Skip to main content
Article thumbnail
Location of Repository

Computing Reeb Graphs as a Union of Contour Trees

By Harish Doraiswamy and Vijay Natarajan

Abstract

The Reeb graph of a scalar function tracks the evolution of the topology of its level sets. This paper describes a fast algorithm to compute the Reeb graph of a piecewise-linear (PL) function defined over manifolds and non-manifolds. The key idea in the proposed approach is to maximally leverage the efficient contour tree algorithm to compute the Reeb graph. The algorithm proceeds by dividing the input into a set of subvolumes that have loop-free Reeb graphs using the join tree of the scalar function and computes the Reeb graph by combining the contour trees of all the subvolumes. Since the key ingredient of this method is a series of union-find operations, the algorithm is fast in practice. Experimental results demonstrate that it outperforms current generic algorithms by a factor of up to two orders of magnitude, and has a performance on par with algorithms that are catered to restricted classes of input. The algorithm also extends to handle large data that do not fit in memory

Topics: Computer Science & Automation (Formerly, School of Automation), Supercomputer Education & Research Centre
Publisher: IEEE COMPUTER SOC
Year: 2013
DOI identifier: 10.1109/TVCG.2012.115
OAI identifier: oai:eprints.iisc.ernet.in:45651

Suggested articles

Citations

  1. (2002). An Introduction to Morse Theory.
  2. (2003). Computing contour trees in all dimensions. doi
  3. (2001). Geometry and Topology for Mesh Generation. doi
  4. (2009). Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees. doi
  5. (2004). Loops in Reeb graphs of 2-manifolds. doi
  6. (2007). Robust on-line computation of Reeb graphs: simplicity and speed. doi
  7. (1946). Sur les points singuliers d’une forme de pfaff compl` etement int´ egrable ou d’une fonction num´ erique. Comptes Rendus de L’Acad´ emie ses S´ eances,
  8. (2001). Topology matching for fully automatic similarity estimation of 3d shapes. doi
  9. (2007). Topology-controlled volume rendering. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.