Velocity-Guided Tracking of Deformable Contours in Three Dimensional Space

  • Reuven Zaritsky
  • Natan Peterfreund
  • Nahum Shimkin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1842)


This paper presents a 3D active contour model for boundary tracking, motion analysis and position prediction of non-rigid objects, which applies stereo vision and velocity control to the class of deformable contour models, known as snakes. The proposed contour evolves in three dimensional space in reaction to a 3D potential function, which is derived by projecting the contour onto the 2D stereo images. The potential function is augmented by a velocity term, which is related to the three dimensional velocity field along the contour, and is used to guide the contour displacement between subsequent images. This leads to improved spatio-temporal tracking performance, which is demonstrated through experimental results with real and synthetic images. Good tracking performance is obtained with as little as one iteration per frame, which provides a considerable advantage for real time operation.


  1. 1.
    B. Bascle and R Deriche, “Energy-based methods for 2D curve tracking, reconstruction and refinement of 3D curves and applications”, SPIE, Vol. 2031, pp. 282–293, 1993.CrossRefGoogle Scholar
  2. 2.
    B. Bascle and R. Deriche, “Stereo matching, reconstruction and refinement of 3D curves using deformable contours”, IEEE, Int. Conf. on Computer Vision, pp. 421–430, 1993.Google Scholar
  3. 3.
    A. Blake and A. Yuille (nteds.), Active Vision, MIT Press, 1992.Google Scholar
  4. 4.
    A. Blake and M. Isard, Active Contours, Springer, 1998.Google Scholar
  5. 5.
    B. Caselles and B. Coll, “Snakes in movement,” SIAM Journal on Numerical Analysis, Vol. 33, pp. 2445–2456, Dec. 1996.Google Scholar
  6. 6.
    T. Cham and R. Cipolla, “Stereo coupled active contours” Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 1094–1099, 1997.Google Scholar
  7. 7.
    M. P. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall, 1976.Google Scholar
  8. 8.
    D.B. Gennery, “Visual tracking of known three-dimensional objects”, Int. J. of Computer Vision, Vol. 7, No. 3, pp. 243–270, 1992CrossRefGoogle Scholar
  9. 9.
    A.K. Jain, Y. Zhong and M. Dubuisson-Jolly, “Deformable template models: a review” Signal Processing 71, 1998, pp. 109–129.zbMATHCrossRefGoogle Scholar
  10. 10.
    M. Kass, A. Witkin and D. Terzopoulos, “Snakes: active contour models”, Int. J. of Computer Vision, Vol. 1, No. 4, pp. 321–331, 1987.CrossRefGoogle Scholar
  11. 11.
    B.K.P. Horn, Robot Vision, MIT Press, 1986.Google Scholar
  12. 12.
    D.G. Lowe, “Robust model-based motion-tracking through the integration of search and estimation”, Int. J. of Computer Vision, Vol. 8, No. 2, pp. 113–122, 1992CrossRefGoogle Scholar
  13. 13.
    T. McInerney, and D. Terzopoulos, “Deformable models in medical image analysis: a survey”, Medical Image Analysis, Vol. 1, No. 2, 91–108, 1996.CrossRefGoogle Scholar
  14. 14.
    N. Paragios and R. Derichee, “A PDE based level set approach for detection and tracking of moving objects”, Proc. 6th Intern. Conf. on Computer Vision, Bombay, India, Jan. 1998.Google Scholar
  15. 15.
    N. Peterfreund, “Robust tracking of position and velocity with Kalman snakes”, IEEE Trans. on PAMI, 21(6), June 1999.Google Scholar
  16. 16.
    N. Peterfreund, “The velocity snake”, Proc. IEEE Non Rigid and Articulated Motion, Puerto Ricoh, 1997.Google Scholar
  17. 17.
    N. Peterfreund, “The velocity snake: deformable contour for tracking in spatiovelocity space”, Computer Vision and Image Understanding, 73(3), 346–356, 1999.zbMATHCrossRefGoogle Scholar
  18. 18.
    D. Terzopoulos and R. Szeliski, “Tracking with Kalman Snakes”, in A. Blake and A. Yuille (nteds.), Active Vision, pp. 3–20, MIT Press, 1992.Google Scholar
  19. 19.
    Z. Zhang and O. D. Faugeras, “Three-Dimensional Motion Computation and Object Segmentation on a Long Sequence of Stereo Frames”, Intl. J. of Computer Vision, Vol. 7, No. 3, pp. 211–241, 1992.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Reuven Zaritsky
    • 1
  • Natan Peterfreund
    • 2
  • Nahum Shimkin
    • 1
  1. 1.Department of Electrical EngineeringTechnion - Israel Institute of TechnologyHaifaIsrael
  2. 2.Oak Ridge National LaboratoryOak RidgeUSA

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