Affine-Invariant Multi-reference Shape Priors for Active Contours

  • Alban Foulonneau
  • Pierre Charbonnier
  • Fabrice Heitz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3952)


We present a new way of constraining the evolution of a region-based active contour with respect to a set of reference shapes. The approach is based on a description of shapes by the Legendre moments computed from their characteristic function. This provides a region-based representation that can handle arbitrary shape topologies. Moreover, exploiting the properties of moments, it is possible to include intrinsic affine invariance in the descriptor, which solves the issue of shape alignment without increasing the number of d.o.f. of the initial problem and allows introducing geometric shape variabilities. Our new shape prior is based on a distance between the descriptors of the evolving curve and a reference shape. The proposed model naturally extends to the case where multiple reference shapes are simultaneously considered. Minimizing the shape energy, leads to a geometric flow that does not rely on any particular representation of the contour and can be implemented with any contour evolution algorithm. We introduce our prior into a two-class segmentation functional, showing its benefits on segmentation results in presence of severe occlusions and clutter. Examples illustrate the ability of the model to deal with large affine deformation and to take into account a set of reference shapes of different topologies.


Segmentation Result Active Contour Shape Descriptor Canonical Representation Normalize Mean Square Error 
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.
    Terzopoulos, D., Metaxas, D.: Dynamic 3D models with local and global deformations: Deformable superquadrics. IEEE Transactions on Pattern Analysis and Machine Intelligence 13(7), 703–714 (1991)CrossRefGoogle Scholar
  2. 2.
    Cootes, T., Cooper, D., Taylor, C., Graham, J.: Active shape models - their training and application. Computer Vision and Image Understanding 61(1), 38–59 (1995)CrossRefGoogle Scholar
  3. 3.
    Cremers, D., Kohlberger, T., Schnörr, C.: Shape statistics in kernel space for variational image segmentation. Pattern Recognition: Special Issue on Kernel and Subspace Methods in Computer Vision 36(9), 1929–1943 (2003)CrossRefzbMATHGoogle Scholar
  4. 4.
    Leventon, M., Grimson, W., Faugeras, O.: Statistical shape influence in geodesic active contours. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, Hilton Head Island, Southern Carolina, USA, pp. 1316–1323 (2000)Google Scholar
  5. 5.
    Rousson, M., Paragios, N.: Shape priors for level set representations. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2351, pp. 78–92. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Riklin-Raviv, T., Kiryati, N., Sochen, N.A.: Unlevel-sets: Geometry and prior-based segmentation. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3024, pp. 50–61. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Tsai, A., Yezzi, A., Wells, W., Tempany, C., Tucker, D., Fan, A., Grimson, W., Willsky, A.: A shape-based approach to the segmentation of medical imagery using level sets. IEEE Transactions on Medical Imaging 22(2), 137–154 (2003)CrossRefGoogle Scholar
  8. 8.
    Aubert, G., Barlaud, M., Faugeras, O., Jehan-Besson, S.: Image segmentation using active contours: calculus of variations or shape gradients? SIAM, Journal on Applied Mathematics 63(6), 2128–2154 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Teague, M.: Image analysis via the general theory of moments. Journal of the Optical Society of America 70(8), 920–930 (1980)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Cremers, D., Osher, S.J., Soatto, S.: Kernel density estimation and intrinsic alignment for knowledge-driven segmentation: Teaching level sets to walk. In: Rasmussen, C.E., Bülthoff, H.H., Schölkopf, B., Giese, M.A., et al. (eds.) DAGM 2004. LNCS, vol. 3175, pp. 36–44. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Foulonneau, A., Charbonnier, P., Heitz, F.: Geometric shape priors for region-based active contours. In: Proc. of IEEE Conference on Image Processing, Barcelona, Spain, vol. 3, pp. 413–416 (2003)Google Scholar
  12. 12.
    Pei, S., Lin, C.: Image normalization for pattern recognition. Image and Vision Computing 13(10), 711–723 (1995)CrossRefGoogle Scholar
  13. 13.
    Foulonneau, A., Charbonnier, P., Heitz, F.: Affine-invariant geometric shape priors for region-based active contours. Technical Report RR-AF01-2005, LRPC ERA 27 LCPC/LSIIT UMR 7005 CNRS (2005), available online:
  14. 14.
    Precioso, F., Barlaud, M.: B-spline active contour with handling of topology changes for fast video segmentation. Eurasip Journal on Applied Signal Processing, special issue: image analysis for multimedia interactive services - PART II 2002(6), 555–560 (2002)CrossRefzbMATHGoogle Scholar
  15. 15.
    Osher, S., Sethian, J.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics 79(1), 12–49 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Chan, T., Vese, L.: Active contours without edges. IEEE Transactions on Image Processing 10(2), 266–277 (2001)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Alban Foulonneau
    • 1
  • Pierre Charbonnier
    • 1
  • Fabrice Heitz
    • 2
  1. 1.ERA 27 LCPC, Laboratoire des Ponts et ChausséesStrasbourgFrance
  2. 2.Laboratoire des Sciences de l’Image, de l’Informatique et de la Télédétection, UMR 7005 CNRSStrasbourg I UniversityIllkirchFrance

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