Please use this identifier to cite or link to this item: doi:10.22028/D291-26359
Title: A general structure tensor concept and coherence-enhancing diffusion filtering for matrix fields
Author(s): Burgeth, Bernhard
Didas, Stephan
Weickert, Joachim
Language: English
Year of Publication: 2007
Free key words: matrix field
symmetric matrix
diffusion tensor MRI
structure tensor
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: 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.
Link to this record: urn:nbn:de:bsz:291-scidok-47275
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 197
Date of registration: 20-Mar-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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