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.
Digital Object Identifier: 10.2969/aspm/06710131