Stochastic motion clustering

  • P H S Torr
  • D W Murray
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 801)


This paper presents a new method for motion segmentation, the clustering together of features that belong to independently moving objects. The method exploits the fact that two views of a rigidly connected 3D point set are linked by the 3×3 Fundamental Matrix which contains all the information on the motion of a given set of point correspondences. The segmentation problem is transformed into one of finding a set of Fundamental Matrices which optimally describe the observed temporal correspondences, where the optimization is couched as a maximization of the a posteriori probability of an interpretation given the data. To reduce the search space, feasible clusters are hypothesized using robust statistical techniques, and a multiple hypothesis test performed to determine which particular combination of the many feasible clusters is most likely to represent the actual feature motions observed. This test is shown to be to computable in terms of a 0–1 integer programming method, alleviating the combinatorial computing difficulties inherent in such problems.


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  1. 1.
    G. Adiv. Inherent ambiguities in recovering 3-d motion and structure from a noisy flow field. In Proceedings, CVPR '85 (IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Francisco, CA, June 10–13, 1985), IEEE Publ. 85CH2145-1., pages 70–77. IEEE, IEEE, 1985.Google Scholar
  2. 2.
    Y. Bar-Shalom and T.E. Fortmann. Tracking and Data Association. Academic Press, 1988.Google Scholar
  3. 3.
    S. Demey, A. Zisserman, and P. A. Beardsley. Affine and projective structure from motion. In D. Hogg, editor, Proc. British Machine Vision Conference, pages 49–58. Springer-Verlag, Sept 1992. Leeds.Google Scholar
  4. 4.
    O.D. Faugeras. What can be seen in three dimensions with an uncalibrated stereo rig? In Proceedings of 3rd European Conference on Computer Vision, pages 563–578, 1992.Google Scholar
  5. 5.
    E. FranÇois and P. Bouthemy. Multiframe based identification of mobile components of a scene with a moving camera. In Proc. CVPR., 1991.Google Scholar
  6. 6.
    Numerical Algorithms Group. NAG Fortran Library vol 7. NAG, 1988.Google Scholar
  7. 7.
    R. Hartley. Estimation of relative camera positions for uncalibrated cameras. In Proc. ECCV-92, pages 579–87, 1992.Google Scholar
  8. 8.
    F. Heitz and P. Bouthemy. Multimodal motion estimation and segmentation using markov random fields. In Proc. 10th Int. Conf. Pattern Recognition, pages 378–383, 1991.Google Scholar
  9. 9.
    Q. T. Luong, R. Deriche, O. D. Faugeras, and T. Papadopoulo. On determining the fundamental matrix: analysis of different methods and experimental results. Technical Report 1894, INRIA (Sophia Antipolis), 1993.Google Scholar
  10. 10.
    P. F. McLauchlan, I. Reid, and D. W. Murray. Coarse image motion for saccade control. In D. Hogg, editor, Proc. British Machine Vision Conference. Springer-Verlag, Sept 1992. Leeds.Google Scholar
  11. 11.
    P. L. Meyer. Introductory Probability and Statistical Applications. Addison-Wesley, 1970.Google Scholar
  12. 12.
    C. L. Morefield. Applications of 0–1 integer programming to multitarget tracking problems. IEEE Transactions on Automatic Control, 22:302–312, 1977.Google Scholar
  13. 13.
    D.W. Murray and B.F. Buxton. Scene segmentation from visual motion using global optimization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8:220–228, 1987.Google Scholar
  14. 14.
    D.W. Murray and N.S. Williams. Detecting the image boundaries between optical flow fields from several moving planar facets. Pattern Recognition Letters, 4:87–92, 1986.Google Scholar
  15. 15.
    P. J. Rousseeuw. Robust Regression and Outlier Detection. Wiley, New York, 1987.Google Scholar
  16. 16.
    L.S. Shapiro. Affine Analysis of Image Sequences. PhD thesis, Oxford University, 1993.Google Scholar
  17. 17.
    S. M. Smith and J. M. Brady. A scene segmenter; visual tracking of moving vehicles. In Intelligent Autonomous Vehicles, pages 119–126, 1993.Google Scholar
  18. 18.
    W.B. Thompson and T.C. Pong. Detecting moving objects. International Journal of Computer Vision, 4(1):39–58, 1990.Google Scholar
  19. 19.
    S. Ullman. Relaxed and constrained optimisation by local processes. Computer Graphics and Image Processing, 10:115–125, 1979.Google Scholar
  20. 20.
    A.M. Waxman and J.H. Duncan. Binocular image flows: Steps toward stereomotion fusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8:715–729, 1986.Google Scholar
  21. 21.
    A. Zisserman. Notes on geometric invariance in vision. BMVC Tutorial, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • P H S Torr
    • 1
  • D W Murray
    • 1
  1. 1.Department of Engineering ScienceUniversity of OxfordOxfordUK

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