Please use this identifier to cite or link to this item: doi:10.22028/D291-26281
Title: Median and related local filters for tensor-valued images
Author(s): Welk, Martin
Weickert, Joachim
Becker, Florian
Schnörr, Christoph
Feddern, Christian
Burgeth, Bernhard
Language: English
Year of Publication: 2005
Free key words: tensor image processing
local image filter
median filtering
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: 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 to this record: urn:nbn:de:bsz:291-scidok-45024
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 135
Date of registration: 18-Jan-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

Files for this record:
File Description SizeFormat 
preprint_135_05.pdf805,85 kBAdobe PDFView/Open

Items in SciDok are protected by copyright, with all rights reserved, unless otherwise indicated.