Gradient estimates for the Perona-Malik equation

DOI10.1007/s00208-006-0047-1zbMath1130.35081OpenAlexW2043475383MaRDI QIDQ877161

Massimo Gobbino, Marina Ghisi

Publication date: 19 April 2007

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-006-0047-1

zbMATH Keywords

a priori estimatesimage processinggradient flowsemi-discrete schemePerona-Malik equationgradient estimatesbackward-parabolicforward-parabolic

Mathematics Subject Classification ID

Computing methodologies for image processing (68U10) Nonlinear parabolic equations (35K55) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) PDEs of mixed type (35M10) Maximum principles in context of PDEs (35B50) A priori estimates in context of PDEs (35B45)

Related Items (16)

Entire Solutions of the One-Dimensional Perona-Malik Equation ⋮ Classification of equilibria and \(\Gamma \)-convergence for the discrete Perona-Malik functional ⋮ PASSING TO THE LIMIT IN MAXIMAL SLOPE CURVES: FROM A REGULARIZED PERONA–MALIK EQUATION TO THE TOTAL VARIATION FLOW ⋮ A quantitative variational analysis of the staircasing phenomenon for a second order regularization of the Perona-Malik functional ⋮ Monotonicity Properties of Limits of Solutions to the Semidiscrete Scheme for a Class of Perona–Malik Type Equations ⋮ Convergence of discrete schemes for the Perona-Malik equation ⋮ Qualitative properties for Perona-Malik type equations ⋮ Upper bounds on the coarsening rate of discrete, ill‐posed nonlinear diffusion equations ⋮ A backward-forward regularization of the Perona-Malik equation ⋮ The Γ-limit for singularly perturbed functionals of Perona–Malik type in arbitrary dimension ⋮ \(BV\) functions and parabolic initial boundary value problems on domains ⋮ A new nonlocal nonlinear diffusion of image processing ⋮ An Example of Global Classical Solution for the Perona-Malik Equation ⋮ A class of local classical solutions for the one-dimensional Perona-Malik equation ⋮ Two-phase entropy solutions of a forward-backward parabolic equation ⋮ Non-uniqueness results for entropy two-phase solutions of forward-backward parabolic problems with unstable phase

Cites Work

• Unnamed Item
• Axioms and fundamental equations of image processing
• Maximum and comparison principle for one-dimensional anisotropic diffusion
• Existence of Infinitely Many Solutions for a Forward Backward Heat Equation
• From Mumford–Shah to Perona–Malik in image processing
• Stability Properties of the Perona--Malik Scheme
• The Perona--Malik Paradox
• An analysis of the Perona-Malik scheme
• A new approach to variational problems with multiple scales
• Entire Solutions of the One-Dimensional Perona-Malik Equation
• Global Solutions to the Gradient Flow Equation of a Nonconvex Functional

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