The Perona-Malik Paradox

Summary

The Perona--Malik equation is a formally ill-posed parabolic equation for which simple discretizations are nevertheless numerically found to be stable.

Keywords

Simple (philosophy), Mathematics, Computation, Applied mathematics, Parabolic partial differential equation

References

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Cited by

Analytical Approximations for Nonlinear Diffusion Time in Multiscale Edge EnhancementCarlos Platero, Javier Sanguino, María C. Tobar — 2009
Perona-Malik equation and its numerical propertiesMaciek Wielgus — 2014
Image Segmentation using PDE, Variational, Morphological and Probabilistic MethodsYongsheng Pan — 2007
Iterative solvers for image denoising with diffusion models: A comparative studySubit K. Jain, Rajendra K. Ray, Arnav Bhavsar — 2015
Advanced numerical methods for image denoising and segmentationXiao-Yang Liu — 2013
Régularisation d'Images Multivaluées par EDP et ApplicationsDavid Tschumperlé — 2002
Anisotropic diffusion in image processingJoachim Weickert — 1996
Von Pixeln zu Regionen: partielle Differentialgleichungen in der BildanalyseThomas Brox — 2005
Gaussian processes of nonlinear diffusion filteringRamūnas Girdziušas, Jorma Laaksonen — 2005
PAIRED ANISOTROPIC DISTRIBUTION FOR IMAGE SELECTIVE SMOOTHINGA Madankan — 2011
Image Segmentation Using Curve Evolution and Anisotropic Diffusion: An Integrated ApproachYongsheng Pan, Douglas Birdwell, Seddik M. Djouadi — 2005
A Review of Nonlinear Diffusion FilteringJoachim Weickert — 1997
Study of Image Local Scale Structure Using Nonlinear DiffusionYan Wang — 2013
Nonlinear scale-space analysis in image processingIlya Pollak, Alan S. Willsky, Hamid Krim — 1999
DIFFUSION MODELS AND THEIR ACCELERATED SOLUTION IN IMAGE AN D SURFACE PROCESSINGU. Diewald, Tobias Preußer, Martin Rumpf — 2000
Sharp Operator Based Edge DetectionM. K. Ahmad, Stephan Didas, Alemdar Hasanov — 2015
NONLINEAR EVOLUTIONARY PDEs IN IMAGE PROCESSING AND COMPUTER VISIONKexue Liu — 2004
A Simple Yet Effective Improvement to the Bilateral Filter for Image DenoisingKollipara Rithwik, Kunal N. Chaudhury — 2015
Speckle Reduction and Edge Detection in Ultrasound ImagerySean P. Finn — 2010
Mathematical analysis of a reaction diffusion model for image restorationSalim Mesbahi, Nour Eddine Alaa — 2015

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