Global calibrations for the non-homogeneous Mumford-Shah functional
نویسنده
چکیده
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
منابع مشابه
Local Calibrations for Minimizers of the Mumford-shah Functional with a Triple Junction
We prove that, if u is a function satisfying all Euler conditions for the Mumford-Shah functional and the discontinuity set of u is given by three line segments meeting at the origin with equal angles, then there exists a neighbourhood U of the origin such that u is a minimizer of the Mumford-Shah functional on U with respect to its own boundary conditions on ∂U . The proof is obtained by using...
متن کاملLocal calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets
Using a calibration method, we prove that, if w is a function which satisfies all Euler conditions for the Mumford-Shah functional on a two-dimensional open set Ω, and the discontinuity set of w is a segment connecting two boundary points, then for every point (x0, y0) of Ω there exists a neighbourhood U of (x0, y0) such that w is a minimizer of the Mumford-Shah functional on U with respect to ...
متن کاملLocal calibrations for minimizers of the Mumford-Shah functional with a regular discontinuity set
Using a calibration method, we prove that, if w is a function which satisfies all Euler conditions for the Mumford-Shah functional on a two-dimensional open set Ω, and the discontinuity set Sw of w is a regular curve connecting two boundary points, then there exists a uniform neighbourhood U of Sw such that w is a minimizer of the Mumford-Shah functional on U with respect to its own boundary co...
متن کاملApproximation and Optimization in Image Restoration and Reconstruction
We will present a convex representation for the minimal partition problem, based on the notion of “paired calibrations” [2], [3]. We propose an efficient algorithm for minimizing this problem, and discuss the practical implementation with “many” labels. It can be applied to a number of problems, from segmentation to stereo reconstruction. The quality of the results is substantially better than ...
متن کاملSome remarks on the analyticity of minimizers of free discontinuity problems
In this paper we give a partial answer to a conjecture of De Giorgi, namely we prove that in dimension two the regular part of the discontinuity set of a local minimizer of the homogeneous Mumford-Shah functional is analytic with the exception of at most a countable number of isolated points.
متن کامل