Measuring distance between Reeb graphs Conference Paper


Author(s): Bauer, Ulrich; Ge, Xiaoyin; Wang, Yusu
Title: Measuring distance between Reeb graphs
Affiliation IST Austria
Abstract: We propose a metric for Reeb graphs, called the functional distortion distance. Under this distance, the Reeb graph is stable against small changes of input functions. At the same time, it remains discriminative at differentiating input functions. In particular, the main result is that the functional distortion distance between two Reeb graphs is bounded from below by the bottleneck distance between both the ordinary and extended persistence diagrams for appropriate dimensions. As an application of our results, we analyze a natural simplification scheme for Reeb graphs, and show that persistent features in Reeb graph remains persistent under simplification. Understanding the stability of important features of the Reeb graph under simplification is an interesting problem on its own right, and critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s).
Conference Title: SoCG: Symposium on Computational Geometry
Conference Dates: June 8-11, 2014
Conference Location: Kyoto, Japan
ISBN: 978-1-4503-2594-3
Publisher: ACM  
Date Published: 2014-06-01
Start Page: 464
End Page: 473
Sponsor: National Science Foundation under grants CCF-1319406, CCF-1116258, and by the Toposys project FP7-ICT-318493-STREP.
URL:
DOI: 10.1145/2582112.2582169
Notes: We thank Facundo Mémoli for helpful discussions about variants of the Gromov–Hausdorff distance, which lead to improvements in our definition of the functional distortion distance.
Open access: yes (repository)
IST Austria Authors
  1. Ulrich Bauer
    12 Bauer
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