Advanced Studies in Pure Mathematics

Anisotropic diffusions of image processing from Perona–Malik on

Patrick Guidotti

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Many reasons can be cited for the desire to harness the power of nonlinear anisotropic diffusion in image processing. Perona and Malik proposed one of the pioneering models which, while numerically viable, proves mathematically ill-posed. This discrepancy between its analytical properties and those of its numerical implementations spurred a significant amount of research in the past twenty years or so. An overview of the latter is the topic of this article.

Article information

Variational Methods for Evolving Objects, L. Ambrosio, Y. Giga, P. Rybka and Y. Tonegawa, eds. (Tokyo: Mathematical Society of Japan, 2015), 131-156

Received: 16 January 2013
First available in Project Euclid: 19 October 2018

Permanent link to this document euclid.aspm/1539916036

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35-02
Secondary: 35K55: Nonlinear parabolic equations 35K65: Degenerate parabolic equations

Anisotropic diffusion Perona–Malik equation regularization relaxation semi-discretization forward-backward diffusion gradient systems


Guidotti, Patrick. Anisotropic diffusions of image processing from Perona–Malik on. Variational Methods for Evolving Objects, 131--156, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06710131.

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