Finite-differences discretizations of the mumford-shah functional
نویسندگان
چکیده
منابع مشابه
Finite-differences discretizations of the Mumford-Shah functional
About two years ago, Gobbmo [21] gave a proof of a De Giorgi's conjecture on the approximation of the Mumford-Shah energy by means of finite-differences based non-local functionals In this work, we introducé a discretized version of De Giorgi's approximation, that may be seen as a generahzation of Blake and Zisserman's "weak membrane" energy (first mtroduced m the image segmentation framework) ...
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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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متن کاملImplementation of an adaptive finite-element approximation of the Mumford-Shah functional
where Ω ⊂ R2 is the image domain (a bounded open two-dimensional domain), g ∈ L∞(Ω) is the original image, that has to be segmented, K is a closed set of Hausdorff one-dimensional measure H1(K) and u ∈ C1(Ω \K). The set K is supposed to represent the edges of the segmented image u that is regular out of K and can be discontinuous across K (see Appendix A.2 for details). The actual minimization ...
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ژورنال
عنوان ژورنال: ESAIM: Mathematical Modelling and Numerical Analysis
سال: 1999
ISSN: 0764-583X,1290-3841
DOI: 10.1051/m2an:1999115