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Unlevel-Sets: Geometry and Prior-Based Segmentation

  • Tammy Riklin-Raviv
  • Nahum Kiryati
  • Nir Sochen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3024)

Abstract

We present a novel variational approach to top-down image segmentation, which accounts for significant projective transformations between a single prior image and the image to be segmented. The proposed segmentation process is coupled with reliable estimation of the transformation parameters, without using point correspondences. The prior shape is represented by a generalized cone that is based on the contour of the reference object. Its unlevel sections correspond to possible instances of the visible contour under perspective distortion and scaling. We extend the Chan-Vese energy functional by adding a shape term. This term measures the distance between the currently estimated section of the generalized cone and the region bounded by the zero-crossing of the evolving level set function. Promising segmentation results are obtained for images of rotated, translated, corrupted and partly occluded objects. The recovered transformation parameters are compatible with the ground truth.

References

  1. 1.
    Aubert, G., Kornprobst, P.: Mathematical Problems. In: Image Processing: Partial Differential Equations and the Calculus of Variations. Springer, Heidelberg (2002)Google Scholar
  2. 2.
    Binford, T.O.: Visual perception by computer. In: Proc. IEEE Conf. Systems and Control (December 1971)Google Scholar
  3. 3.
    Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Processing 10(2), 266–277 (2001)zbMATHCrossRefGoogle Scholar
  4. 4.
    Chen, Y., Thiruvenkadam, S., Tagare, H.D., Huang, F., Wilson, D.: On the incorporation of shape priors into geometric active contours. In: VLSM 2001, pp. 145–152 (2001)Google Scholar
  5. 5.
    Cremers, D., Kohlberger, T., Schnorr, C.: Nonlinear shape statistics via kernel spaces. In: Radig, B., Florczyk, S. (eds.) DAGM 2001. LNCS, vol. 2191, pp. 269–276. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Cremers, D., Kohlberger, T., Schnorr, C.: Nonlinear shape statistics in mumfordshah based segmentation. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2351, pp. 93–108. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Cremers, D., Sochen, N., Schnorr, C.: Towards recognition-based variational segmentation using shape priors and dynamic labeling. In: Intl. Conf. on Scale- Space Theories in Computer Vision, June 2003, pp. 388–400 (2003)Google Scholar
  8. 8.
    Faugeras, O.: Three-Dimensional Computer Vision: A Geometric Viewpoint. MIT Press, Cambridge (1993)Google Scholar
  9. 9.
    Faugeras, O., Luong, Q.T., Papadopoulo, T.: The Geometry of Multiple Images. MIT Press, Cambridge (2001)zbMATHGoogle Scholar
  10. 10.
    Forsyth, D.A., Ponce, J.: Computer Vision: A Modern Approach. Prentice Hall, Englewood Cliffs (2003)Google Scholar
  11. 11.
    Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  12. 12.
    Irani, M., Anandan, P.: All about direct methods. In: Triggs, B., Zisserman, A., Szeliski, R. (eds.) ICCV-WS 1999. LNCS, vol. 1883, p. 267. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  13. 13.
    Leventon, M., Faugeraus, O., Grimson, W., Wells III, W.: Level set based segmentation with intensity and curvature priors. In: Proceedings Workshop on Mathematical Methods in Biomedical Image Analysis, June 2000, pp. 4–11 (2000)Google Scholar
  14. 14.
    Leventon, M.E., Grimson, W.E.L., Faugeras, O.: Statistical shape influence in geodesic active contours. In: CVPR 2000, vol. I, pp. 316–323 (2000)Google Scholar
  15. 15.
    Marr, D.: Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. W.H. Freeman, New York (1982)Google Scholar
  16. 16.
    Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics 42, 577–684 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics 79, 12–49 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Rao, K.G., Medioni, G.: Generalized cones: Useful geometric properties. In: CVIP 1992, pp. 185–208 (1992)Google Scholar
  19. 19.
    Tsai, A., Yezzi Jr., A., Wells III, W.M., Tempany, C., Tucker, D., Fan, A., Grimson, W.E.L., Willsky, A.S.: Model-based curve evolution technique for image segmentation. In: CVPR 2001, vol. I, pp. 463–468 (2001)Google Scholar
  20. 20.
    Ullman, S.: High-Level Vision: Object Recognition and Visual Cognition. MIT Press, Cambridge (1996)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Tammy Riklin-Raviv
    • 1
  • Nahum Kiryati
    • 1
  • Nir Sochen
    • 2
  1. 1.School of Electrical Engineering 
  2. 2.Dept. of Applied MathematicsTel Aviv UniversityTel AvivIsrael

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