Fast parallel algorithms for a broad class of nonlinear variational diffusion approaches

Weickert, Joachim ; Heers, Josef ; Schnörr, Christoph ; Zuiderveld, Karel J. ; Scherzer, Otmar ; Stiehl, H. Siegfried

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URN: urn:nbn:de:bsz:180-madoc-19418
Document Type: Working paper
Year of publication: 1999
The title of a journal, publication series: Technical Report / Department for Mathematics and Computer Science, University of Mannheim
Place of publication: Mannheim
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Informatik > Technical Reports
Subject: 004 Computer science, internet
Subject headings (SWD): Energieeinsparung , Segmentierung , Nichtlineare Diffusion , Parallelverarbeitung , Bildgebendes Verfahren
Keywords (English): energy minimization , variational segmentation , nonlinear diffusion , numericallinear algebra , parallel computing , medical imaging
Abstract: Variational segmentation and nonlinear diffusion approaches have been very active research areas in the fields of image processing and computer vision during the last years. In the present paper, we review recent advances in the development of efficient numerical algorithms for these approaches. The performance of parallel implement at ions of these algorithms on general-purpose hardware is assessed. A mathematically clear connection between variational models and nonlinear diffusion filters is presented that allows to interpret one approach as an approximation of the other, and vice versa. Numerical results confirm that, depending on the parametrization, this approximation can be made quite accurate. Our results provide a perspective for uniform implement at ions of both nonlinear variational models and diffusion filters on parallel architectures.
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