Second-Order Edge-Penalization in the Ambrosio--Tortorelli functional

DOI10.1137/15M1020848zbMath1332.49016arXiv1504.05115OpenAlexW2123551903MaRDI QIDQ3459659

Teresa Esposito, Caterina Ida Zeppieri, Martin Burger

Publication date: 11 January 2016

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.05115

zbMATH Keywords

\(\Gamma\)-convergencefree-discontinuity problemsAmbrosio-Tortorelli approximationvariational image segmentation

Mathematics Subject Classification ID

Computing methodologies for image processing (68U10) Energy minimization in equilibrium problems in solid mechanics (74G65) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Methods involving semicontinuity and convergence; relaxation (49J45)

Related Items

Second-Order Edge-Penalization in the Ambrosio--Tortorelli functional ⋮ Crack kinking in a variational phase-field model of brittle fracture with strongly anisotropic surface energy ⋮ Higher order Ambrosio-Tortorelli scheme with non-negative spatially dependent parameters ⋮ Discrete stochastic approximations of the Mumford-Shah functional ⋮ \(\Gamma\)-convergence and stochastic homogenisation of singularly-perturbed elliptic functionals ⋮ Phase-field approximation of a vectorial, geometrically nonlinear cohesive fracture energy ⋮ Anisotropic free-discontinuity functionals as the Γ-limit of second-order elliptic functionals ⋮ Binary recovery via phase field regularization for first-arrival traveltime tomography ⋮ \(\Gamma\)-convergence for high order phase field fracture: continuum and isogeometric formulations ⋮ Numerical approximation of the Steiner problem in dimension $2$ and $3$ ⋮ Approximation of the Mumford–Shah functional by phase fields of bounded variation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic analysis of a second-order singular perturbation model for phase transitions
• Approximation of free-discontinuity problems
• Variational methods in image segmentation with 7 image processing experiments
• An inexact Newton-CG-type active contour approach for the minimization of the Mumford-Shah functional
• A global method for relaxation in \(W^{1,p}\) and in SBV\(_p\)
• The gradient theory of phase transitions and the minimal interface criterion
• Higher-order TV methods -- enhancement via Bregman iteration
• A variational framework for region-based segmentation incorporating physical noise models
• Singular perturbation models in phase transitions for second-order materials
• Optimal approximations by piecewise smooth functions and associated variational problems
• From Mumford–Shah to Perona–Malik in image processing
• Approximation of functional depending on jumps by elliptic functional via t-convergence
• Second-Order Edge-Penalization in the Ambrosio--Tortorelli functional
• Analysis of a Two-Scale Cahn–Hilliard Model for Binary Image Inpainting
• Quasi-Convex Integrands and Lower Semicontinuity in $L^1 $
• Γ-limit for the extended Fisher–Kolmogorov equation
• Finite difference approximation of the Mumford-Shah functional
• Active contours without edges
• Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification
• Second Order Singular Perturbation Models for Phase Transitions
• Image Registration Based on Multiscale Energy Information

This page was built for publication: Second-Order Edge-Penalization in the Ambrosio--Tortorelli functional