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

Benoît Merlet

Displaying similar documents to “Numerical study of a new global minimizer for the Mumford-Shah functional in R3”

Weighted regularization for composite materials in electromagnetism

Patrick Ciarlet Jr., François Lefèvre, Stéphanie Lohrengel, Serge Nicaise (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, a weighted regularization method for the time-harmonic Maxwell equations with perfect conducting or impedance boundary condition in composite materials is presented. The computational domain is the union of polygonal or polyhedral subdomains made of different materials. As a result, the electromagnetic field presents singularities near geometric singularities, which are the interior and exterior edges and corners. The variational formulation of the weighted regularized...

Local minimizers of functionals with multiple volume constraints

Édouard Oudet, Marc Oliver Rieger (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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We study variational problems with volume constraints, , with level sets of prescribed measure. We introduce a numerical method to approximate local minimizers and illustrate it with some two-dimensional examples. We demonstrate numerically nonexistence results which had been obtained analytically in previous work. Moreover, we show the existence of discontinuous dependence of global minimizers from the data by using a -limit argument and illustrate this with numerical computations....

Model problems from nonlinear elasticity: partial regularity results

Menita Carozza, Antonia Passarelli di Napoli (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we prove that every weak and strong local minimizer $u \in W^{1, 2} (Ω, ℝ^{3})$ of the functional $I (u) = \int_{Ω} {| D u |}^{2} + f (Adj D u) + g (\det D u),$ where $u : Ω \subset ℝ^{3} \to ℝ^{3}$ , grows like ${| Adj D u |}^{p}$ , grows like ${| \det D u |}^{q}$ and , is $C^{1, α}$ on an open subset $Ω_{0}$ of such that $𝑚𝑒𝑎𝑠 (Ω ∖ Ω_{0}) = 0$ . Such functionals naturally arise from nonlinear elasticity problems. The key point in order to obtain the partial regularity result is to establish an energy estimate of Caccioppoli type, which is based on an appropriate choice of the test functions. The limit case $p = q \leq 2$ is also treated for weak local minimizers. ...

Analysis of gradient flow of a regularized Mumford-Shah functional for image segmentation and image inpainting

Xiaobing Feng, Andreas Prohl (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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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 initial data possesses a global weak solution, and it has a unique global in time strong solution, which has at most finite number of point singularities in the space-time, when the initial data are in . A family of fully discrete...