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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Reynolds, C.W.: Flocks, herds, and schools: A distributed behavioral model. Computer Graphics 21, 25–34 (1987)
Pearl, J.: Causality: Models, Reasoning, and Inference. Cambridge University Press (2000)
Granger, C.W.J.: Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 424–438 (1969)
Mataric, M.J.: Designing and understanding adaptive group behaviors. Adaptive Behavior 4, 51–80 (1995)
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)
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)
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)
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)
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)
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)
Koch, W., Feldmann, M.: Cluster tracking under kinematical constraints using random matrices. Robotics and Autonomous Systems 57(3), 296–309 (2009)
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)
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)
Carmi, A., Septier, F., Godsill, S.J.: The Gaussian mixture MCMC particle algorithm for dynamic cluster tracking. Automatica (2010) (accepted)
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)
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)
Helbing, D.: Traffic and related self-driven many-particle systems. Review of Modern Physics 73, 1067–1141 (2002)
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)
Celikkanat, H., Sahin, E.: Steering self-organized robot flocks through externally guided individuals. Neural Computing & and Applications 19, 849–865 (2010)
Mahler, R.: Statistical Multisource-multitarget Information Fusion. Artech House, Boston (2007)
Dorogovtsev, S.N., Mendes, J.F.F.: Evolution of networks. Advances in Physics 51, 1079–1187 (2002)
Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Reviews of Modern Physics 74(1), 47–97 (2002)
Bar-Shalom, Y., Blair, W.: Multitarget-Multisensor Tracking: Applications and Advances, vol. III. Artech House, Boston (2000)
Blackman, S., Popoli, R.: Design and Analysis of Modern Tracking Systems. Artech House Radar Library (1999)
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)
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)
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)
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)
Gilholm, K., Godsill, S., Maskell, S., Salmond, D.: Poisson models for extended target and group tracking. In: Proceedings of SPIE, vol. 5913 (2005)
Ristic, B., Arulampalam, S., Gordon, N.: Beyond the Kalman Filter: Particle Filters for Tracking Applications. Artech House, London (2004)
Koch, W.: On exploiting ‘negative’ sensor evidence for target tracking and sensor data fusion. Inf. Fusion 8(1), 28–39 (2007)
Ulmke, M., Koch, W.: Road-map assisted ground moving target tracking. IEEE Transactions on Aerospace and Electronic Systems 42(4), 1264–1274 (2006)
Mihaylova, L., Boel, R., Hegyi, A.: Freeway traffic estimation within recursive Bayesian framework. Automatica 43(2), 290–300 (2007)
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)
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)
Angelova, D., Mihaylova, L.: Extended object tracking using Monte Carlo methods. IEEE Transactions on Signal Processing 56(2), 825–832 (2008)
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)
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)
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)
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)
Stephens, M.: Dealing with Label Switching in Mixture Models. Journal of the Royal Statistical Society (2000)
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)
Goodman, I., Mahler, R., Nguyen, H.: Mathematics of Data Fusion. Kluwer Academic Publishing Co., Boston (1997)
Mahler, R.: Multi-Target Bayes Filtering via First-Order Multi-Target Moments. IEEE Transactions on Aerospace and Electronic Systems 39(4), 1152–1178 (2003)
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)
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)
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)
Green, P.J.: Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination. Biometrika 82(4), 711–732 (1995)
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)
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)
Bar-Shalom, Y., Li, X.R.: Estimation and Tracking: Principles, Techniques and Software. Artech House (1993)
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)
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)
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)
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)
Rasmussen, C.E.: The Infinite Gaussian Mixture Model. In: Advances in Neural Information Processing Systems, vol. 12, pp. 554–560. MIT Press (2000)
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)
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)
Bar-Yam, Y.: Dynamics of Complex Systems, 1st edn. Addison-Wesley (1997)
Gleick, J.: Chaos – Making a New Science, Penguin USA, Paper (1988)
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)
Beni, G., Wang, J.: Swarm intelligence in cellular robotic systems. In: Proceedings of the NATO Advanced Workshop on Robotics and Biological Systems (1989)
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)
Wiener, N.: The Theory of Prediction. In: Modern Mathematics for Engineers, McGraw-Hill, New York (1956)
Geweke, J.: Measurement of linear dependence and feedback between multiple time series. Journal of American Statistical Association 77, 304–313 (1982)
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)
Hosoya, Y.: Elimination of third-series effect and defining partial measures of causality. Journal of Time Series Analysis 22, 537–554 (2001)
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)
Geffner, H.: Default Reasoning: Causal and Conditional Theories. MIT Press (1992)
Shoam, Y.: Reasoning About Change: Time and Cauzation from the Standpoint of Artificial Intelligence. MIT Press (1988)
Sprites, P., Glymour, C., Scheines, R.: Cauzation, Prediction, and Search. MIT Press (2000)
Glymour, C., Cooper, G. (eds.): Computation, Cauzation, and Discovery. MIT Press (1999)
Friedman, N., Nachman, I., Peer, D.: Learning Bayesian network structure from massive datasets: The “sparse candidate” algorithm, pp. 206–215 (1999)
Cooper, G.F., Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9, 309–347 (1992)
Friedman, N., Koller, D.: Being Bayesian about network structure. A Bayesian approach to structure discovery in Bayesian networks. Machine Learning 50, 95–125 (2003)
Heckerman, D.: A Tutorial on Learning with Bayesian Networks. In: Learning in Graphical Models. MIT Press (1999)
Heckerman, D., Meek, C., Cooper, G.: A Bayesian Approach to Causal Discovery. In: Computation, Cauzation and Discovery. MIT Press (1999)
Tenenbaum, J.B., Griffiths, T.L.: Structure learning in human causal induction. In: Advances in Neural Information Processing Systems (2001)
Murphy, K.P.: Active learning of causal Bayes net structure. Tech. Rep., U.C. Berkeley (2001)
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)
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)
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)
Gourieroux, C., Monfort, A.: Time series and dynamic models. Cambridge Press (1997)
Golyandina, N., Nekrutkin, V., Zhigljavsky, A. (eds.): Analysis of Time Series Structure: SSA and related techniques. Chapman and Hall (2001)
Holland, P.W.: Statistics and causal inference. Journal of the American Statistical Association 81, 945–960 (1986)
Lowe, D.G.: Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision 60(2), 91–110 (2004)
Vedaldi, A.: An open implementation of the SIFT detector and descriptor, Tech. Rep., Technical Report 070012, UCLA CSD. (February 2007)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-28696-4_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28695-7
Online ISBN: 978-3-642-28696-4
eBook Packages: EngineeringEngineering (R0)