Computing Consensus Curves

  • Livio De La Cruz
  • Stephen Kobourov
  • Sergey Pupyrev
  • Paul S. Shen
  • Sankar Veeramoni
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8504)

Abstract

We study the problem of extracting accurate average ant trajectories from many (inaccurate) input trajectories contributed by citizen scientists. Although there are many generic software tools for motion tracking and specific ones for insect tracking, even untrained humans are better at this task. We consider several local (one ant at a time) and global (all ants together) methods. Our best performing algorithm uses a novel global method, based on finding edge-disjoint paths in a graph constructed from the input trajectories. The underlying optimization problem is a new and interesting network flow variant. Even though the problem is NP-complete, two heuristics work well in practice, outperforming all other approaches, including the best automated system.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alt, H., Godau, M.: Computing the Fréchet distance between two polygonal curves. Internat. J. Comput. Geom. Appl. 5(1), 75–91 (1995)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Betke, M., Hirsh, D., Bagchi, A., Hristov, N., Makris, N., Kunz, T.: Tracking large variable numbers of objects in clutter. In: CVPR, pp. 1–8. IEEE Computer Society, Washington (2007)Google Scholar
  3. 3.
    Buchin, K., Buchin, M., Gudmundsson, J.: Constrained free space diagrams: a tool for trajectory analysis. Int. J. Geogr. Inf. Sci. 24(7), 1101–1125 (2010)CrossRefGoogle Scholar
  4. 4.
    Buchin, K., Buchin, M., Kreveld, M., Löffler, M., Silveira, R., Wenk, C., Wiratma, L.: Median trajectories. Algorithmica 66(3), 595–614 (2013)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    De La Cruz, L., Kobourov, S., Pupyrev, S., Shen, P., Veeramoni, S.: Computing consensus curves. Arxiv report (2013), http://arxiv.org/abs/1212.0935
  6. 6.
    Even, S., Itai, A., Shamir, A.: On the complexity of timetable and multicommodity flow problems. SIAM J. Comput. 5(4), 691–703 (1976)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Fletcher, M., Dornhaus, A., Shin, M.: Multiple ant tracking with global foreground maximization and variable target proposal distribution. In: WACV, pp. 570–576. IEEE Computer Society, Washington (2011)Google Scholar
  8. 8.
    Khan, Z., Balch, T., Dellaert, F.: MCMC-based particle filtering for tracking a variable number of interacting targets. IEEE TPAMI 27(11), 1805–1819 (2005)CrossRefGoogle Scholar
  9. 9.
    van Kreveld, M., Wiratma, L.: Median trajectories using well-visited regions and shortest paths. In: GIS, pp. 241–250. ACM, New York (2011)Google Scholar
  10. 10.
    Lloyd, S.: Least squares quantization in PCM. IEEE Trans. Inf. Theory 28(2), 129–137 (1982)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Maitra, P., Schneider, S., Shin, M.: Robust bee tracking with adaptive appearance template and geometry-constrained resampling. In: WACV, pp. 1–6. IEEE Computer Society, Washington (2009)Google Scholar
  12. 12.
    Marx, D.: Eulerian disjoint paths problem in grid graphs is NP-complete. Discrete Appl. Math. 143(1-3), 336–341 (2004)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Nguyen, N., Keller, S., Norris, E., Huynh, T., Clemens, M., Shin, M.: Tracking colliding cells in vivo microscopy. IEEE Trans. Biomed. Eng. 58(8), 2391–2400 (2011)CrossRefGoogle Scholar
  14. 14.
    Poff, C., Hoan, N., Kang, T., Shin, M.: Efficient tracking of ants in long video with GPU and interaction. In: WACV, pp. 57–62. IEEE Computer Society, Washington (2012)Google Scholar
  15. 15.
    Trajcevski, G., Ding, H., Scheuermann, P., Tamassia, R., Vaccaro, D.: Dynamics-aware similarity of moving objects trajectories. In: GIS, pp. 1–8. ACM, New York (2007)Google Scholar
  16. 16.
    Veeraraghavan, A., Chellappa, R., Srinivasan, M.: Shape-and-behavior encoded tracking of bee dances. IEEE TPAMI 30(3), 463–476 (2008)CrossRefGoogle Scholar
  17. 17.
    Yilmaz, A., Javed, O., Shah, M.: Object tracking: a survey. ACM Comput. Surv. 38, 1–45 (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Livio De La Cruz
    • 1
  • Stephen Kobourov
    • 1
  • Sergey Pupyrev
    • 1
    • 2
  • Paul S. Shen
    • 1
  • Sankar Veeramoni
    • 1
  1. 1.Department of Computer ScienceUniversity of ArizonaTucsonUSA
  2. 2.Institute of Mathematics and Computer ScienceUral Federal UniversityEkaterinburgRussia

Personalised recommendations