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Nonlinear Diffusion Scale-Spaces: From the Continuous to the Discrete Setting

  • 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.

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Author:Joachim Weickert
URN (permanent link):urn:nbn:de:hbz:386-kluedo-5581
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (156)
Document Type:Article
Language of publication:English
Year of Completion:1995
Year of Publication:1995
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:nonlinear diffusion filtering; scale-space; well-posedness
Source:M.-O. Berger, R.Deriche, I. Herlin, J. Jaffre, J.-M. Morel (EDs.),ICAOS ´96: Images, Wavelets and PDEs; Lecture Notes in Control and Information Sciences, Vol 219,Springer, London, 111 - 118, 1996
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q80 PDEs in connection with classical thermodynamics and heat transfer
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011