Monte Carlo-Based Bayesian Group Object Tracking and Causal Reasoning

  • Avishy Y. Carmi
  • Lyudmila Mihaylova
  • Amadou Gning
  • Pini Gurfil
  • Simon J. Godsill
Part of the Studies in Computational Intelligence book series (SCI, volume 410)

Abstract

We present algorithms for tracking and reasoning of local traits in the subsystem level based on the observed emergent behavior of multiple coordinated groups in potentially cluttered environments. Our proposed Bayesian inference schemes, which are primarily based on (Markov chain) Monte Carlo sequential methods, include: 1) an evolving network-based multiple object tracking algorithm that is capable of categorizing objects into groups, 2) a multiple cluster tracking algorithm for dealing with prohibitively large number of objects, and 3) a causality inference framework for identifying dominant agents based exclusively on their observed trajectories.We use these as building blocks for developing a unified tracking and behavioral reasoning paradigm. Both synthetic and realistic examples are provided for demonstrating the derived concepts.

Keywords

Probability Density Function Markov Chain Monte Carlo Object Tracking Sequential Monte Carlo Causal Reasoning 
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.

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References

  1. 1.
    Reynolds, C.W.: Flocks, herds, and schools: A distributed behavioral model. Computer Graphics 21, 25–34 (1987)CrossRefGoogle Scholar
  2. 2.
    Pearl, J.: Causality: Models, Reasoning, and Inference. Cambridge University Press (2000)Google Scholar
  3. 3.
    Granger, C.W.J.: Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 424–438 (1969)CrossRefGoogle Scholar
  4. 4.
    Mataric, M.J.: Designing and understanding adaptive group behaviors. Adaptive Behavior 4, 51–80 (1995)CrossRefGoogle Scholar
  5. 5.
    Gurfil, P., Kivelevitch, E.: Flock properties effect on task assignment and formation flying of cooperating unmanned aerial vehicles. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 221(3), 401–416 (2007)CrossRefGoogle Scholar
  6. 6.
    Khan, Z., Balch, T., Dellaert, F.: Efficient particle filter-based tracking of multiple intercating targets using an MRF-based motion model. In: Proc. of the 2003 IEEE/RSJ Intl. Conf. on Intelligent Robots and Systems, USA, October 27-31 (2003)Google Scholar
  7. 7.
    Khan, Z., Balch, T., Dellaert, F.: A Rao-Blackwellized particle filter for eigentracking. In: Proc. of the IEEE Conf. on Computer Vision and Pattern Recognition (June 2004)Google Scholar
  8. 8.
    Khan, Z., Balch, T., Dellaert, F.: MCMC-based particle filtering for tracking a variable number of interacting targets. IEEE Transactions on Pattern Analysis and Machine Intelligence 27(11), 1805–1819 (2005)CrossRefGoogle Scholar
  9. 9.
    Gning, A., Mihaylova, L., Maskell, S., Pang, S.K., Godsill, S.: Group object structure and state estimation with evolving networks and Monte Carlo methods. IEEE Transactions on Signal Processing 12(2), 523–536 (2011)Google Scholar
  10. 10.
    Pang, S.K., Li, J., Godsill, S.J.: Detection and tracking of coordinated groups. IEEE Transactions on Aerospace and Electronic Systems 47(1), 472–502 (2011)CrossRefGoogle Scholar
  11. 11.
    Koch, W., Feldmann, M.: Cluster tracking under kinematical constraints using random matrices. Robotics and Autonomous Systems 57(3), 296–309 (2009)CrossRefGoogle Scholar
  12. 12.
    Koch, W., Saul, R.: A Bayesian approach to extended object tracking and tracking of loosely structured target groups. In: Proc. of the 8th International Conf. on Inform. Fusion, ISIF (2005)Google Scholar
  13. 13.
    Koch, J.W.: Bayesian approach to extended object and cluster tracking using random matrices. IEEE Transactions on Aerospace and Electronic Systems 44(3), 1042–1059 (2008)CrossRefGoogle Scholar
  14. 14.
    Carmi, A., Septier, F., Godsill, S.J.: The Gaussian mixture MCMC particle algorithm for dynamic cluster tracking. Automatica (2010) (accepted)Google Scholar
  15. 15.
    Ali, S., Shah, M.: Floor Fields for Tracking in High Density Crowd Scenes. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part II. LNCS, vol. 5303, pp. 1–14. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75(6), 1226–1229 (1995)CrossRefGoogle Scholar
  17. 17.
    Helbing, D.: Traffic and related self-driven many-particle systems. Review of Modern Physics 73, 1067–1141 (2002)Google Scholar
  18. 18.
    Waxman, M.J., Drummond, O.E.: A bibliography of cluster (group) tracking. In: Drummond, O.E. (ed.) Proceedings of the SPIE Signal and Data Processing of Small Targets, vol. 5428, pp. 551–560 (August 2004)Google Scholar
  19. 19.
    Celikkanat, H., Sahin, E.: Steering self-organized robot flocks through externally guided individuals. Neural Computing & and Applications 19, 849–865 (2010)CrossRefGoogle Scholar
  20. 20.
    Mahler, R.: Statistical Multisource-multitarget Information Fusion. Artech House, Boston (2007)MATHGoogle Scholar
  21. 21.
    Dorogovtsev, S.N., Mendes, J.F.F.: Evolution of networks. Advances in Physics 51, 1079–1187 (2002)CrossRefGoogle Scholar
  22. 22.
    Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Reviews of Modern Physics 74(1), 47–97 (2002)MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Bar-Shalom, Y., Blair, W.: Multitarget-Multisensor Tracking: Applications and Advances, vol. III. Artech House, Boston (2000)Google Scholar
  24. 24.
    Blackman, S., Popoli, R.: Design and Analysis of Modern Tracking Systems. Artech House Radar Library (1999)Google Scholar
  25. 25.
    Clark, D., Godsill, S.: Group target tracking with the Gaussian mixture probability density filter. In: Proc. of the 3rd International Conf. on Intelligent Sensors, Sensor Networks and Information Processing (2007)Google Scholar
  26. 26.
    Pang, S.K., Li, J., Godsill, S.: Models and Algorithms for Detection and Tracking of Coordinated Groups. In: Proceedings of the IEEE Aerospace Conf. (March 2008)Google Scholar
  27. 27.
    Ristic, B., Clark, D., Vo, B.-N.: Improved SMC implementation of the PHD filter. In: Proceedings of the 13th Conference on Information Fusion (FUSION), July 2010, pp. 1–8 (2010)Google Scholar
  28. 28.
    Salmond, D.J., Gordon, N.J.: Group and extended object tracking. In: Proc. IEE Colloquium on Target Tracking: Algorithms and Applications, pp. 16/1–16/4 (1999)Google Scholar
  29. 29.
    Gilholm, K., Godsill, S., Maskell, S., Salmond, D.: Poisson models for extended target and group tracking. In: Proceedings of SPIE, vol. 5913 (2005)Google Scholar
  30. 30.
    Ristic, B., Arulampalam, S., Gordon, N.: Beyond the Kalman Filter: Particle Filters for Tracking Applications. Artech House, London (2004)MATHGoogle Scholar
  31. 31.
    Koch, W.: On exploiting ‘negative’ sensor evidence for target tracking and sensor data fusion. Inf. Fusion 8(1), 28–39 (2007)CrossRefGoogle Scholar
  32. 32.
    Ulmke, M., Koch, W.: Road-map assisted ground moving target tracking. IEEE Transactions on Aerospace and Electronic Systems 42(4), 1264–1274 (2006)CrossRefGoogle Scholar
  33. 33.
    Mihaylova, L., Boel, R., Hegyi, A.: Freeway traffic estimation within recursive Bayesian framework. Automatica 43(2), 290–300 (2007)MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    Hegyi, A., Mihaylova, L., Boel, R., Lendek, Z.: Parallelized particle filtering for freeway traffic state tracking. In: Proceedings of the European Control Conference, Kos, Greece, July 2-5, pp. 2442–2449 (2007)Google Scholar
  35. 35.
    Arulampalam, M., Maskell, S., Gordon, N., Clapp, T.: A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans. on Signal Proc. 50(2), 174–188 (2002)CrossRefGoogle Scholar
  36. 36.
    Angelova, D., Mihaylova, L.: Extended object tracking using Monte Carlo methods. IEEE Transactions on Signal Processing 56(2), 825–832 (2008)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Petrov, N., Mihaylova, L., Gning, A., Angelova, D.: A novel sequential monte carlo approach for extended object tracking based on border parameterization. In: Proceedings of the 14th International Conference on Information Fusion (Fusion 2011), Chicago, USA (2011)Google Scholar
  38. 38.
    Baum, M., Hanebeck, U.D.: Random hypersurface models for extended object tracking. In: Proc. of the IEEE International Symp. on Signal Processing and Information Technology (ISSPIT), pp. 178–183 (2009)Google Scholar
  39. 39.
    Baum, M., Feldmann, M., Fränken, D., Hanebeck, U.D., Koch, W.: Extended object and group tracking: A Comparison of Random Matrices and Random Hypersurface Models. LNCS (2010)Google Scholar
  40. 40.
    Jasra, A., Holmes, C.C., Stephens, D.A.: Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling. Statistical Science 1, 50–67 (2005)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Stephens, M.: Dealing with Label Switching in Mixture Models. Journal of the Royal Statistical Society (2000)Google Scholar
  42. 42.
    Vo, B., Singh, S., Doucet, A.: Sequential Monte Carlo Methods for Multi-Target Filtering with Random Finite Sets. IEEE Transactions on Aerospace and Electronic Systems 41(4), 1224–1245 (2005)CrossRefGoogle Scholar
  43. 43.
    Goodman, I., Mahler, R., Nguyen, H.: Mathematics of Data Fusion. Kluwer Academic Publishing Co., Boston (1997)MATHGoogle Scholar
  44. 44.
    Mahler, R.: Multi-Target Bayes Filtering via First-Order Multi-Target Moments. IEEE Transactions on Aerospace and Electronic Systems 39(4), 1152–1178 (2003)CrossRefGoogle Scholar
  45. 45.
    Granström, K., Lundquist, C., Orguner, U.: A Gaussian Mixture PHD filter for extended target tracking. In: Proceedings of the International Conference on Information Fusion, Edinburgh, UK (2010)Google Scholar
  46. 46.
    Ng, W., Li, J., Godsill, S.J., Pang, S.K.: Multitarget Initiation, Tracking and Termination Using Bayesian Monte Carlo Methods. Computer Journal 50(6), 674–693 (2007)CrossRefGoogle Scholar
  47. 47.
    Berzuini, C., Nicola, G., Gilks, W.R., Larizza, C.: Dynamic Conditional Independence Models and Markov Chain Monte Carlo Methods. Journal of the American Statistical Association 92(440), 1403–1412 (1997)MathSciNetCrossRefGoogle Scholar
  48. 48.
    Green, P.J.: Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination. Biometrika 82(4), 711–732 (1995)MathSciNetMATHCrossRefGoogle Scholar
  49. 49.
    Godsill, S.J.: On the relationship between Markov chain Monte Carlo methods for model uncertainty. Journal of Comp. Graph. Stats. 10(2), 230–248 (2001)MathSciNetCrossRefGoogle Scholar
  50. 50.
    Li, X.R., Jilkov, V.: A survey of maneuveuvering target tracking. Part I: Dynamic models. IEEE Trans. on Aerosp. and Electr. Systems 39(4), 1333–1364 (2003)CrossRefGoogle Scholar
  51. 51.
    Bar-Shalom, Y., Li, X.R.: Estimation and Tracking: Principles, Techniques and Software. Artech House (1993)Google Scholar
  52. 52.
    AlRashidi, M.R., El-Hawary, M.E.: A survey of particle swarm optimization applications in electric power systems. IEEE Transactions on Evolutionary Computation 13(4), 913–918 (2009)CrossRefGoogle Scholar
  53. 53.
    Gning, A., Mihaylova, L., Maskell, S., Pang, S.K., Godsill, S.: Evolving networks for group object motion estimation. In: Proc. of IET Seminar on Target Tracking and Data Fusion: Algorithms and Applications, Birmingham, UK, pp. 99–106 (2008)Google Scholar
  54. 54.
    Gilks, W.R., Berzuini, C.: Following a moving target-monte carlo inference for dynamic bayesian models. Journal of the Royal Statistical Society. Series B (Statistical Methodology) 63(1), 127–146 (2001)MathSciNetMATHCrossRefGoogle Scholar
  55. 55.
    Gilholm, K., Godsill, S., Maskell, S., Salmond, D.: Poisson Models for Extended Target and Group Tracking. In: Proceedings of the SPIE Conference, pp. 230–241 (August 2005)Google Scholar
  56. 56.
    Rasmussen, C.E.: The Infinite Gaussian Mixture Model. In: Advances in Neural Information Processing Systems, vol. 12, pp. 554–560. MIT Press (2000)Google Scholar
  57. 57.
    Godsill, S., Doucet, A., West, M.: Maximum a posteriori inference sequence estimation using monte carlo particle filters. Annals of the Institute of Statistical Mathematics 53(1), 82–96 (2001)MathSciNetMATHCrossRefGoogle Scholar
  58. 58.
    Djuric, P.M., Chun, J.: An MCMC Sampling Approach to Estimation of Nonstationary Hidden Markov Models. IEEE Transactions on Signal Processing 50(5), 1113–1123 (2002)CrossRefGoogle Scholar
  59. 59.
    Bar-Yam, Y.: Dynamics of Complex Systems, 1st edn. Addison-Wesley (1997)Google Scholar
  60. 60.
    Gleick, J.: Chaos – Making a New Science, Penguin USA, Paper (1988)Google Scholar
  61. 61.
    Reif, J.H., Wang, H.: Social potential fields: A distributed behavioral control for autonomous robots. In: Workshop on Algorithmic Foundations of Robotics, WAFR 1994 (1994)Google Scholar
  62. 62.
    Beni, G., Wang, J.: Swarm intelligence in cellular robotic systems. In: Proceedings of the NATO Advanced Workshop on Robotics and Biological Systems (1989)Google Scholar
  63. 63.
    Guadiano, P., Shargel, B., Bonabeau, E., Clough, B.: Control of UAV swarms: What the bugs can teach us. In: Proceedings of the 2nd AIAA Unmanned Unlimited Systems, Technologies, and Operations-Aerospace. AIAA, San Diego,; number AIAA 2003-6624 (2003)Google Scholar
  64. 64.
    Wiener, N.: The Theory of Prediction. In: Modern Mathematics for Engineers, McGraw-Hill, New York (1956)Google Scholar
  65. 65.
    Geweke, J.: Measurement of linear dependence and feedback between multiple time series. Journal of American Statistical Association 77, 304–313 (1982)MathSciNetMATHCrossRefGoogle Scholar
  66. 66.
    Chena, Y., Bressler, S.L., Ding, M.: Frequency decomposition of conditional granger causality and application to multivariate neural field potential data. Journal of Neuroscience Methods 150, 228–237 (2006)CrossRefGoogle Scholar
  67. 67.
    Hosoya, Y.: Elimination of third-series effect and defining partial measures of causality. Journal of Time Series Analysis 22, 537–554 (2001)MathSciNetMATHCrossRefGoogle Scholar
  68. 68.
    Pearl, J., Verma, T.S.: A theory of inferred cauzation. In: Proceedings of the 2nd International Conference on Principles of Knowledge Representation and Reasoning, San Mateo, CA, pp. 441–452 (1991) Google Scholar
  69. 69.
    Geffner, H.: Default Reasoning: Causal and Conditional Theories. MIT Press (1992)Google Scholar
  70. 70.
    Shoam, Y.: Reasoning About Change: Time and Cauzation from the Standpoint of Artificial Intelligence. MIT Press (1988)Google Scholar
  71. 71.
    Sprites, P., Glymour, C., Scheines, R.: Cauzation, Prediction, and Search. MIT Press (2000)Google Scholar
  72. 72.
    Glymour, C., Cooper, G. (eds.): Computation, Cauzation, and Discovery. MIT Press (1999)Google Scholar
  73. 73.
    Friedman, N., Nachman, I., Peer, D.: Learning Bayesian network structure from massive datasets: The “sparse candidate” algorithm, pp. 206–215 (1999)Google Scholar
  74. 74.
    Cooper, G.F., Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9, 309–347 (1992)MATHGoogle Scholar
  75. 75.
    Friedman, N., Koller, D.: Being Bayesian about network structure. A Bayesian approach to structure discovery in Bayesian networks. Machine Learning 50, 95–125 (2003)MATHCrossRefGoogle Scholar
  76. 76.
    Heckerman, D.: A Tutorial on Learning with Bayesian Networks. In: Learning in Graphical Models. MIT Press (1999)Google Scholar
  77. 77.
    Heckerman, D., Meek, C., Cooper, G.: A Bayesian Approach to Causal Discovery. In: Computation, Cauzation and Discovery. MIT Press (1999)Google Scholar
  78. 78.
    Tenenbaum, J.B., Griffiths, T.L.: Structure learning in human causal induction. In: Advances in Neural Information Processing Systems (2001)Google Scholar
  79. 79.
    Murphy, K.P.: Active learning of causal Bayes net structure. Tech. Rep., U.C. Berkeley (2001)Google Scholar
  80. 80.
    Tong, S., Koller, D.: Active learning for structure in Bayesian networks. In: Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence, Seattle, WA, pp. 863–869 (2001)Google Scholar
  81. 81.
    Cheng, J., Greiner, R., Kelly, J., Bell, D., Liu, W.: Learning Bayesian network from data: An information-theory based approach. Artificial Intelligence 1-2, 43–90 (2002)MathSciNetCrossRefGoogle Scholar
  82. 82.
    Hlavackova-Schindlera, K., Palusb, M., Vejmelkab, M., Bhattacharyaa, J.: Causality detection based on information-theoretic approaches in time series analysis. Physics Reports 441, 1–46 (2007)CrossRefGoogle Scholar
  83. 83.
    Gourieroux, C., Monfort, A.: Time series and dynamic models. Cambridge Press (1997)Google Scholar
  84. 84.
    Golyandina, N., Nekrutkin, V., Zhigljavsky, A. (eds.): Analysis of Time Series Structure: SSA and related techniques. Chapman and Hall (2001)Google Scholar
  85. 85.
    Holland, P.W.: Statistics and causal inference. Journal of the American Statistical Association 81, 945–960 (1986)MathSciNetMATHCrossRefGoogle Scholar
  86. 86.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision 60(2), 91–110 (2004)CrossRefGoogle Scholar
  87. 87.
    Vedaldi, A.: An open implementation of the SIFT detector and descriptor, Tech. Rep., Technical Report 070012, UCLA CSD. (February 2007)Google Scholar
  88. 88.
    MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297 (1967)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2013

Authors and Affiliations

  • Avishy Y. Carmi
    • 1
  • Lyudmila Mihaylova
    • 2
  • Amadou Gning
    • 2
  • Pini Gurfil
    • 3
  • Simon J. Godsill
    • 4
  1. 1.Department of Mechanical and Aerospace EngineeringNanyang Technological UniversitySingaporeSingapore
  2. 2.School of Computing and CommunicationsLancaster UniversityLancasterUnited Kingdom
  3. 3.Department of Aerospace EngineeringTechnion – Israel Institute of TechnologyHaifaIsrael
  4. 4.Department of EngineeringUniversity of CambridgeCambridgeUnited Kingdom

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