The Anisotropy Introduced by the Mesh in the Finite Element Approximation of the Mumford-shah Functional
نویسنده
چکیده
We compute explicitly the anisotropy eeect in the H 1 term, generated in the approximation of the Mumford-Shah functional by nite element spaces deened on structured triangulations.
منابع مشابه
Implementation 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 ...
متن کاملFree and Forced Vibration Analysis of Functionally Graded Material Cylinders by a Mesh-Free Method
In this paper, free and forced vibration analysis of functionally graded material cylinders was carried out by mesh-free and finite element method. In this analysis, MLS shape functions are used for approximation of displacement field in the weak form of motion equation and essential boundary conditions are imposed by transformation method. Resulted set of differential equations are solved usin...
متن کاملAnalysis of Gradient Flow of a Regularized Mumford-shah Functional for Image Segmentation and Image Inpainting
Abstract. This paper studies the gradient flow of a regularized Mumford-Shah functional proposed by Ambrosio and Tortorelli (1990, 1992) for image segmentation, and adopted by Esedoglu and Shen (2002) for image inpainting. It is shown that the gradient flow with L2×L∞ initial data possesses a global weak solution, and it has a unique global in time strong solution, which has at most finite numb...
متن کاملΓ-convergence approximation of fracture and cavitation in nonlinear elasticity
Our starting point is a variational model in nonlinear elasticity that allows for cavitation and fracture that was introduced by Henao and Mora-Corral (2010). The total energy to minimize is the sum of the elastic energy plus the energy produced by crack and surface formation. It is a free discontinuity problem, since the crack set and the set of new surface are unknowns of the problem. The exp...
متن کاملAn 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...
متن کامل