Numerical study of a new global minimizer for the Mumford-Shah functional in R3

DOI10.1051/cocv:2007026zbMath1152.49045arXivmath/0504237OpenAlexW2158934224MaRDI QIDQ5428418

Benoît Merlet

Publication date: 22 November 2007

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504237

zbMATH Keywords

Mumford-Shah functionalnumerical analysisboundary value problems for second-orderelliptic equations in domains with corners

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Variational problems in a geometric measure-theoretic setting (49Q20) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (4)

On the homogeneity of global minimizers for the Mumford-Shah functional when \(K\) is a smooth cone ⋮ A rigidity result for global Mumford-Shah minimizers in dimension three ⋮ A numerical solution for the inhomogeneous Dirichlet boundary value problem on a non-convex polygon ⋮ A selective review on Mumford-Shah minimizers

Cites Work

• Unnamed Item
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• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• The singular complement method for 2d scalar problems
• Singular sets of minimizers for the Mumford-Shah functional
• Existence theorem for a minimum problem with free discontinuity set
• On the regularity of edges in image segmentation
• Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques. I : Résultats généraux pour le problème de Dirichlet
• Optimal approximations by piecewise smooth functions and associated variational problems
• Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques. II : Quelques opérateurs particuliers
• Coefficients of the Singularities for Elliptic Boundary Value Problems on Domains with Conical Points. III: Finite Element Methods on Polygonal Domains
• Éléments finis: théorie, applications, mise en œuvre.

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