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Titel: Nonlinear structure tensors
Verfasser: Brox, Thomas
Weickert, Joachim
Burgeth, Bernhard
Mrázek, Pavel
Sprache: Englisch
Erscheinungsjahr: 2004
Freie Schlagwörter: PDEs
diffusion
orientation estimation
DDC-Sachgruppe: 510 Mathematik
Dokumentart : Preprint (Vorabdruck)
Kurzfassung: In this article we introduce nonlinear versions of the popular structure tensor, also known as second moment matrix. These nonlinear structure tensors replace the Gaussian smoothing of the classical structure tensor by discontinuity-preserving nonlinear diffusions. While nonlinear diffusion is a well-established tool for scalar and vector-valued data, it has not often been used for tensor images so far. Two types of nonlinear diffusion processes for tensor data are studied: an isotropic one with a scalar-valued diffusivity, and its anisotropic counterpart with a diffusion tensor. We prove that these schemes preserve the positive semidefiniteness of a matrix field and are therefore appropriate for smoothing structure tensor fields. The use of diffusivity functions of total variation (TV) type allows us to construct nonlinear structure tensors without specifying additional parameters compared to the conventional structure tensor. The performance of nonlinear structure tensors is demonstrated in three fields where the classic structure tensor is frequently used: orientation estimation, optic flow computation, and corner detection. In all these cases the nonlinear structure tensors demonstrate their superiority over the classical linear one. Our experiments also show that for corner detection based on nonlinear structure tensors, anisotropic nonlinear tensors give the most precise localisation.
Link zu diesem Datensatz: urn:nbn:de:bsz:291-scidok-44720
hdl:20.500.11880/26321
http://dx.doi.org/10.22028/D291-26265
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Band: 113
SciDok-Publikation: 16-Jan-2012
Fakultät: Fakultät 6 - Naturwissenschaftlich-Technische Fakultät I
Fachrichtung: MI - Mathematik
Fakultät / Institution:MI - Fakultät für Mathematik und Informatik

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