New Algorithms for Controlling Active Contours Shape and Topology

  • H. Delingette
  • J. Montagnat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1843)


In recent years, the field of active-contour based image segmentation have seen the emergence of two competing approaches. The first and oldest approach represents active contours in an explicit (or parametric) manner corresponding to the Lagrangian formulation. The second approach represent active contours in an implicit manner corresponding to the Eulerian framework. After comparing these two approaches, we describe several new topological and physical constraints applied on parametric active contours in order to combine the advantages of these two contour representations. We introduce three key algorithms for independently controlling active contour parameterization, shape and topology. We compare our result to the level-set method and show similar results with a significant speed-up.


Internal Force Active Contour Hash Table Active Contour Model Topology Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    G. Aubert and L. Blanc-Féraud. Some Remarks on the Equivalence between 2D and 3D Classical Snakes and Geodesic Active Contours. International Journal of Computer Vision, 34(1):5–17, September 1999.Google Scholar
  2. 2.
    V. Caselles, R. Kimmel, and G. Sapiro. Geodesic Active Contours. International Journal of Computer Vision, 22(l):61–79, 1997.zbMATHCrossRefGoogle Scholar
  3. 3.
    I. Cohen, L.D. Cohen, and N. Ayache. Using Deformable Surfaces to Segment 3-D Images and Infer Differential Structures. Computer Vision, Graphics, and Image Processing: Image Understanding, 56(2)242–263, September 1992.Google Scholar
  4. 4.
    L.D. Cohen. On Active Contour Models and Balloons. Computer Vision, Graphics, and Image Processing: Image Understanding, 53(2):211–218, March 1991.Google Scholar
  5. 5.
    H. Delingette. Intrinsic stabilizers of planar curves. In third European Conference on Computer Vision ( ECCV’94 ), Stockholm, Sweden, June 1994.Google Scholar
  6. 6.
    J. Hug, C. Brechbüler, and G. Székely. Tamed Snake: A Particle System for Robust Semi-automatic Segmentation. In Medical Image Computing and Computer-Assisted Intervention (MICCAI’99), volume 1679 of Lectures Notes in Computer Science, pages 106–115, Cambridge, UK, September 1999. Springer.Google Scholar
  7. 7.
    J. Ivins and J. Porrill. Active Region models for segmenting textures and colours. Image and Vision Computing, 13(5):431–438, June 1995.Google Scholar
  8. 8.
    M. Kass, A. Witkin, and D. Terzopoulos. Snakes: Active Contour Models. International Journal of Computer Vision, 1:321–331, 1988.CrossRefGoogle Scholar
  9. 9.
    B. Kimia, A. Tannenbaum, and S. Zucker. On the evolution of curves via a function of curvature i. the classical case. Journal of Mathematical Analysis and Applications, 163:438–458, 1992.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    J.-O. Lachaud and A. Montanvert. Deformable meshes with automated topology changes for coarse-to-fine three-dimensional surface extraction. Medical Image Analysis, 3(2): 187–207, 1999.CrossRefGoogle Scholar
  11. 11.
    F. Leitner and P. Cinquin. Complex topology 3d objects segmentation. In SPIE Conf. on Advances in Intelligent Robotics Systems, volume 1609, Boston, November 1991.Google Scholar
  12. 12.
    S. Lobregt and M. Viergever. A Discrete Dynamic Contour Model. IEEE Transactions on Medical Imaging, 14(l):12–23, 1995.CrossRefGoogle Scholar
  13. 13.
    R. Malladi, J.A. Sethian, and B.C. Vemuri. Shape Modeling with Front Propagation: A Level Set Approach. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(2): 158–174, 1995.CrossRefGoogle Scholar
  14. 14.
    T. Mclnerney and D. Terzopoulos. Topologically adaptable snakes. In International Conference on Computer Vision ( ICCV’95), pages 840–845, Cambridge, USA, June 1995.Google Scholar
  15. 15.
    T. Mclnerney and D. Terzopoulos. Deformable models in medical image analysis: a survey. Medical Image Analysis, l(2):91–108, 1996.CrossRefGoogle Scholar
  16. 16.
    S. Menet, P. Saint-Marc, and G. Medioni. Active Contour Models: Overview, Implementation and Applications. IEEE Trans, on Systems, Man and Cybernetics, pages 194–199, 1993.Google Scholar
  17. 17.
    D. Metaxas and D. Terzopoulos. Constrained Deformable Superquadrics and non-rigid Motion Tracking. In International Conference on Computer Vision and Pattern Recognition (CVPR’91), pages 337–343, Maui, Hawai, June1991.Google Scholar
  18. 18.
    N. Paragios and R. Deriche. A PDE-based Level-Set Approach for Detection and Tracking of Moving Objects. In International Conference on Computer Vision ( ICCV’98), pages 1139–1145, Bombay, India, 1998.Google Scholar
  19. 19.
    J.A. Sethian. Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Materials Science. Cambridge University Press, 1996.Google Scholar
  20. 20.
    G. Taubin. Curve and Surface Smoothing Without Shrinkage. In International Conference on Computer Vision ( ICCV’95), pages 852–857, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • H. Delingette
    • 1
  • J. Montagnat
    • 1
  1. 1.Projet EpidaureI.N.R.I.A.Sophia-AntipolisFrance

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