Please use this identifier to cite or link to this item: doi:10.22028/D291-26354
Title: A generic approach to diffusion filtering of matrix-fields
Author(s): Burgeth, Bernhard
Didas, Stephan
Florack, Luc
Weickert, Joachim
Language: English
Year of Publication: 2007
Free key words: DT-MRI
Jordan product
Perona-Malik diffusion
DDC notations: 510 Mathematics
Publikation type: Preprint
Abstract: Diffusion tensor magnetic resonance imaging (DT-MRI), is a image acquisition method, that provides matrix-valued data, so-called matrix fields. Hence image processing tools for the filtering and analysis of these data types are in demand. In this artricle we propose a generic framework that allows us to find the matrix-valued counterparts of the Perona-Malik PDEs with various diffusivity functions. To this end we extend the notion of derivatives and associated differential operators to matrix fields of symmetric matrices by adopting an operator-algebraic point of view. In order to solve these novel matrix-valued PDEs successfully we develop truly matrix-valued analogs to numerical solution schemes of the scalar setting. Numerical experiments performed on both synthetic and real world data substantiate the effectiveness of our novel matrix-valued Perona-Malik diffusion filters.
Link to this record: urn:nbn:de:bsz:291-scidok-47224
hdl:20.500.11880/26410
http://dx.doi.org/10.22028/D291-26354
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 191
Date of registration: 15-Mar-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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