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DOI: 10.4230/DFU.Vol2.SciViz.2011.17

2D Tensor Field Segmentation

Authors: Cornelia Auer, Jaya Sreevalsan-Nair, Valentin Zobel, and Ingrid Hotz

Published in: Dagstuhl Follow-Ups, Volume 2, Scientific Visualization: Interactions, Features, Metaphors (2011)

Abstract

We present a topology-based segmentation as means for visualizing 2D symmetric tensor fields. The segmentation uses directional as well as eigenvalue characteristics of the underlying field to delineate cells of similar (or dissimilar) behavior in the tensor field. A special feature of the resulting cells is that their shape expresses the tensor behavior inside the cells and thus also can be considered as a kind of glyph representation. This allows a qualitative comprehension of important structures of the field. The resulting higher-level abstraction of the field provides valuable analysis. The extraction of the integral topological skeleton using both major and minor eigenvector fields serves as a structural pre-segmentation and renders all directional structures in the field. The resulting curvilinear cells are bounded by tensorlines and already delineate regions of equivalent eigenvector behavior. This pre-segmentation is further adaptively refined to achieve a segmentation reflecting regions of similar eigenvalue and eigenvector characteristics. Cell refinement involves both subdivision and merging of cells achieving a predetermined resolution, accuracy and uniformity of the segmentation. The buildingblocks of the approach can be intuitively customized to meet the demands or different applications. Application to tensor fields from numerical stress simulations demonstrates the effectiveness of our method.

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Cornelia Auer, Jaya Sreevalsan-Nair, Valentin Zobel, and Ingrid Hotz. 2D Tensor Field Segmentation. In Scientific Visualization: Interactions, Features, Metaphors. Dagstuhl Follow-Ups, Volume 2, pp. 17-35, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InCollection{auer_et_al:DFU.Vol2.SciViz.2011.17,
  author =	{Auer, Cornelia and Sreevalsan-Nair, Jaya and Zobel, Valentin and Hotz, Ingrid},
  title =	{{2D Tensor Field Segmentation}},
  booktitle =	{Scientific Visualization: Interactions, Features, Metaphors},
  pages =	{17--35},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-939897-26-2},
  ISSN =	{1868-8977},
  year =	{2011},
  volume =	{2},
  editor =	{Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DFU.Vol2.SciViz.2011.17},
  URN =		{urn:nbn:de:0030-drops-32853},
  doi =		{10.4230/DFU.Vol2.SciViz.2011.17},
  annote =	{Keywords: Tensorfield visualization, surface topology}
}

Document

DOI: 10.4230/DFU.SciViz.2010.110

Tensor Field Reconstruction Based on Eigenvector and Eigenvalue Interpolation

Authors: Ingrid Hotz, Jaya Sreevalsan-Nair, Hans Hagen, and Bernd Hamann

Published in: Dagstuhl Follow-Ups, Volume 1, Scientific Visualization: Advanced Concepts (2010)

Abstract

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.

Cite as

Ingrid Hotz, Jaya Sreevalsan-Nair, Hans Hagen, and Bernd Hamann. Tensor Field Reconstruction Based on Eigenvector and Eigenvalue Interpolation. In Scientific Visualization: Advanced Concepts. Dagstuhl Follow-Ups, Volume 1, pp. 110-123, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InCollection{hotz_et_al:DFU.SciViz.2010.110,
  author =	{Hotz, Ingrid and Sreevalsan-Nair, Jaya and Hagen, Hans and Hamann, Bernd},
  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 =	{Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DFU.SciViz.2010.110},
  URN =		{urn:nbn:de:0030-drops-27003},
  doi =		{10.4230/DFU.SciViz.2010.110},
  annote =	{Keywords: Tensor Field, Eigenvector, Eigenvalue, Interpolation}
}

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2D Tensor Field Segmentation

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Tensor Field Reconstruction Based on Eigenvector and Eigenvalue Interpolation

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