License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/DFU.SciViz.2010.110
URN: urn:nbn:de:0030-drops-27003
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Hotz, Ingrid ; Sreevalsan-Nair, Jaya ; Hagen, Hans ; Hamann, Bernd

Tensor Field Reconstruction Based on Eigenvector and Eigenvalue Interpolation

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Interpolation is an essential step in the visualization process. While most data from simulations or experiments are discrete many visualization methods are based on smooth, continuous data approximation or interpolation methods. We introduce a new interpolation method for symmetrical tensor fields given on a triangulated domain. Differently from standard tensor field interpolation, which is based on the tensor components, we use tensor invariants, eigenvectors and eigenvalues, for the interpolation. This interpolation minimizes the number of eigenvectors and eigenvalues computations by restricting it to mesh vertices and makes an exact integration of the tensor lines possible. The tensor field topology is qualitatively the same as for the component wise-interpolation. Since the interpolation decouples the ``shape'' and ``direction'' interpolation it is shape-preserving, what is especially important for tracing fibers in diffusion MRI data.

BibTeX - Entry

  author =	{Ingrid Hotz and Jaya Sreevalsan-Nair and Hans Hagen and Bernd Hamann},
  title =	{{Tensor Field Reconstruction Based on Eigenvector and Eigenvalue Interpolation}},
  booktitle =	{Scientific Visualization: Advanced Concepts},
  pages =	{110--123},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-939897-19-4},
  ISSN =	{1868-8977},
  year =	{2010},
  volume =	{1},
  editor =	{Hans Hagen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-27003},
  doi =		{10.4230/DFU.SciViz.2010.110},
  annote =	{Keywords: Tensor Field, Eigenvector, Eigenvalue, Interpolation}

Keywords: Tensor Field, Eigenvector, Eigenvalue, Interpolation
Collection: Scientific Visualization: Advanced Concepts
Issue Date: 2010
Date of publication: 02.08.2010

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