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Simplification of Morse Decompositions Using Morse Set Mergers

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Topological Methods in Data Analysis and Visualization III

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

Abstract

A common problem of vector field topology algorithms is the large number of the resulting topological features. This chapter describes a method to simplify Morse decompositions by iteratively merging pairs of Morse sets that are adjacent in the Morse Connection Graph (MCG). When Morse sets A and B are merged, they are replaced by a single Morse set, that can be thought of as the union of A, B and all trajectories connecting A and B. Pairs of Morse sets to be merged can be picked based on a variety of criteria. For example, one can allow only pairs whose merger results in a topologically simple Morse set to be selected, and give preference to mergers leading to small Morse sets.

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Authors and Affiliations

  1. Colorado School of Mines, Golden, CO, 80401, USA

    Levente Sipeki & Andrzej Szymczak

Authors
  1. Levente Sipeki
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  2. Andrzej Szymczak
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Correspondence to Andrzej Szymczak .

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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Sipeki, L., Szymczak, A. (2014). Simplification of Morse Decompositions Using Morse Set Mergers. 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_3

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