The Visual Computer

, Volume 25, Issue 4, pp 309–323 | Cite as

Moving objects forecast in image sequences using autoregressive algorithms

  • José Luis Crespo
  • Marta Zorrilla
  • Pilar Bernardos
  • Eduardo Mora
Original Article


The objective of this paper is to present an overall approach to forecasting the future position of the moving objects of an image sequence after processing the images previous to it. The proposed method makes use of classical techniques such as optical flow to extract objects’ trajectories and velocities, and autoregressive algorithms to build the predictive model. Our method can be used in a variety of applications, where videos with stationary cameras are used, moving objects are not deformed and change their position with time. One of these applications is traffic control, which is used in this paper as a case study with different meteorological conditions to compare with.


Tracking and prediction Image sequence analysis Causal images Autoregressive model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Beauchemin, S., Barron, J.: The computation of optical flow. ACM Comput. Surv. 27(3), 433–467 (1996) CrossRefGoogle Scholar
  2. 2.
    Bergeron, C., Dubois, E.: Gradient-based algorithms for block-oriented map estimation of motion and application to motion-compensated temporal interpolation. IEEE Trans. Circuits Syst. Video Technol. 1, 72–85 (1991) CrossRefGoogle Scholar
  3. 3.
    Bors, A., Pitas, I.: Prediction and tracking of moving objects in image sequences. In: IEEE Trans. Image Processing, vol. 8, pp. 1441–1445 (2000).
  4. 4.
    Bouguet, J.Y.: Pyramidal implementation of the Lucas–Kanade feature tracker (2001).
  5. 5.
    Box, G.E.P., Jenkins, F.M.: Time Series Analysis: Forecasting and Control. Holden-Day, Oakland (1976) MATHGoogle Scholar
  6. 6.
    Carpenter, J., Clifford, P., Fearnhead, P.: Improved particle filter for non-linear problems. IEE Proc. Radar Sonar Navig. 146(1), 2–7 (1999) CrossRefGoogle Scholar
  7. 7.
    Crespo, J.L., Zorrilla, M., Bernardos, P., Mora, E.: A new image prediction model based on spatio-temporal techniques. Vis. Comput. 23, 419–431 (2007). doi:10.1007/s00371-007-0114-y CrossRefGoogle Scholar
  8. 8.
    Cucchiara, R., Piccardi, M., Prati, A.: Detecting moving objects, ghosts and shadows in video stream. In: IEEE Trans. Pattern Anal. Mach. Intell., vol. 25, pp. 1337–1342 (2003) Google Scholar
  9. 9.
    Doucet, A., de Freitas, N., Gordon, N.: Sequential Monte Carlo Methods in Practice. Information Science and Statistics. Springer, New York (2001) MATHGoogle Scholar
  10. 10.
    EC funded Caviar project/IST 2001 37540.
  11. 11.
    Elnagar, A., Gupta, K.: Motion prediction of moving objects based on autoregressive model. IEEE Trans. Syst. MAN, Cybern.—Part A: Syst. Hum. 28(6), 803–810 (1998) CrossRefGoogle Scholar
  12. 12.
    Erkelens, J.: Autoregressive modelling for speech coding: Estimation, interpolation and quantisation. Ph.D. thesis, Delft University of Technology (1996) Google Scholar
  13. 13.
    Gloyer, B., Aghajan, H.K., Siu, K.Y.S., Kailath, T.: Video-based freeway-monitoring system using recursive vehicle tracking. In: R.L. Stevenson, S.A. Rajala (eds.) Proc. SPIE, Image and Video Processing III, vol. 2421, pp. 173–180 (1995) Google Scholar
  14. 14.
    Gordon, N.J., Salmond, D.J., Smith, A.F.M.: A novel approach to nonlinear and non-Gaussian Bayesian state estimation. IEE Proc. F 140(1), 107–113 (1993) Google Scholar
  15. 15.
    Group Prof. Dr. H.-H. Nagel Institut fuer Algorithmen und Kognitive Systeme, F. f.I.U.K.T.: Traffic intersection sequence.
  16. 16.
    Horn, B., Schunk, B.: Determining optical flow. Artif. Intell. 17, 185–203 (1981) CrossRefGoogle Scholar
  17. 17.
    Hsiao, Y.T., Chuang, C.L., Lu, Y.L., Jiang, J.A.: Robust multiple objects tracking using image segmentation and trajectory estimation scheme in video frames. Image Vis. Comput. 24, 1123–1136 (2006) CrossRefGoogle Scholar
  18. 18.
    Kehtarnavaz, N., Griswold, N.: Establishing collision zones for obstacles moving with uncertainty. Comput. Vis. Graph. Image Process. 49(1), 95–103 (1990) CrossRefGoogle Scholar
  19. 19.
    Labit, C., Nicolas, H.: Compact motion representation based on global features for semantic image sequence coding. In: K.H. Tzou, T. Koga (eds.) Proceedings of SPIE, Visual Communications and Image Processing, vol. 1605, pp. 697–708 (1991) Google Scholar
  20. 20.
    Lo, B., Velastin, S.: Automatic congestion detection system for underground platforms. In: Proceedings of the International Symposium on Intelligent Multimedia, Video and Speech Processing, vol. 1, pp. 158–161 (2001) Google Scholar
  21. 21.
    Lucas, B., Kanade, T.: An iterative image registration technique with an application to stereo vision. In: Proceedings of DARPA Image Understanding Workshop, IJCAI, pp. 674–679 (1981).
  22. 22.
    Mitiche, L., Adamou-Mitiche, A.B.H., Berkani, D.: Low-order model for speech signals. Signal Process. 84(10), 1805–1811 (2004) MATHCrossRefGoogle Scholar
  23. 23.
    Pece, A., Worrall, A.: A comparison between feature-based and em-based contour tracking. Image Vis. Comput. 24(11), 1218–1232 (2006) CrossRefGoogle Scholar
  24. 24.
    Pfeifer, P.E., Deutsch, S.J.: A three-stage iterative procedure for space-time modeling. In: Technometrics, vol. 22(1), pp. 35–47 (1980) Google Scholar
  25. 25.
    Piccardi, M.: Background subtraction techniques: a review. In: Proc. of IEEE SMC 2004 International Conference on Systems, Man and Cybernetics, The Hague, The Netherlands., vol. 1, pp. 3099–3104 (2004) Google Scholar
  26. 26.
    Rao, T.S., Antunes, A.M.C.: Spatio-temporal modelling of temperature time series: A comparative study. Time Ser. Anal. Appl. Geophys. Syst. 1, 123–150 (2004) Google Scholar
  27. 27.
    Smith, S.M.: Reviews of optic flow, motion segmentation, edge finding and corner finding. Technical Report TR97SMS1 (1997) Google Scholar
  28. 28.
    Turkmen, I., Guney, K., Karaboga, D.: Genetic tracker with neural network for single and multiple target tracking. Neurocomputing 69(16–18), 2309–2319 (2006) CrossRefGoogle Scholar
  29. 29.
    Weigend, A.S., Gershenfeld, N.A.: Time Series Prediction: Forecasting the Future and Understanding the Past. Addison-Wesley, Reading (1993) Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • José Luis Crespo
    • 1
  • Marta Zorrilla
    • 2
  • Pilar Bernardos
    • 1
  • Eduardo Mora
    • 1
  1. 1.Applied Mathematics and Computer Science DepartmentUniversity of CantabriaSantanderSpain
  2. 2.Mathematics, Statistics and Computation DepartmentUniversity of CantabriaSantanderSpain

Personalised recommendations