Efficient Output-Sensitive Construction of Reeb Graphs

  • Harish Doraiswamy
  • Vijay Natarajan
Conference paper

DOI: 10.1007/978-3-540-92182-0_50

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)
Cite this paper as:
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

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Harish Doraiswamy
    • 1
  • Vijay Natarajan
    • 1
    • 2
  1. 1.Department of Computer Science and Automation 
  2. 2.Supercomputer Education and Research CentreIndian Institute of ScienceBangaloreIndia

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