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

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Advances in Visual Computing (ISVC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11844))

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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.

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Notes

  1. 1.

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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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Authors and Affiliations

  1. University of South Florida, Tampa, FL, 33620, USA

    Junyi Tu & Paul Rosen

  2. The Ohio State University, Columbus, 43210, USA

    Mustafa Hajij

Authors
  1. Junyi Tu
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  2. Mustafa Hajij
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  3. Paul Rosen
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Corresponding author

Correspondence to Paul Rosen .

Editor information

Editors and Affiliations

  1. University of Nevada, Reno, NV, USA

    George Bebis

  2. NASA Ames Research Center, Moffett Field, CA, USA

    Richard Boyle

  3. University of Nevada, Reno, NV, USA

    Bahram Parvin

  4. Desert Research Institute, Reno, NV, USA

    Darko Koracin

  5. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Daniela Ushizima

  6. Latent AI, Palo Alto, CA, USA

    Sek Chai

  7. Texas A&M University, College Station, TX, USA

    Shinjiro Sueda

  8. Louisiana State University, Baton Rouge, LA, USA

    Xin Lin

  9. University of North Carolina at Charlotte, Charlotte, NC, USA

    Aidong Lu

  10. École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Daniel Thalmann

  11. Notre Dame University, Notre Dame, IN, USA

    Chaoli Wang

  12. Bosch Research North America, Palo Alto, CA, USA

    Panpan Xu

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Tu, J., Hajij, M., Rosen, P. (2019). Propagate and Pair: A Single-Pass Approach to Critical Point Pairing in Reeb Graphs. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2019. Lecture Notes in Computer Science(), vol 11844. Springer, Cham. https://doi.org/10.1007/978-3-030-33720-9_8

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  • DOI: https://doi.org/10.1007/978-3-030-33720-9_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33719-3

  • Online ISBN: 978-3-030-33720-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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