Mumford–Shah Functional as Γ-Limit of Discrete Perona–Malik Energies

DOI10.1142/S0218202503002726zbMath1045.49022OpenAlexW2006919211MaRDI QIDQ3043560

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Publication date: 6 August 2004

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202503002726

zbMATH Keywords

\(G\)-convergenceimage segmentationMumford-Shah functionalanisotropic diffusion

Mathematics Subject Classification ID

Computing methodologies for image processing (68U10) Variational problems in a geometric measure-theoretic setting (49Q20) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Methods involving semicontinuity and convergence; relaxation (49J45) Optimality conditions for free problems in two or more independent variables (49K10)

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A Two-Stage Color Image Segmentation Method Based on Saturation-Value Total Variation ⋮ Image Segmentation via Fischer-Burmeister Total Variation and Thresholding ⋮ A quantitative variational analysis of the staircasing phenomenon for a second order regularization of the Perona-Malik functional ⋮ An extended Perona-Malik model based on probabilistic models ⋮ Non-Convex and Convex Coupling Image Segmentation via TGpV Regularization and Thresholding ⋮ Two-stage image segmentation based on nonconvex \(\ell_2-\ell_p\) approximation and thresholding ⋮ Existence of infinitely many solutions for the one-dimensional Perona-Malik model ⋮ Static, quasistatic and dynamic analysis for scaled Perona-Malik functionals ⋮ A nonlocal approximation of free discontinuity problems in SBV and SBD

Cites Work

• Unnamed Item
• Unnamed Item
• Existence theory for a new class of variational problems
• Approximation of free-discontinuity problems
• Phase transition with the line-tension effect
• Non-local approximation of the Mumford-Shah functional
• Image Selective Smoothing and Edge Detection by Nonlinear Diffusion
• Finite-differences discretizations of the mumford-shah functional
• Finite difference approximation of the Mumford-Shah functional
• A density result in SBV with respect to non-isotropic energies

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