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Distributed Contour Trees

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Topological Methods in Data Analysis and Visualization III

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

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Abstract

Topological techniques provide robust tools for data analysis. They are used, for example, for feature extraction, for data de-noising, and for comparison of data sets. This chapter concerns contour trees, a topological descriptor that records the connectivity of the isosurfaces of scalar functions. These trees are fundamental to analysis and visualization of physical phenomena modeled by real-valued measurements.

We study the parallel analysis of contour trees. After describing a particular representation of a contour tree, called local–global representation, we illustrate how different problems that rely on contour trees can be solved in parallel with minimal communication.

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Notes

  1. 1.

    The algorithm of [7] is an exception. It computes many descriptors, Morse–Smale complexes of smaller portions of the domain. However, this information is not sufficient to resolve the Morse–Smale complex of the entire function. In particular, [7] ignores how one would use such a representation for the actual analysis. In our terminology, these descriptors are the local representations.

  2. 2.

    Sometimes authors make distinction between merge trees of super- and sub-level sets, calling the former join and the latter split trees. We prefer a unified terminology in this chapter.

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Acknowledgements

This work was supported by the Director, Office of Advanced Scientific Computing Research, Office of Science, of the U.S. DOE under Contract No. DE-AC02-05CH11231 (Lawrence Berkeley National Laboratory) through the grant “Topology-based Visualization and Analysis of High-dimensional Data and Time-varying Data at the Extreme Scale,” program manager Lucy Nowell.

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Authors and Affiliations

  1. Computational Research Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA, 94720, USA

    Dmitriy Morozov & Gunther H. Weber

Authors
  1. Dmitriy Morozov
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  2. Gunther H. Weber
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Correspondence to Dmitriy Morozov .

Editor information

Editors and Affiliations

  1. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, California, USA

    Peer-Timo Bremer

  2. Comparative Visualization Group, Konrad-Zuse-Zentrum für Informationstechnik, Berlin, Germany

    Ingrid Hotz

  3. School of Computing and SCI Institute, University of Utah, Salt Lake City, Utah, USA

    Valerio Pascucci

  4. Department of Computer Science, ETH Zürich, Zürich, Switzerland

    Ronald Peikert

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Morozov, D., Weber, G.H. (2014). Distributed Contour Trees. In: Bremer, PT., Hotz, I., Pascucci, V., Peikert, R. (eds) Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-04099-8_6

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