By Joachim Weickert
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Additional resources for Anisotropic diffusion in image processing
4 (a),(b). -L. 45) leads to a well-posed filter (cf. ). We observe that v is intended as a time-delay regularization of |∂x u|2 where the parameter τ > 0 determines the delay. These equations arise as a special case of the spatio-temporal regularizations of Nitzberg and Shiota  when neglecting any spatial regularization. Mumford conjectures that this model gives piecewise constant steady-states. In this case, the steady-state solution would solve a segmentation problem. (c) In the context of shear flows, Barenblatt et al.
337, 336] observed that this solution looks fairly blurred since the equations contain diffusion terms such as ∆u. They obtained pronounced edges by replacing such a term by its Perona–Malik counterpart div (g(|∇u|2) ∇u). Related equations are also studied in . 61). The system of Richardson and Mitter is used for edge detection . Shah investigates diffusion–reaction systems for matching stereo images , while Proesmans et al. apply coupled diffusion-reaction equations to image sequence analysis, vector-valued images and stereo vision [336, 338].
It is solved by means of nonlinear Gauß– Seidel iterations. Comparing it with the explicit scheme they report a tradeoff between the larger time step size and the higher computational effort per step. An inherent problem of all finite difference schemes for morphological image evolutions are their dissipative effects which create additional blurring of discontinuities. As a remedy, one can decompose the image into binary level sets, map them into Lipschitz-continuous images by applying a distance transformation, and run a finite difference method on them.
Anisotropic diffusion in image processing by Joachim Weickert