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Monte Carlo-Based Bayesian Group Object Tracking and Causal Reasoning

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Advances in Intelligent Signal Processing and Data Mining

Part of the book series: Studies in Computational Intelligence ((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.

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References

  1. Reynolds, C.W.: Flocks, herds, and schools: A distributed behavioral model. Computer Graphics 21, 25–34 (1987)

    Article  Google Scholar 

  2. Pearl, J.: Causality: Models, Reasoning, and Inference. Cambridge University Press (2000)

    Google Scholar 

  3. Granger, C.W.J.: Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 424–438 (1969)

    Article  Google Scholar 

  4. Mataric, M.J.: Designing and understanding adaptive group behaviors. Adaptive Behavior 4, 51–80 (1995)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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. 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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  11. Koch, W., Feldmann, M.: Cluster tracking under kinematical constraints using random matrices. Robotics and Autonomous Systems 57(3), 296–309 (2009)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  14. Carmi, A., Septier, F., Godsill, S.J.: The Gaussian mixture MCMC particle algorithm for dynamic cluster tracking. Automatica (2010) (accepted)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  Google Scholar 

  17. Helbing, D.: Traffic and related self-driven many-particle systems. Review of Modern Physics 73, 1067–1141 (2002)

    Google Scholar 

  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. Celikkanat, H., Sahin, E.: Steering self-organized robot flocks through externally guided individuals. Neural Computing & and Applications 19, 849–865 (2010)

    Article  Google Scholar 

  20. Mahler, R.: Statistical Multisource-multitarget Information Fusion. Artech House, Boston (2007)

    MATH  Google Scholar 

  21. Dorogovtsev, S.N., Mendes, J.F.F.: Evolution of networks. Advances in Physics 51, 1079–1187 (2002)

    Article  Google Scholar 

  22. Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Reviews of Modern Physics 74(1), 47–97 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  23. Bar-Shalom, Y., Blair, W.: Multitarget-Multisensor Tracking: Applications and Advances, vol. III. Artech House, Boston (2000)

    Google Scholar 

  24. Blackman, S., Popoli, R.: Design and Analysis of Modern Tracking Systems. Artech House Radar Library (1999)

    Google Scholar 

  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. 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. 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. 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. 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. Ristic, B., Arulampalam, S., Gordon, N.: Beyond the Kalman Filter: Particle Filters for Tracking Applications. Artech House, London (2004)

    MATH  Google Scholar 

  31. Koch, W.: On exploiting ‘negative’ sensor evidence for target tracking and sensor data fusion. Inf. Fusion 8(1), 28–39 (2007)

    Article  Google Scholar 

  32. Ulmke, M., Koch, W.: Road-map assisted ground moving target tracking. IEEE Transactions on Aerospace and Electronic Systems 42(4), 1264–1274 (2006)

    Article  Google Scholar 

  33. Mihaylova, L., Boel, R., Hegyi, A.: Freeway traffic estimation within recursive Bayesian framework. Automatica 43(2), 290–300 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    Article  Google Scholar 

  36. Angelova, D., Mihaylova, L.: Extended object tracking using Monte Carlo methods. IEEE Transactions on Signal Processing 56(2), 825–832 (2008)

    Article  MathSciNet  Google Scholar 

  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. 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. 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. 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)

    Article  MathSciNet  Google Scholar 

  41. Stephens, M.: Dealing with Label Switching in Mixture Models. Journal of the Royal Statistical Society (2000)

    Google Scholar 

  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)

    Article  Google Scholar 

  43. Goodman, I., Mahler, R., Nguyen, H.: Mathematics of Data Fusion. Kluwer Academic Publishing Co., Boston (1997)

    MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  48. Green, P.J.: Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination. Biometrika 82(4), 711–732 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  51. Bar-Shalom, Y., Li, X.R.: Estimation and Tracking: Principles, Techniques and Software. Artech House (1993)

    Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  59. Bar-Yam, Y.: Dynamics of Complex Systems, 1st edn. Addison-Wesley (1997)

    Google Scholar 

  60. Gleick, J.: Chaos – Making a New Science, Penguin USA, Paper (1988)

    Google Scholar 

  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. 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. 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. Wiener, N.: The Theory of Prediction. In: Modern Mathematics for Engineers, McGraw-Hill, New York (1956)

    Google Scholar 

  65. Geweke, J.: Measurement of linear dependence and feedback between multiple time series. Journal of American Statistical Association 77, 304–313 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  67. Hosoya, Y.: Elimination of third-series effect and defining partial measures of causality. Journal of Time Series Analysis 22, 537–554 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  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. Geffner, H.: Default Reasoning: Causal and Conditional Theories. MIT Press (1992)

    Google Scholar 

  70. Shoam, Y.: Reasoning About Change: Time and Cauzation from the Standpoint of Artificial Intelligence. MIT Press (1988)

    Google Scholar 

  71. Sprites, P., Glymour, C., Scheines, R.: Cauzation, Prediction, and Search. MIT Press (2000)

    Google Scholar 

  72. Glymour, C., Cooper, G. (eds.): Computation, Cauzation, and Discovery. MIT Press (1999)

    Google Scholar 

  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. Cooper, G.F., Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9, 309–347 (1992)

    MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  76. Heckerman, D.: A Tutorial on Learning with Bayesian Networks. In: Learning in Graphical Models. MIT Press (1999)

    Google Scholar 

  77. Heckerman, D., Meek, C., Cooper, G.: A Bayesian Approach to Causal Discovery. In: Computation, Cauzation and Discovery. MIT Press (1999)

    Google Scholar 

  78. Tenenbaum, J.B., Griffiths, T.L.: Structure learning in human causal induction. In: Advances in Neural Information Processing Systems (2001)

    Google Scholar 

  79. Murphy, K.P.: Active learning of causal Bayes net structure. Tech. Rep., U.C. Berkeley (2001)

    Google Scholar 

  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. 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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  83. Gourieroux, C., Monfort, A.: Time series and dynamic models. Cambridge Press (1997)

    Google Scholar 

  84. Golyandina, N., Nekrutkin, V., Zhigljavsky, A. (eds.): Analysis of Time Series Structure: SSA and related techniques. Chapman and Hall (2001)

    Google Scholar 

  85. Holland, P.W.: Statistics and causal inference. Journal of the American Statistical Association 81, 945–960 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  86. Lowe, D.G.: Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision 60(2), 91–110 (2004)

    Article  Google Scholar 

  87. Vedaldi, A.: An open implementation of the SIFT detector and descriptor, Tech. Rep., Technical Report 070012, UCLA CSD. (February 2007)

    Google Scholar 

  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 

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Carmi, A.Y., Mihaylova, L., Gning, A., Gurfil, P., Godsill, S.J. (2013). Monte Carlo-Based Bayesian Group Object Tracking and Causal Reasoning. In: Georgieva, P., Mihaylova, L., Jain, L. (eds) Advances in Intelligent Signal Processing and Data Mining. Studies in Computational Intelligence, vol 410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28696-4_2

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