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Titel: Curvature-driven PDE methods for matrix-valued images
Verfasser: Feddern, Christian
Weickert, Joachim
Burgeth, Bernhard
Welk, Martin
Sprache: Englisch
Erscheinungsjahr: 2004
DDC-Sachgruppe: 510 Mathematik
Dokumentart : Preprint (Vorabdruck)
Kurzfassung: Matrix-valued data sets arise in a number of applications including diffusion tensor magnetic resonance imaging (DT-MRI) and physical measurements of anisotropic behaviour. Consequently, there arises the need to filter and segment such tensor fields. In order to detect edgelike structures in tensor fields, we first generalise Di Zenzo's concept of a structure tensor for vector-valued images to tensor-valued data. This structure tensor allows us to extend scalar-valued mean curvature motion and self-snakes to the tensor setting. We present both two-dimensional and three-dimensional formulations, and we prove that these filters maintain positive semidefiniteness if the initial matrix data are positive semidefinite. We give an interpretation of tensorial mean curvature motion as a process for which the corresponding curve evolution of each generalised level line is the gradient descent of its total length. Moreover, we propose a geodesic active contour model for segmenting tensor fields and interpret it as a minimiser of a suitable energy functional with a metric induced by the tensor image. Since tensorial active contours incorporate information from all channels, they give a contour representation that is highly robust under noise. Experiments on three-dimensional DT-MRI data and an indefinite tensor field from fluid dynamics show that the proposed methods inherit the essential properties of their scalar-valued counterparts.
Link zu diesem Datensatz: urn:nbn:de:bsz:291-scidok-44622
hdl:20.500.11880/26314
http://dx.doi.org/10.22028/D291-26258
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Band: 104
SciDok-Publikation: 12-Jan-2012
Fakultät: Fakultät 6 - Naturwissenschaftlich-Technische Fakultät I
Fachrichtung: MI - Mathematik
Fakultät / Institution:MI - Fakultät für Mathematik und Informatik

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