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International Symposium on Visual Computing

ISVC 2019: Advances in Visual Computing pp 99–113Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((LNIP,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.

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Notes

  1. 1.

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References

  1. Agarwal, P.K., Edelsbrunner, H., Harer, J., Wang, Y.: Extreme elevation on a 2-manifold. Discrete Comput. Geom. 36(4), 553–572 (2006)

    Article  MathSciNet  Google Scholar 

  2. Attene, M., Biasotti, S., Spagnuolo, M.: Shape understanding by contour-driven retiling. Vis. Comput. 19(2), 127–138 (2003)

    Article  Google Scholar 

  3. Bajaj, C.L., Pascucci, V., Schikore, D.R.: The contour spectrum. In: Proceedings of the 8th IEEE Visualization, p. 167-ff (1997)

    Google Scholar 

  4. Bauer, U., Ge, X., Wang, Y.: Measuring distance between Reeb graphs. In: Symposium on Computational Geometry, p. 464 (2014)

    Google Scholar 

  5. Boyell, R.L., Ruston, H.: Hybrid techniques for real-time radar simulation. In: Proceedings of the November 12–14, Fall Joint Computer Conference, pp. 445–458 (1963)

    Google Scholar 

  6. Carr, H., Snoeyink, J., Axen, U.: Computing contour trees in all dimensions. Comput. Geom. Theory Appl. 24(2), 75–94 (2003)

    Article  MathSciNet  Google Scholar 

  7. Carr, H., Snoeyink, J., van de Panne, M.: Simplifying flexible isosurfaces using local geometric measures. In: Proceedings of the 15th IEEE Visualization, pp. 497–504 (2004)

    Google Scholar 

  8. Cole-McLaughlin, K., Edelsbrunner, H., Harer, J., Natarajan, V., Pascucci, V.: Loops in Reeb graphs of 2-manifolds. In: Symposium on Computational Geometry, pp. 344–350 (2003)

    Google Scholar 

  9. Doraiswamy, H., Natarajan, V.: Efficient output-sensitive construction of Reeb graphs. In: Hong, S.-H., Nagamochi, H., Fukunaga, T. (eds.) ISAAC 2008. LNCS, vol. 5369, pp. 556–567. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-92182-0_50

    Chapter  Google Scholar 

  10. Doraiswamy, H., Natarajan, V.: Efficient algorithms for computing Reeb graphs. Comput. Geom. 42(6), 606–616 (2009)

    Article  MathSciNet  Google Scholar 

  11. Doraiswamy, H., Natarajan, V.: Computing Reeb graphs as a union of contour trees. IEEE Trans. Visual Comput. Graphics 19(2), 249–262 (2013)

    Article  Google Scholar 

  12. Edelsbrunner, H., Harer, J., Mascarenhas, A., Pascucci, V.: Time-varying Reeb graphs for continuous space-time data. In: Symposium on Computational Geometry, pp. 366–372 (2004)

    Google Scholar 

  13. Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. In: Symposium on Foundations of Computer Science, pp. 454–463 (2000)

    Google Scholar 

  14. Harvey, W., Wang, Y., Wenger, R.: A randomized O (m log m) time algorithm for computing Reeb graphs of arbitrary simplicial complexes. In: Symposium on Computational Geometry, pp. 267–276 (2010)

    Google Scholar 

  15. Hilaga, M., Shinagawa, Y.: Topology matching for fully automatic similarity estimation of 3D shapes. In: SIGGRAPH, pp. 203–212 (2001)

    Google Scholar 

  16. Kweon, I.S., Kanade, T.: Extracting topographic terrain features from elevation maps. CVGIP Image Underst. 59(2), 171–182 (1994)

    Article  Google Scholar 

  17. Munch, E.: A user’s guide to topological data analysis. J. Learn. Analytics 4(2), 47–61 (2017)

    Article  MathSciNet  Google Scholar 

  18. Parsa, S.: A deterministic \(O(m \log m)\) time algorithm for the Reeb graph. In: ACM Symposium on Computational Geometry (SoCG), pp. 269–276 (2012)

    Google Scholar 

  19. Pascucci, V., Cole-McLaughlin, K., Scorzelli, G.: Multi-resolution computation and presentation of contour trees. In: IASTED Conference on Visualization, Imaging, and Image Processing, pp. 452–290 (2004)

    Google Scholar 

  20. Pascucci, V., Scorzelli, G., Bremer, P.T., Mascarenhas, A.: Robust on-line computation of Reeb graphs: simplicity and speed. ACM Trans. Graph. 26(3), 58.1–58.9 (2007)

    Article  Google Scholar 

  21. Reeb, G.: Sur les points singuliers dune forme de pfaff completement intgrable ou dune fonction numrique. CR Acad. Sci. Paris 222, 847–849 (1946)

    MATH  Google Scholar 

  22. Rosen, P., et al.: Using contour trees in the analysis and visualization of radio astronomy data cubes. In: TopoInVis (2019)

    Google Scholar 

  23. Singh, G., Mémoli, F., Carlsson, G.E.: Topological methods for the analysis of high dimensional data sets and 3D object recognition. In: Eurographics SPBG, pp. 91–100 (2007)

    Google Scholar 

  24. Takahashi, S., Takeshima, Y., Fujishiro, I.: Topological volume skeletonization and its application to transfer function design. Graph. Models 66(1), 24–49 (2004)

    Article  Google Scholar 

  25. Tierny, J., Vandeborre, J.P., Daoudi, M.: Partial 3D shape retrieval by Reeb pattern unfolding. Comput. Graphics Forum 28(1), 41–55 (2009)

    Article  Google Scholar 

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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

  • Published:

  • 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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