Please use this identifier to cite or link to this item: doi:10.22028/D291-26208
Title: Diffusion and regularization of vector- and matrix-valued images
Author(s): Weickert, Joachim
Brox, Thomas
Language: English
Year of Publication: 2002
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: The goal of this paper is to present a unified description of diffusion and regularization techniques for vector-valued as well a matrix-valued data fields. In the vector-valued setting, we first review a number of existing methods and classify them into linear and nonlinear as well as isotropic and anisotopic methods. For these approaches we present corresponding regularization methods. This taxonomy is applied to the design of regularization methods for variational motion analysis in image sequences. Our vector-valued framework is then extended to the smoothing of positive semidefinite matrix fields. In this context a novel class of anisotropic diffusion and regularization methods is derived and it is shown that suitable algorithmic realizations preserve the positive semidefinitness of the matrix field without any additional constraints. As an application, we present an anisotopic nonlinear structure tensor and illustrate its advantages over the linear structure tensor.
Link to this record: urn:nbn:de:bsz:291-scidok-43834
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 58
Date of registration: 2-Dec-2011
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_58_02.pdf3,34 MBAdobe PDFView/Open

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