Learning Higher-Order Markov Models for Object Tracking in Image Sequences

  • Michael Felsberg
  • Fredrik Larsson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5876)


This work presents a novel object tracking approach, where the motion model is learned from sets of frame-wise detections with unknown associations. We employ a higher-order Markov model on position space instead of a first-order Markov model on a high-dimensional state-space of object dynamics. Compared to the latter, our approach allows the use of marginal rather than joint distributions, which results in a significant reduction of computation complexity. Densities are represented using a grid-based approach, where the rectangular windows are replaced with estimated smooth Parzen windows sampled at the grid points. This method performs as accurately as particle filter methods with the additional advantage that the prediction and update steps can be learned from empirical data. Our method is compared against standard techniques on image sequences obtained from an RC car following scenario. We show that our approach performs best in most of the sequences. Other potential applications are surveillance from cheap or uncalibrated cameras and image sequence analysis.


Root Mean Square Error Object Tracking Channel Vector Label Ground Truth Association Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Felsberg, M., Larsson, F.: Learning Bayesian tracking for motion estimation. In: International Workshop on Machine Learning for Vision-based Motion Analysis (2008)Google Scholar
  2. 2.
    Arulampalam, M.S., Maskell, S., Gordon, N., Clapp, T.: A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans. Sig. P. 50, 174–188 (2002)CrossRefGoogle Scholar
  3. 3.
    Isard, M., Blake, A.: CONDENSATION – conditional density propagation for visual tracking. International Journal of Computer Vision 29, 5–28 (1998)CrossRefGoogle Scholar
  4. 4.
    Coué, C., Fraichard, T., Bessière, P., Mazer, E.: Using Bayesian programming for multi-sensor multitarget tracking in automotive applications. In: ICRA (2003)Google Scholar
  5. 5.
    Granlund, G.H.: An Associative Perception-Action Structure Using a Localized Space Variant Information Representation. In: Proceedings of the AFPAC Workshop (2000)Google Scholar
  6. 6.
    Johansson, B., et al.: The application of an oblique-projected landweber method to a model of supervised learning. Mathematical and Computer Modelling 43, 892–909 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Jonsson, E., Felsberg, M.: Correspondence-free associative learning. In: ICPR (2006)Google Scholar
  8. 8.
    Felsberg, M., Forssén, P.E., Scharr, H.: Channel smoothing: Efficient robust smoothing of low-level signal features. PAMI 28, 209–222 (2006)Google Scholar
  9. 9.
    Georgiev, A.A.: Nonparamtetric system identification by kernel methods. IEEE Trans. on Automatic Control 29 (1984)Google Scholar
  10. 10.
    Han, B., Joo, S.W., Davis, L.S.: Probabilistic fusion tracking using mixture kernel-based Bayesian filtering. In: IEEE Int. Conf. on Computer Vision (2007)Google Scholar
  11. 11.
    North, B., Blake, A.: Learning dynamical models using expectation-maximisation. In: ICCV 1998 (1998)Google Scholar
  12. 12.
    Ardö, H., Åström, K., Berthilsson, R.: Real time viterbi optimization of hidden markov models for multi target tracking. In: Proceedings of the WMVC (2007)Google Scholar
  13. 13.
    Streit, R.L., Luginbuhl, T.E.: Probabilistic multi-hypothesis tracking. Technical report, 10, NUWC-NPT (1995)Google Scholar
  14. 14.
    Shalom, B.Y., Tse, E.: Tracking in a cluttered environment with probabilistic data association. Automatica 11, 451–460 (1975)zbMATHCrossRefGoogle Scholar
  15. 15.
    Stauffer, C., Grimson, W.E.L.: Learning patterns of activity using real-time tracking. IEEE Trans. Pattern Analysis and Machine Intell. 22, 747–757 (2000)CrossRefGoogle Scholar
  16. 16.
    Jonker, R., Volgenant, A.: A shortest augmenting path algorithm for dense and sparse linear assignment problems. Computing 38, 325–340 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Snippe, H.P., Koenderink, J.J.: Discrimination thresholds for channel-coded systems. Biological Cybernetics 66, 543–551 (1992)zbMATHCrossRefGoogle Scholar
  18. 18.
    Pampalk, E., Rauber, A., Merkl, D.: Using Smoothed Data Histograms for Cluster Visualization in Self-Organizing Maps. In: Dorronsoro, J.R. (ed.) ICANN 2002. LNCS, vol. 2415, pp. 871–876. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  19. 19.
    Forssén, P.E.: Low and Medium Level Vision using Channel Representations. PhD thesis, Linköping University, Sweden (2004)Google Scholar
  20. 20.
    Felsberg, M.: Spatio-featural scale-space. In: Tai, X.-C., et al. (eds.) SSVM 2009. LNCS, vol. 5567, pp. 235–246. Springer, Heidelberg (2009)Google Scholar
  21. 21.
    Yakowitz, S.J.: Nonparametric density estimation, prediction, and regression for markov sequences. Journal of the American Statistical Association 80 (1985)Google Scholar
  22. 22.
    Baum, L.E., et al.: A maximization technique occuring in the statistical analysis of probabilistic functions of Markov chains. Ann. Math. Stat. 41, 164–171 (1970)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Rao, R.P.N.: An optimal estimation approach to visual perception and learning. Vision Research 39, 1963–1989 (1999)CrossRefGoogle Scholar
  24. 24.
    Therrien, C.W.: Decision, estimation, and classification: an introduction into pattern recognition and related topics. John Wiley & Sons, Inc., Chichester (1989)Google Scholar
  25. 25.
    Sochman, J., Matas, J.: Waldboost - learning for time constrained sequential detection. In: Proc. Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 150–157 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Michael Felsberg
    • 1
  • Fredrik Larsson
    • 1
  1. 1.Linköping UniversityDepartment of Electrical Engineering 

Personalised recommendations