One-Shot Integral Invariant Shape Priors for Variational Segmentation

  • Siddharth Manay
  • Daniel Cremers
  • Anthony Yezzi
  • Stefano Soatto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3757)


We match shapes, even under severe deformations, via a smooth re-parametrization of their integral invariant signatures. These robust signatures and correspondences are the foundation of a shape energy functional for variational image segmentation. Integral invariant shape templates do not require registration and allow for significant deformations of the contour, such as the articulation of the object’s parts. This enables generalization to multiple instances of a shape from a single template, instead of requiring several templates for searching or training. This paper motivates and presents the energy functional, derives the gradient descent direction to optimize the functional, and demonstrates the method, coupled with a data term, on real image data where the object’s parts are articulated.


Active Contour Disparity Function Data Term Lawrence Livermore National Laboratory Active Shape Model 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kendall, D.G.: The diffusion of shape. Advances in Appl. Probability 9, 428–430 (1977)CrossRefGoogle Scholar
  2. 2.
    Pitiot, A., Delingette, H., Toga, A., Thompson, P.: Learning Object Correspondences with the Observed Transport Shape Measure. In: Taylor, C.J., Noble, J.A. (eds.) IPMI 2003. LNCS, vol. 2732, pp. 25–37. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Manay, S., Hong, B., Yezzi, A., Soatto, S.: Integral invariant signatures. In: European Conf. Comp. Vis. (2004)Google Scholar
  4. 4.
    Manay, S., Hong, B., Cremers, D., Yezzi, A., Soatto, S.: Integral invariants and shape matching. Pat. Anal. and Mach. Intell (2005) (submitted)Google Scholar
  5. 5.
    Bookstein, F.: The Measurement of Biological Shape and Shape Change. Lect. Notes in Biomath., vol. 24. Springer, New York (1978)zbMATHGoogle Scholar
  6. 6.
    Cootes, T.F., Taylor, C.J., Cooper, D.M., Graham, J.: Active shape models – their training and applications. Comp. Vision Image Underst. 61, 38–59 (1995)CrossRefGoogle Scholar
  7. 7.
    Cremers, D., Osher, S., Soatto, S.: Kernel density estimation and instrinsic alignment for knowledge-driven segmentation: Teaching level sets to walk. In: Rasmussen, C.E., Bülthoff, H.H., Schölkopf, B., Giese, M.A. (eds.) DAGM 2004. LNCS, vol. 3175, pp. 36–44. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Dryden, I.L., Mardia, K.V.: Statistical Shape Analysis. Wiley, Chichester (1998)zbMATHGoogle Scholar
  9. 9.
    Fréchet, M.: Les courbes aléatoires. Bull. Inst. Int’l Stat. 38, 499–504 (1961)zbMATHGoogle Scholar
  10. 10.
    Klassen, E., Srivastava, A., Mio, W., Joshi, S.H.: Analysis of planar shapes using geodesic paths on shape spaces. Pat. Anal. and Mach. Intell. 26, 373–383 (2004)Google Scholar
  11. 11.
    Grenander, U.: Lectures in Pattern Theory. Springer, Berlin (1976)zbMATHGoogle Scholar
  12. 12.
    Grenander, U., Chow, Y., Keenan, D.M.: Hands: A Pattern theoretic Study of Biological Shapes. Springer, New York (1991)Google Scholar
  13. 13.
    Trouvé, A.: Diffeomorphisms, groups, and pattern matching in image analysis. Int. J. Computer Vision 28, 213–221 (1998)CrossRefGoogle Scholar
  14. 14.
    Younes, L.: Computable elastic distances between shapes. SIAM J. Appl. Math. 58, 565–586 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Basri, R., Costa, L., Geiger, D., Jacobs, D.: Determining the similarity of deformable shapes. Vision Research 38, 2365–2385 (1998)CrossRefGoogle Scholar
  16. 16.
    Gdalyahu, Y., Weinshall, D.: Flexible syntactic matching of curves and its application to automatic hierarchical classication of silhouettes. Pat. Anal. and Mach. Intell. 21, 1312–1328 (1999)CrossRefGoogle Scholar
  17. 17.
    Kass, M., Witkin, A., Terzopoulis, D.: Snakes: Active contour models. Int. J. Computer Vision 1, 321–323 (1987)CrossRefGoogle Scholar
  18. 18.
    Kichenassamy, S., Kumar, A., Olver, P.J., Tannenbaum, A., Yezzi, A.: Analysis of planar shape influnce in geodesic active contours. In: Int. Conf. Comp. Vis., pp. 810–815 (1995)Google Scholar
  19. 19.
    Chan, T., Vese, L.: Active contours without edges. IEEE Trans. on Image Proc. 10, 266–277 (2001)zbMATHCrossRefGoogle Scholar
  20. 20.
    Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. In: Int. Conf. Comp. Vis., pp. 694–699 (1995)Google Scholar
  21. 21.
    Tsai, A., Yezzi, A., Willsky, A.: Curve evolution implementation of the Mumford Shah functional for image segmentation, denoising, interpolation, and magnification. IEEE Trans. on Image Proc. 10, 1169–1186 (2001)zbMATHCrossRefGoogle Scholar
  22. 22.
    Leventon, M.E., Grimson, W.E.L., Faugeras, O.: Statistical shape influence in geodesic active contours. In: Proc. Conf. Comput. Vision and Pat. Rec., vol. 1, pp. 316–323 (2000)Google Scholar
  23. 23.
    Tsai, A., Yezzi, A., Wells, W., Tempany, C., Tucker, D., Fan, A., Grimson, E., Willsky, A.: Model-based curve evolution technique for image segmentation. In: Proc. Conf. Comput. Vision and Pat. Rec., pp. 463–468 (2001)Google Scholar
  24. 24.
    Chen, Y., Tagare, H., Thiruvenkadam, S., Huang, F., Wilson, D., Gopinath, K.S., Briggs, R.W., Geiser, E.: Using shape priors in geometric active contours in a variational framework. Int. J. Computer Vision 50, 315–328 (2002)zbMATHCrossRefGoogle Scholar
  25. 25.
    Rousson, M., Paragios, N.: Shape priors of level set represenations. In: European Conf. Comp. Vis., pp. 78–92 (2002)Google Scholar
  26. 26.
    Rousson, M., Paragios, N., Deriche, R.: Implicit active shape models for 3D segmentation in MRI imaging. In: Int. Conf. Medical Image Computing and Computer Assited Intervention, pp. 209–216 (2004)Google Scholar
  27. 27.
    Bakircioglu, M., Grenander, U., Khaneja, N., Miller, M.I.: Curve matching on brain surfaces using frenet distances. Human Brain Mapping 6, 329–333 (1998)zbMATHCrossRefGoogle Scholar
  28. 28.
    Sebastian, T., Klein, P., Kimia, B.: Alignment-based recognition of shape outlines. In: Arcelli, C., Cordella, L.P., Sanniti di Baja, G. (eds.) IWVF 2001. LNCS, vol. 2059, p. 606. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  29. 29.
    Tomasi, C., Manduchi, R.: Stereo without search. In: European Conf. Comp. Vis., pp. 452–465 (1996)Google Scholar
  30. 30.
    Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Comm. on Pure and Applied Math. 42 (1989)Google Scholar
  31. 31.
    Zhu, S.C., Yuille, A.: Region competition: Unifying snakes, region growing, and Bayes/MDL for multiband image segmentation. Pat. Anal. and Mach. Intell. 18, 884–900 (1996)CrossRefGoogle Scholar
  32. 32.
    Nain, D., Yezzi, A., Turk, G.: Vessel segmentation using a shape driven flow. In: Int. Conf. Medical Image Computing and Computer Assited Intervention (2004)Google Scholar
  33. 33.
    Osher, S., Sethian, J.: Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. of Comp. Physics 79, 12–49 (1988)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Siddharth Manay
    • 1
  • Daniel Cremers
    • 2
  • Anthony Yezzi
    • 3
  • Stefano Soatto
    • 4
  1. 1.Lawrence Livermore National Laboratory 
  2. 2.Siemens Corporate Research 
  3. 3.Georgia Institute of Technology 
  4. 4.University of California at Los Angeles 

Personalised recommendations