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URN: urn:nbn:de:bsz:291-scidok-47224
URL: http://scidok.sulb.uni-saarland.de/volltexte/2012/4722/


A generic approach to diff usion filtering of matrix-fields

Burgeth, Bernhard ; Didas, Stephan ; Florack, Luc ; Weickert, Joachim

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Freie Schlagwörter (Englisch): DT-MRI , Jordan product , Perona-Malik diffusion
Institut: Fachrichtung 6.1 - Mathematik
DDC-Sachgruppe: Mathematik
Dokumentart: Preprint (Vorabdruck)
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universit├Ąt des Saarlandes
Bandnummer: 191
Sprache: Englisch
Erstellungsjahr: 2007
Publikationsdatum: 15.03.2012
Kurzfassung auf Englisch: 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.
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