Nonlocal infinity Laplacian equation on graphs with applications in image processing and machine learning

DOI10.1016/j.matcom.2014.01.007OpenAlexW2023877921WikidataQ125757666 ScholiaQ125757666MaRDI QIDQ2229878

Lézoray Olivier, Elmoataz Abderrahim, Desquesnes Xavier, Lakhdari Zakaria

Publication date: 18 February 2021

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2014.01.007

zbMATH Keywords

image processingweighted graphstug-of-war gamepartial difference equationsnonlocal infinity Laplaciansemi-supervised data clustering

Mathematics Subject Classification ID

Computer science (68-XX) Information and communication theory, circuits (94-XX)

Related Items (15)

Nonlocal total variation system for the restoration of textured images ⋮ Nonlocal PDEs on graphs: from tug-of-war games to unified interpolation on images and point clouds ⋮ Non-local discrete \(\infty \)-Poisson and Hamilton Jacobi equations. From stochastic game to generalized distances on images, meshes, and point clouds ⋮ On the $p$-Laplacian and $\infty$-Laplacian on Graphs with Applications in Image and Data Processing ⋮ An inhomogeneous evolution equation involving the normalized infinity Laplacian with a transport term ⋮ Convergence of the Weighted Nonlocal Laplacian on Random Point Cloud ⋮ BOUNDARY BLOW-UP SOLUTIONS TO EQUATIONS INVOLVING THE INFINITY LAPLACIAN ⋮ Continuum limit of p-Laplacian evolution problems on graphs: L^q graphons and sparse graphs ⋮ Weighted nonlocal Laplacian on interpolation from sparse data ⋮ Convergence of least energy sign-changing solutions for logarithmic Schrödinger equations on locally finite graphs ⋮ Loss of Double-Integral Character During Relaxation ⋮ Nonlocal $p$-Laplacian Evolution Problems on Graphs ⋮ Hölder estimates for viscosity solutions of equations of fractional \(p\)-Laplace type ⋮ A weighted eigenvalue problem of the biased infinity Laplacian ^* ⋮ On the game p-Laplacian on weighted graphs with applications in image processing and data clustering

Cites Work

• The \(\infty\)-eigenvalue problem
• Extrapolation of vector fields using the infinity Laplacian and with applications to image segmentation
• On the evolution governed by the infinity Laplacian
• Extension of functions satisfying Lipschitz conditions
• Tug-of-war and the infinity Laplacian
• Dynamic Programming Principle for tug-of-war games with noise
• A Hölder infinity Laplacian
• Scaling Theorems for Zero Crossings
• An axiomatic approach to image interpolation
• A convergent difference scheme for the infinity Laplacian: construction of absolutely minimizing Lipschitz extensions
• A tour of the theory of absolutely minimizing functions
• Nonlocal PDEs-Based Morphology on Weighted Graphs for Image and Data Processing
• Uniqueness of ∞-Harmonic Functions and the Eikonal Equation
• A Visit with the ∞-Laplace Equation

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