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Titel: Median and related local filters for tensor-valued images
Verfasser: Welk, Martin
Weickert, Joachim
Becker, Florian
Schnörr, Christoph
Feddern, Christian
Burgeth, Bernhard
Sprache: Englisch
Erscheinungsjahr: 2005
Freie Schlagwörter: tensor image processing
local image filter
median filtering
DDC-Sachgruppe: 510 Mathematik
Dokumentart : Preprint (Vorabdruck)
Kurzfassung: We develop a concept for the median filtering of tensor data. The main part of this concept is the definition of median for symmetric matrices. This definition is based on the minimisation of a geometrically motivated objective function which measures the sum of distances of a variable matrix to the given data matrices. This theoretically wellfounded concept fits into a context of similarly defined median filters for other multivariate data. Unlike some other approaches, we do not require by definition that the median has to be one of the given data values. Nevertheless, it happens so in many cases, equipping the matrix-valued median even with root signals similar to the scalar-valued situation. Like their scalar-valued counterparts, matrix-valued median filters show excellent capabilities for structure-preserving denoising. Experiments on diffusion tensor imaging, fluid dynamics and orientation estimation data are shown to demonstrate this. The orientation estimation examples give rise to a new variant of a robust adaptive structure tensor which can be compared to existing concepts. For the efficient computation of matrix medians, we present a convex programming framework. By generalising the idea of the matrix median filters, we design a variety of other local matrix filters. These include matrix-valued mid-range filters and, more generally, M-smoothers but also weighted medians and \alpha-quantiles. Mid-range filters and quantiles allow also interesting cross-links to fundamental concepts of matrix morphology.
Link zu diesem Datensatz: urn:nbn:de:bsz:291-scidok-45024
hdl:20.500.11880/26337
http://dx.doi.org/10.22028/D291-26281
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Band: 135
SciDok-Publikation: 18-Jan-2012
Fakultät: Fakultät 6 - Naturwissenschaftlich-Technische Fakultät I
Fachrichtung: MI - Mathematik
Fakultät / Institution:MI - Fakultät für Mathematik und Informatik

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