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Preprint (Vorabdruck) zugänglich unter
URN: urn:nbn:de:bsz:291-scidok-44720
URL: http://scidok.sulb.uni-saarland.de/volltexte/2012/4472/


Nonlinear structure tensors

Brox, Thomas ; Weickert, Joachim ; Burgeth, Bernhard ; Mrázek, Pavel

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Dokument 1.pdf (5.663 KB)

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SWD-Schlagwörter:
Freie Schlagwörter (Englisch): PDEs , diffusion , orientation estimation
Institut: Fachrichtung 6.1 - Mathematik
DDC-Sachgruppe: Mathematik
Dokumentart: Preprint (Vorabdruck)
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Bandnummer: 113
Sprache: Englisch
Erstellungsjahr: 2004
Publikationsdatum: 16.01.2012
Kurzfassung auf Englisch: 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.
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