Scale-Space Properties of Nonlinear Diffusion Filtering with a Diffusion Tensor

  • In spite of its lack of theoretical justification, nonlinear diffusion filtering has become a powerful image enhancement tool in the recent years. The goal of the present paper is to provide a mathematical foundation for nonlinear diffusion filtering as a scale-space transformation which is flexible enough to simplify images without loosing the capability of enhancing edges. By stuying the Lyapunow functional, it is shown that nonlinear diffusion reduces Lp norms and central moments and increases the entropy of images. The proposed anisotropic class utilizes a diffusion tensor which may be adapted to the image structure. It permits existence, uniqueness and regularity results, the solution depends continuously on the initial image, and it fulfills an extremum principle. All considerations include linear and certain nonlinear isotropic models and apply to m-dimensional vector-valued images. The results are juxtaposed to linear and morphological scale-spaces.

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Verfasserangaben:Joachim Weickert
URN (Permalink):urn:nbn:de:hbz:386-kluedo-5083
Schriftenreihe (Bandnummer):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (110)
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:1994
Jahr der Veröffentlichung:1994
Veröffentlichende Institution:Technische Universität Kaiserslautern
Datum der Publikation (Server):03.04.2000
Freies Schlagwort / Tag:anisotropic diffusion; image processing; scale-space; well-posedness
Fachbereiche / Organisatorische Einheiten:Fachbereich Mathematik
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Klassifikation (Mathematik):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
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011