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Propagate and Pair: A Single-Pass Approach to Critical Point Pairing in Reeb Graphs

  • Junyi Tu
  • Mustafa Hajij
  • Paul RosenEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11844)

Abstract

With the popularization of Topological Data Analysis, the Reeb graph has found new applications as a summarization technique in the analysis and visualization of large and complex data, whose usefulness extends beyond just the graph itself. Pairing critical points enables forming topological fingerprints, known as persistence diagrams, that provides insights into the structure and noise in data. Although the body of work addressing the efficient calculation of Reeb graphs is large, the literature on pairing is limited. In this paper, we discuss two algorithmic approaches for pairing critical points in Reeb graphs, first a multipass approach, followed by a new single-pass algorithm, called Propagate and Pair.

Keywords

Topological Data Analysis Reeb graph Critical point pairing 

Notes

Acknowledgments

This project was supported in part by National Science Foundation (IIS-1513616 and IIS-1845204). Mesh data are provided by AIM@SHAPE Repository.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of South FloridaTampaUSA
  2. 2.The Ohio State UniversityColumbusUSA

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