Skip to main content
SpringerLink
Log in

Computing Consensus Curves

  • Conference paper
Experimental Algorithms (SEA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8504))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alt, H., Godau, M.: Computing the Fréchet distance between two polygonal curves. Internat. J. Comput. Geom. Appl. 5(1), 75–91 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  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. 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)

    Article  Google Scholar 

  4. Buchin, K., Buchin, M., Kreveld, M., Löffler, M., Silveira, R., Wenk, C., Wiratma, L.: Median trajectories. Algorithmica 66(3), 595–614 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  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. Even, S., Itai, A., Shamir, A.: On the complexity of timetable and multicommodity flow problems. SIAM J. Comput. 5(4), 691–703 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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. Lloyd, S.: Least squares quantization in PCM. IEEE Trans. Inf. Theory 28(2), 129–137 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  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. Marx, D.: Eulerian disjoint paths problem in grid graphs is NP-complete. Discrete Appl. Math. 143(1-3), 336–341 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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. Veeraraghavan, A., Chellappa, R., Srinivasan, M.: Shape-and-behavior encoded tracking of bee dances. IEEE TPAMI 30(3), 463–476 (2008)

    Article  Google Scholar 

  17. Yilmaz, A., Javed, O., Shah, M.: Object tracking: a survey. ACM Comput. Surv. 38, 1–45 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Arizona, Tucson, AZ, USA

    Livio De La Cruz, Stephen Kobourov, Sergey Pupyrev, Paul S. Shen & Sankar Veeramoni

  2. Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg, Russia

    Sergey Pupyrev

Authors
  1. Livio De La Cruz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stephen Kobourov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sergey Pupyrev
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Paul S. Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Sankar Veeramoni
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of IT, University of Sydney, Building J12, 2006, Sydney, NSW, Australia

    Joachim Gudmundsson

  2. Department of Computer Science, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen East, Denmark

    Jyrki Katajainen

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

De La Cruz, L., Kobourov, S., Pupyrev, S., Shen, P.S., Veeramoni, S. (2014). Computing Consensus Curves. In: Gudmundsson, J., Katajainen, J. (eds) Experimental Algorithms. SEA 2014. Lecture Notes in Computer Science, vol 8504. Springer, Cham. https://doi.org/10.1007/978-3-319-07959-2_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-07959-2_19

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07958-5

  • Online ISBN: 978-3-319-07959-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation