We study the pointwise convergence and the Γ-convergence of a family of nonlocal functionals defined in L 1 loc (R n ) to a local functional F (u) that depends on the gradient of u and on the set of discontinuity points of u. We apply this result to approximate a minimum problem introduced by Mumfor
Non-local approximation of the Mumford-Shah functional
✍ Scribed by A. Braides; G. Dal Maso
- Publisher
- Springer
- Year
- 1997
- Tongue
- English
- Weight
- 251 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0944-2669
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📜 SIMILAR VOLUMES
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 , and the discontinuity set S w of w is a regular curve connecting two boundary points, then there exists a uniform neighbourhood U of S w
We show the -convergence of a family of discrete functionals to the Mumford and Shah image segmentation functional. The functionals of the family are constructed by modifying the elliptic approximating functionals proposed by Ambrosio and Tortorelli. The quadratic term of the energy related to the e