Open-Curve Shape Correspondence Without Endpoint Correspondence

  • Theodor Richardson
  • Song Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4190)


Shape correspondence is the foundation for accurate statistical shape analysis; this is usually accomplished by identifying a set of sparsely sampled and well-corresponded landmark points across a population of shape instances. However, most available shape correspondence methods can only effectively deal with complete-shape correspondence, where a one-to-one mapping is assumed between any two shape instances. In this paper, we present a novel algorithm to correspond 2D open-curve partial-shape instances where one shape instance may only be mapped to part of the other, i.e., the endpoints of these open-curve shape instances are not presumably corresponded. In this algorithm, some initially identified landmarks, including the ones at or near the endpoints of the shape instances, are refined by allowing them to slide freely along the shape contour to minimize the shape-correspondence error. To avoid being trapped into local optima, we develop a simple method to construct a better initialization of the landmarks and introduce some additional constraints to the landmark sliding. We evaluate the proposed algorithm on 32 femur shape instances in comparison to some current methods.


Minimum Description Length Target Shape Active Shape Model Statistical Shape Modeling Shape Contour 
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  1. 1.
    Bookstein, F.: Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Transactions on Pattern Analysis and Machine Intelligence 11(6), 567–585 (1989)zbMATHCrossRefGoogle Scholar
  2. 2.
    Bookstein, F.: Landmark methods for forms without landmarks: Morphometrics of group differences in outline shape. Medical Image Analysis 1(3), 225–243 (1997)CrossRefGoogle Scholar
  3. 3.
    Cootes, T., Taylor, C., Cooper, D., Graham, J.: Active shape models - their training and application. Computer Vision and Image Understanding 61(1), 38–59 (1995)CrossRefGoogle Scholar
  4. 4.
    Davies, R., Twining, C., Cootes, T., Waterton, J., Taylor, C.: A minimum description length approach to statistical shape modeling. IEEE Transactions on Medical Imaging 21(5), 525–537 (2002)CrossRefGoogle Scholar
  5. 5.
    Duchon, J.: Splines minimizing rotation-invariant semi-norms in Sobolev space. In: Constructive Theory of Functions of Several Variables. Lecture Notes in Mathematics, vol. 571, pp. 85–100 (1977)Google Scholar
  6. 6.
    Heimann, T., Wolf, I., Williams, T., Meinzer, H.-P.: 3D active shape models using gradient descent optimization of description length. In: Information Processing for Medical Imaging Conference (2005)Google Scholar
  7. 7.
    Kendall, D., Barden, D., Carne, T., Le., H.: Shape and Shape Theory. John Wiley & Sons, Ltd., Chichester (1999)zbMATHCrossRefGoogle Scholar
  8. 8.
    Leventon, M., Grimson, E., Faugeras, O.: Statistical shape influence in geodesic active contours. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 316–323 (2000)Google Scholar
  9. 9.
    Richardson, T., Wang, S.: Nonrigid shape correspondence using landmark sliding, insertion and deletion. In: International Conference on Medical Image Computing and Computer Assisted Intervention, pp. II–435–II–442 (2005)Google Scholar
  10. 10.
    Small, C.: The Statistical Theory of Shape. Springer, Heidelberg (1996)zbMATHGoogle Scholar
  11. 11.
    Styner, M., Rajamani, K., Nolte, L.-P., Zsemlye, G., Szekely, G., Taylor, C., Davies, R.: Evaluation of 3D correspondence methods for model building. In: Information Processing for Medical Imaging Conference (2003)Google Scholar
  12. 12.
    Thodberg, H.: Minimum description length shape and appearance models. In: Taylor, C.J., Noble, J.A. (eds.) IPMI 2003. LNCS, vol. 2732, pp. 51–62. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Wang, S., Kubota, T., Richardson, T.: Shape correspondence through landmark sliding. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. I–143–I–150 (2004)Google Scholar
  14. 14.
    Xie, J., Heng, P.: Shape modeling using automatic landmarking. In: International Conference on Medical Image Computing and Computer Assisted Intervention, pp. II–709–II–716 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Theodor Richardson
    • 1
  • Song Wang
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of South CarolinaColumbiaUSA

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