By Joachim Weickert
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Extra info for Anisotropic diffusion in image processing
Hence, this model behaves really anisotropic. If we let the regularization parameter σ tend to 0, we end up with the isotropic Perona–Malik process. Another anisotropic model which can be regarded as a regularization of an isotropic nonlinear diffusion filter has been described in . (b) Anisotropic models for smoothing one-dimensional objects A second motivation for introducing anisotropy into diffusion processes arises from the wish to process one-dimensional features such as line-like structures.
When studying the evolution of isophotes under MCM, it can be shown that, if one isophote is enclosed by another, this ordering is preserved [129, 227]. 100) that it takes the time T = 21 σ 2 to remove all isophotes within a circle of radius σ. This shows that the 40 CHAPTER 1. PARTIAL DIFFERENTIAL EQUATIONS relation between temporal and spatial scale for MCM is the same as for linear diffusion filtering (cf. 14)). Moreover, two level sets cannot move closer to one another than they were initially [129, 227].
4 Generalizations Higher dimensions. It is easily seen that many of the previous results can be generalized to higher dimensions. g. medical image sequences from computerized tomography (CT) or magnetic resonance imaging (MRI), or when applying diffusion filters to the postprocessing of fluctuating higher-dimensional numerical data. The first three-dimensional nonlinear diffusion filters have been investigated by Gerig et al.  in the isotropic case and by Rambaux and Gar¸con  in the anisotropic case.
Anisotropic diffusion in image processing by Joachim Weickert