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URN: urn:nbn:de:bsz:291-scidok-47275
URL: http://scidok.sulb.uni-saarland.de/volltexte/2012/4727/


A general structure tensor concept and coherence-enhancing diffusion filtering for matrix fields

Burgeth, Bernhard ; Didas, Stephan ; Weickert, Joachim

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Freie Schlagwörter (Englisch): matrix field , symmetric matrix , diffusion tensor MRI , CED , structure tensor
Institut: Fachrichtung 6.1 - Mathematik
DDC-Sachgruppe: Mathematik
Dokumentart: Preprint (Vorabdruck)
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Bandnummer: 197
Sprache: Englisch
Erstellungsjahr: 2007
Publikationsdatum: 20.03.2012
Kurzfassung auf Englisch: Coherence-enhancing diffusion filtering is a striking application of the structure tensor concept in image processing. The technique deals with the problem of completion of interrupted lines and enhancement of flow-like features in images. The completion of line-like structures is also a major concern in diffusion tensor magnetic resonance imaging (DT-MRI). This medical image acquisition technique outputs a 3D matrix field of symmetric 3×3-matrices, and it helps to visualise, for example, the nerve fibers in brain tissue. As any physical measurement DT-MRI is subjected to errors causing faulty representations of the tissue corrupted by noise and with visually interrupted lines or fibers.
In this paper we address that problem by proposing a coherence-enhancing diffusion filtering methodology for matrix fields. The approach is based on a generic structure tensor concept for matrix fields that relies on the operator-algebraic properties of symmetric matrices, rather than their channel-wise treatment of earlier proposals. Numerical experiments with artificial and real DT-MRI data confirm the gap-closing and flow-enhancing qualities of the technique presented.
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