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Preprint (Vorabdruck) zugänglich unter
A generic approach to diff usion filtering of matrix-fields
URN: urn:nbn:de:bsz:291-scidok-47224
URL: http://scidok.sulb.uni-saarland.de/volltexte/2012/4722/
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Dokument 1.pdf (2.543 KB)
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, Universität 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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