Please use this identifier to cite or link to this item: doi:10.22028/D291-26265
Title: Nonlinear structure tensors
Author(s): Brox, Thomas
Weickert, Joachim
Burgeth, Bernhard
Mrázek, Pavel
Language: English
Year of Publication: 2004
Free key words: PDEs
orientation estimation
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: 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 to this record: urn:nbn:de:bsz:291-scidok-44720
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 113
Date of registration: 16-Jan-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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