ISSN: 1292-8119,1262-3377
DOI: 10.1051/cocv:2007026