Applications of nonlinear diffusion in image processing and computer vision

Weickert, Joachim

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URN: urn:nbn:de:bsz:180-madoc-18454
Document Type: Working paper
Year of publication: 2000
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Mathematik und Informatik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Informatik > Technical Reports
Subject: 004 Computer science, internet
Classification: MSC: 94A08 68W10 65M06 35K35 35K55 ,
Subject headings (SWD): Nichtlineare Diffusion , Variationsrechnung , Bildverarbeitung , Finite-Differenzen-Methode , Paralleler Algorithmus
Keywords (English): nonlinear diffusion , variational methods , image processing , computer vision , finite difference methods , parallel algorithms
Abstract: Nonlinear diffusion processes can be found in many recent methods for image processing and computer vision. In this article, four applications are surveyed: nonlinear diffusion filtering, variational image regularization, optic flow estimation, and geodesic active contours. For each of these techniques we explain the main ideas, discuss theoretical properties and present an appropriate numerical scheme. The numerical schemes are based on additive operator splittings (AOS). In contrast to traditional multiplicative splittings such as ADI, LOD or D'yakonov splittings, all axes are treated in the same manner, and additional possibilities for efficient realizations on parallel and distributed architectures appear. Geodesic active contours lead to equations that resemble mean curvature motion. For this application, a novel AOS scheme is presented that uses harmonie averaging and does not require reinitializations of the distance function in each iteration step.
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