Skip to main content
SpringerLink
Log in

Multi-Reference Shape Priors for Active Contours

  • Published:
International Journal of Computer Vision Aims and scope Submit manuscript

Abstract

In this paper, we present a new way of constraining the evolution of an active contour with respect to a set of fixed reference shapes. This 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, in terms of descriptors, between the evolving curve and the reference shapes. Minimizing the corresponding 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aubert, G., Barlaud, M., Faugeras, O., & Jehan-Besson, S. (2003). Image segmentation using active contours: calculus of variations or shape gradients? SIAM Journal on Applied Mathematics, 63(6), 2128–2154.

    Article  MATH  MathSciNet  Google Scholar 

  • Bresson, X., Vandergheynst, P., & Thiran, J. P. (2006). A variational model for object segmentation using boundary information and shape prior driven by the Mumford-Shah functional. International Journal of Computer Vision, 68(2), 145–162.

    Article  Google Scholar 

  • Chan, T., & Vese, L. (2001). Active contours without edges. IEEE Transactions on Image Processing, 10(2), 266–277.

    Article  MATH  Google Scholar 

  • Chen, Y., Tagare, H., Thiruvenkadam, S., Huang, F., Wilson, D., Gopinath, K., Briggs, R., & Geiser, E. (2002). Using prior shapes in geometric active contours in a variational framework. International Journal of Computer Vision, 50(3), 315–328.

    Article  MATH  Google Scholar 

  • Cootes, T., Cooper, D., Taylor, C., & Graham, J. (1995). Active shape models—their training and application. Computer Vision and Image Understanding, 61(1), 38–59.

    Article  Google Scholar 

  • Cremers, D., Kohlberger, T., & Schnörr, C. (2003). Shape statistics in kernel space for variational image segmentation. Pattern Recognition, 36(9), 1929–1943. Special Issue on Kernel and Subspace Methods in Computer Vision.

    Article  MATH  Google Scholar 

  • Cremers, D., Tischhäuser, F., Weickert, J., & Schnörr, C. (2002). Diffusion snakes: Introducing statistical shape knowledge into the Mumford-Shah functional. International Journal of Computer Vision, 50(3), 295–313.

    Article  MATH  Google Scholar 

  • Cremers, D., Osher, S. J., & Soatto, S. (2006a). Kernel density estimation and intrinsic alignment for shape priors in level set segmentation. International Journal of Computer Vision, 69(3), 335–351.

    Article  Google Scholar 

  • Cremers, D., Sochen, N., & Schnörr, C. (2006b). A multiphase dynamic labeling model for variational recognition-driven image segmentation. International Journal of Computer Vision, 66(1), 67–81.

    Article  Google Scholar 

  • Foulonneau, A. (2004). A contribution to the introduction of geometric shape constraints in region-based active contours (in French). PhD thesis, University Louis Pasteur, Strasbourg I. Available online: http://lsiit-miv.u-strasbg.fr/lsiit/perso/Charbonnier.htm.

  • Foulonneau, A., Charbonnier, P., & Heitz, F. (2003). Geometric shape priors for region-based active contours. In Proc. of IEEE conference on image processing (Vol. 3., pp. 413–416). Barcelona, Spain.

  • Foulonneau, A., Charbonnier, P., & Heitz, F. (2006a). Affine-invariant geometric shape priors for region-based active contours. IEEE Transactions On Pattern Analysis and Machine Intelligence, 28(8), 1352–1357.

    Article  Google Scholar 

  • Foulonneau, A., Charbonnier, P., & Heitz, F. (2006b). Affine-invariant multi-reference shape priors for active contours. In LNCS : Vol. 3952. Computer Vision—ECCV 2006 (pp. 601–613). Berlin: Springer.

    Chapter  Google Scholar 

  • Foulonneau, A., Charbonnier, P., & Heitz, F. (2008). Multi-reference affine-invariant geometric shape priors for region-based active contours (Technical Report RR-AF01-08). LRPC ERA 27 LCPC/LSIIT UMR 7005 CNRS. Available online: http://lsiit.u-strasbg.fr/Publications/2008/FCH08/RR-AF01-08.pdf.

  • Gastaud, M., Aubert, G., & Barlaud, M. (2003). Tracking video objects using active contours and geometric priors (Technical Report RR-2003-07-FR, I3S). Nice-Sophia Antipolis, France.

  • Joshi, S., Mio, W., Srivastava, A., & Liu, X. (2005). Statistical shape analysis: Clustering, learning, and testing. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(4), 590–602.

    Article  Google Scholar 

  • Leventon, M., Grimson, W., & Faugeras, O. (2000). Statistical shape influence in geodesic active contours. In Proc. of IEEE conference on computer vision and pattern recognition (pp. 1316–1323). Hilton Head Island, Southern Carolina, USA.

  • Liao, S., & Pawlak, M. (1996). On image analysis by moments. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(3), 254–266.

    Article  Google Scholar 

  • Mansouri, A., Mukherjee, D., & Acton, S. (2004). Constraining active contour evolution via Lie groups of transformation. IEEE Transactions on Image Processing, 13(6), 853–863.

    Article  MathSciNet  Google Scholar 

  • Mukundan, R., & Ramakrishnan, K. (1998). Moments functions in image analysis—theory and applications. Singapore: World Scientific. ISBN 981-02-3524-0.

    Google Scholar 

  • Osher, S., & Sethian, J. (1988). Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 79(1), 12–49.

    Article  MATH  MathSciNet  Google Scholar 

  • Pei, S., & Lin, C. (1995). Image normalization for pattern recognition. Image and Vision Computing, 13(10), 711–723.

    Article  Google Scholar 

  • Precioso, F., & Barlaud, M. (2002). B-spline active contour with handling of topology changes for fast video segmentation. Eurasip Journal on Applied Signal Processing, 2002(6), 555–560. Special issue: image analysis for multimedia interactive services—PART II.

    Article  MATH  Google Scholar 

  • Riklin-Raviv, T., Kiryati, N., & Sochen, N. (2004). Unlevel-sets: geometry and prior-based segmentation. In Lecture notes in computer science: Vol. 3024. Proc. of the 8th European conference on computer vision (pp. 50–61). Prague, Czech Republic.

  • Rousson, M., & Paragios, N. (2002). Shape priors for level set representations. In Lecture notes in computer science: Vol. 2351. Proc. of 7th European conference on computer vision (pp. 78–93). Copenhagen, Denmark.

  • Staib, L., & Duncan, J. (1992). Boundary finding with parametrically deformable models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(11), 1061–1075.

    Article  Google Scholar 

  • Székely, G., Kelemen, A., Brechbüler, C., & Gerig, G. (1996). Segmentation of 2D and 3D objects from MRI volume data using constrained elastic deformations of flexible Fourier surface models. Medical Image Analysis, 1(1), 19–34.

    Google Scholar 

  • Talenti, G. (1987). Recovering a function from a finite number of moments. Inverse Problems, 3, 501–517.

    Article  MATH  MathSciNet  Google Scholar 

  • Teague, M. (1980). Image analysis via the general theory of moments. Journal of the Optical Society of America, 70(8), 920–930.

    Article  MathSciNet  Google Scholar 

  • Terzopoulos, D., & Metaxas, D. (1991). Dynamic 3D models with local and global deformations: Deformable superquadrics. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(7), 703–714.

    Article  Google Scholar 

  • Tsai, A., Yezzi, A., Wells, W., Tempany, C., Tucker, D., Fan, A., Grimson, W., & Willsky, A. (2003). A shape-based approach to the segmentation of medical imagery using level sets. IEEE Transactions on Medical Imaging, 22(2), 137–154.

    Article  Google Scholar 

  • Unal, G., Krim, H., & Yezzi, A. (2002). Stochastic differential equations and geometric flows. IEEE Transactions on Image Processing, 11(12), 1405–1416.

    Article  MathSciNet  Google Scholar 

  • Zhang, T., & Freedman, D. (2003). Tracking objects using density matching and shape priors. In Proc. of 9th IEEE international conference on computer vision (pp. 1056–1062). Nice, France.

Download references

Author information

Authors and Affiliations

  1. ERA 27 LCPC, Laboratoire des Ponts et Chaussées, 11 rue Jean Mentelin, B.P. 9, 67035, Strasbourg, France

    Alban Foulonneau & Pierre Charbonnier

  2. Laboratoire des Sciences de l’Image, de l’Informatique et de la Télédétection, UMR 7005 CNRS, Strasbourg I University, Bd Sébastien Brandt, 67400, Illkirch, France

    Fabrice Heitz

Authors
  1. Alban Foulonneau
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pierre Charbonnier
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fabrice Heitz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alban Foulonneau.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Foulonneau, A., Charbonnier, P. & Heitz, F. Multi-Reference Shape Priors for Active Contours. Int J Comput Vis 81, 68–81 (2009). https://doi.org/10.1007/s11263-008-0163-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11263-008-0163-3

Keywords

Search

Navigation