J. Weickert,
Nonlinear diffusion scale-spaces: From the continuous to the
discrete setting,
M.-O. Berger, R. Deriche, I. Herlin, J. Jaffré, J.-M. Morel (Eds.),
ICAOS '96: Images, Wavelets and PDEs;
Lecture Notes in Control and Information Sciences, Vol. 219,
Springer, London, 111-118, 1996.
A survey on continuous, semidiscrete and discrete well-posedness
and scale-space results for a class of nonlinear diffusion filters is
presented. This class does not require any monotony assumption
(comparison principle) and, thus, allows image restoration as well.
The theoretical results include existence, uniqueness, continuous
dependence on the initial image, maximum-minimum principles, average
grey level invariance, smoothing Lyapunov functionals,
and convergence to a constant steady state.
The full paper is available
online as well.
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