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Feature Tracking Using Reeb Graphs

  • Gunther Weber
  • Peer-Timo Bremer
  • Marcus Day
  • John Bell
  • Valerio Pascucci
Chapter
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

Tracking features and exploring their temporal dynamics can aid scientists in identifying interesting time intervals in a simulation and serve as basis for performing quantitative analyses of temporal phenomena. In this paper, we develop a novel approach for tracking subsets of isosurfaces, such as burning regions in simulated flames, which are defined as areas of high fuel consumption on a temperature isosurface. Tracking such regions as they merge and split over time can provide important insights into the impact of turbulence on the combustion process. However, the convoluted nature of the temperature isosurface and its rapid movement make this analysis particularly challenging.

Our approach tracks burning regions by extracting a temperature isovolume from the four-dimensional space-time temperature field. It then obtains isosurfaces for the original simulation time steps and labels individual connected “burning” regions based on the local fuel consumption value. Based on this information, a boundary surface between burning and non-burning regions is constructed. TheReeb graph of this boundary surface is thetracking graph for burning regions.

Key words

Topological data analysis Feature tracking Combustion simulation Reeb graph Tracking graph Tracking accuracy 

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Notes

Acknowledgements

This work was supported by the Director, Office of Advanced Scientific Computing Research, Office of Science, of the U.S. Department of Energy under Contract Nos. DE-AC02-05CH11231 (Lawrence Berkeley National Laboratory), DE-AC52-07NA27344 (Lawrence Livermore National Laboratory) and DE-FC02-06ER25781 (University of Utah) through the Scientific Discovery through Advanced Computing (SciDAC) program’s Visualization and Analytics Center for Enabling Technologies (VACET) and the use of resources of the National Energy Research Scientific Computing Center (NERSC).

References

  1. 1.
    Lorensen, W., Cline, H.: Marching cubes: A high resolution 3d surface construction algorithm. SIGGRAPH Comp. Graph. 21(4) (1987) 163–169CrossRefGoogle Scholar
  2. 2.
    Nielson, G.: On marching cubes. IEEE Trans. Vis. Comp. Graph. 9(3) (2003) 341–351CrossRefGoogle Scholar
  3. 3.
    Bhaniramka, P., Wenger, R., Crawfis, R.: Isosurface construction in any dimension using convex hulls. IEEE Trans. Vis. Comp. Graph. 10(2) (2004) 130–141CrossRefGoogle Scholar
  4. 4.
    Pascucci, V., Scorzelli, G., Bremer, P.T., Mascarenhas, A.: Robust on-line computation of Reeb graphs: Simplicity and speed. ACM Trans. Graph. 26(3) (2007) 58.1–58.9Google Scholar
  5. 5.
    Mascarenhas, A., Snoeyink, J. In: Isocontour based Visualization of Time-varying Scalar Fields. Springer Verlag (2009) 41–68 ISBN 978-3-540-25076-0.Google Scholar
  6. 6.
    Samtaney, R., Silver, D., Zabusky, N., Cao, J.: Visualizing features and tracking their evolution. IEEE Computer 27(7) (1994) 20–27Google Scholar
  7. 7.
    Silver, D., Wang, X.: Tracking and visualizing turbulent 3d features. IEEE Trans. Vis. Comp. Graph. 3(2) (1997) 129–141CrossRefGoogle Scholar
  8. 8.
    Silver, D., Wang, X.: Tracking scalar features in unstructured datasets. In: Proc. IEEE Visualization ’98. (1998) 79–86Google Scholar
  9. 9.
    Laney, D., Bremer, P.T., Mascarenhas, A., Miller, P., Pascucci, V.: Understanding the structure of the turbulent mixing layer in hydrodynamic instabilities. IEEE Trans. Vis. Comp. Graph. 12(5) (2006) 1052–1060CrossRefGoogle Scholar
  10. 10.
    Ji, G., Shen, H.W., Wegner, R.: Volume tracking using higher dimensional isocontouring. In: Proc. IEEE Visualization ’03. (2003) 209–216Google Scholar
  11. 11.
    Ji, G., Shen, H.W.: Efficient isosurface tracking using precomputed correspondence table. In: Proc. IEEE/Eurographics Symposium Visualization ’04. (2004) 283–292Google Scholar
  12. 12.
    Edelsbrunner, H., Harer, J., Mascarenhas, A., Pascuccii, V., Snoeyink, J.: Time-varying Reeb graphs for continuous space-time data. Comp. Geom. 41(3) (2008) 149–166MATHCrossRefGoogle Scholar
  13. 13.
    Szymczak, A.: Subdomain-aware contour trees and contour tree evolution in time-dependent scalar fields. In: Proc. Shape Modeling International ’05. (2005) 136–144Google Scholar
  14. 14.
    Edelsbrunner, H., Harer, J.: Jacobi sets of multiple Morse functions. In: Found. of Comput. Math., Minneapolis 2002. Cambridge Univ. Press, England (2002) 37–57Google Scholar
  15. 15.
    Sohn, B.S., Bajaj, C.: Time-varying contour topology. IEEE Trans. Vis. Comp. Graph. 12(1) (2006) 14–25CrossRefGoogle Scholar
  16. 16.
    Bremer, P.T., Weber, G., Pascucci, V., Day, M., Bell, J.: Analyzing and tracking burning structures in lean premixed hydrogen flames. IEEE Trans. Vis. Comp. Graph. 16(2) (2010)Google Scholar
  17. 17.
    Edelsbrunner, H., Letscher, D., Zomorodian., A.: Topological persistence and simplification. Disc. Comput. Geom. 28(4) (2002) 511–533Google Scholar
  18. 18.
    Agarwal, P., Edelsbrunner, H., Harer, J., Wang, Y.: Extreme elevation on a 2-manifold. Disc. Comput. Geom. 36(4) (2006) 553–572MATHMathSciNetCrossRefGoogle Scholar
  19. 19.
    Koutsofios, E., North, S.: Drawing graphs with dot. Technical Report 910904-59113-08TM, AT&T Bell Laboratories, Murray Hill, NJ (1991)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2011

Authors and Affiliations

  • Gunther Weber
    • 1
  • Peer-Timo Bremer
    • 2
  • Marcus Day
    • 1
  • John Bell
    • 1
  • Valerio Pascucci
    • 3
  1. 1.Lawrence Berkeley National LaboratoryBerkeleyUSA
  2. 2.Lawrence Livermore National LaboratoryLivermoreUSA
  3. 3.University of UtahSalt Lake CityUSA

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