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Efficient Output-Sensitive Construction of Reeb Graphs

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Algorithms and Computation (ISAAC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5369))

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Abstract

The Reeb graph tracks topology changes in level sets of a scalar function and finds applications in scientific visualization and geometric modeling. This paper describes a near-optimal two-step algorithm that constructs the Reeb graph of a Morse function defined over manifolds in any dimension. The algorithm first identifies the critical points of the input manifold, and then connects these critical points in the second step to obtain the Reeb graph. A simplification mechanism based on topological persistence aids in the removal of noise and unimportant features. A radial layout scheme results in a feature-directed drawing of the Reeb graph. Experimental results demonstrate the efficiency of the Reeb graph construction in practice and its applications.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Automation, India

    Harish Doraiswamy & Vijay Natarajan

  2. Supercomputer Education and Research Centre, Indian Institute of Science, Bangalore, 560012, India

    Vijay Natarajan

Authors
  1. Harish Doraiswamy
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  2. Vijay Natarajan
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Editor information

Editors and Affiliations

  1. School of Information Technologies, University of Sydney, Australia

    Seok-Hee Hong

  2. Graduate School of Informatics, Kyoto University, 606-8501, Kyoto, Japan

    Hiroshi Nagamochi

  3. Graduate School of Informatics, Kyoto University, Japan

    Takuro Fukunaga

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© 2008 Springer-Verlag Berlin Heidelberg

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Doraiswamy, H., Natarajan, V. (2008). Efficient Output-Sensitive Construction of Reeb Graphs. In: Hong, SH., Nagamochi, H., Fukunaga, T. (eds) Algorithms and Computation. ISAAC 2008. Lecture Notes in Computer Science, vol 5369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92182-0_50

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  • DOI: https://doi.org/10.1007/978-3-540-92182-0_50

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92181-3

  • Online ISBN: 978-3-540-92182-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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