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Visualizing Symmetric Indefinite 2D Tensor Fields using the Heat Kernel Signature
Leipzig University, Leipzig, Germany.
Institute of Science and Technology Austria, Klosterneuburg, Austria.
Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering. (vetenskapliga visualisering)ORCID iD: 0000-0001-7285-0483
2015 (English)In: Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data / [ed] Ingrid Hotz, Thomas Schultz, Cham: Springer, 2015, 257-267 p.Chapter in book (Refereed)
Abstract [en]

The Heat Kernel Signature (HKS) is a scalar quantity which is derived from the heat kernel of a given shape. Due to its robustness, isometry invariance, and multiscale nature, it has been successfully applied in many geometric applications. From a more general point of view, the HKS can be considered as a descriptor of the metric of a Riemannian manifold. Given a symmetric positive definite tensor field we may interpret it as the metric of some Riemannian manifold and thereby apply the HKS to visualize and analyze the given tensor data. In this paper, we propose a generalization of this approach that enables the treatment of indefinite tensor fields, like the stress tensor, by interpreting them as a generator of a positive definite tensor field. To investigate the usefulness of this approach we consider the stress tensor from the two-point-load model example and from a mechanical work piece.

Place, publisher, year, edition, pages
Cham: Springer, 2015. 257-267 p.
Series
, Mathematics and Visualization, ISSN 1612-3786 ; 2015
Keyword [en]
tensor field visualization
National Category
Computer Vision and Robotics (Autonomous Systems)
Identifiers
URN: urn:nbn:se:liu:diva-127651DOI: 10.1007/978-3-319-15090-1_13ISI: 000380461100013ISBN: 9783319150895 (Print)ISBN: 9783319150901 (online)OAI: oai:DiVA.org:liu-127651DiVA: diva2:926337
Available from: 2016-05-06 Created: 2016-05-06 Last updated: 2016-08-19Bibliographically approved

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Hotz, Ingrid
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Computer Vision and Robotics (Autonomous Systems)

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