Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature Journal Article


Author(s): Zobel, Valentin; Reininghaus, Jan; Hotz, Ingrid
Article Title: Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature
Affiliation IST Austria
Abstract: 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.
Keywords: Geometry; Stresses; Geometric applications; Heat kernel signatures; Indefinite tensors; Multiscale nature; Positive definite; Riemannian manifold; Symmetric indefinite; Symmetric positive definite; Tensors
Journal Title: Mathematics and Visualization
Volume: 40
ISSN: 1612-3786
Publisher: Springer  
Date Published: 2015-01-01
Start Page: 257
End Page: 267
DOI: 10.1007/978-3-319-15090-1_13
Open access: no
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