---
_id: '1531'
abstract:
- lang: eng
  text: 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.
alternative_title:
- Mathematics and Visualization
article_processing_charge: No
author:
- first_name: Valentin
  full_name: Zobel, Valentin
  last_name: Zobel
- first_name: Jan
  full_name: Reininghaus, Jan
  id: 4505473A-F248-11E8-B48F-1D18A9856A87
  last_name: Reininghaus
- first_name: Ingrid
  full_name: Hotz, Ingrid
  last_name: Hotz
citation:
  ama: 'Zobel V, Reininghaus J, Hotz I. Visualizing symmetric indefinite 2D tensor
    fields using The Heat Kernel Signature. In: Hotz I, Schultz T, eds. <i>Visualization
    and Processing of Higher Order Descriptors for Multi-Valued Data</i>. Vol 40.
    1st ed. Springer; 2015:257-267. doi:<a href="https://doi.org/10.1007/978-3-319-15090-1_13">10.1007/978-3-319-15090-1_13</a>'
  apa: Zobel, V., Reininghaus, J., &#38; Hotz, I. (2015). Visualizing symmetric indefinite
    2D tensor fields using The Heat Kernel Signature. In I. Hotz &#38; T. Schultz
    (Eds.), <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued
    Data</i> (1st ed., Vol. 40, pp. 257–267). Springer. <a href="https://doi.org/10.1007/978-3-319-15090-1_13">https://doi.org/10.1007/978-3-319-15090-1_13</a>
  chicago: Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualizing Symmetric
    Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” In <i>Visualization
    and Processing of Higher Order Descriptors for Multi-Valued Data</i>, edited by
    Ingrid Hotz and Thomas Schultz, 1st ed., 40:257–67. Springer, 2015. <a href="https://doi.org/10.1007/978-3-319-15090-1_13">https://doi.org/10.1007/978-3-319-15090-1_13</a>.
  ieee: V. Zobel, J. Reininghaus, and I. Hotz, “Visualizing symmetric indefinite 2D
    tensor fields using The Heat Kernel Signature,” in <i>Visualization and Processing
    of Higher Order Descriptors for Multi-Valued Data</i>, 1st ed., vol. 40, I. Hotz
    and T. Schultz, Eds. Springer, 2015, pp. 257–267.
  ista: 'Zobel V, Reininghaus J, Hotz I. 2015.Visualizing symmetric indefinite 2D
    tensor fields using The Heat Kernel Signature. In: Visualization and Processing
    of Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization,
    vol. 40, 257–267.'
  mla: Zobel, Valentin, et al. “Visualizing Symmetric Indefinite 2D Tensor Fields
    Using The Heat Kernel Signature.” <i>Visualization and Processing of Higher Order
    Descriptors for Multi-Valued Data</i>, edited by Ingrid Hotz and Thomas Schultz,
    1st ed., vol. 40, Springer, 2015, pp. 257–67, doi:<a href="https://doi.org/10.1007/978-3-319-15090-1_13">10.1007/978-3-319-15090-1_13</a>.
  short: V. Zobel, J. Reininghaus, I. Hotz, in:, I. Hotz, T. Schultz (Eds.), Visualization
    and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., Springer,
    2015, pp. 257–267.
date_created: 2018-12-11T11:52:33Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2022-06-10T09:50:14Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-319-15090-1_13
edition: '1'
editor:
- first_name: Ingrid
  full_name: Hotz, Ingrid
  last_name: Hotz
- first_name: Thomas
  full_name: Schultz, Thomas
  last_name: Schultz
intvolume: '        40'
language:
- iso: eng
month: '01'
oa_version: None
page: 257 - 267
publication: Visualization and Processing of Higher Order Descriptors for Multi-Valued
  Data
publication_identifier:
  isbn:
  - 978-3-319-15089-5
publication_status: published
publisher: Springer
publist_id: '5640'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 40
year: '2015'
...