Advertisement

Evolutionary fronts for topology-independent shape modeling and recovery

  • R. Malladi
  • J. A. Sethian
  • B. C. Vemuri
Geometry and Shape I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 800)

Abstract

This paper presents a novel framework for shape modeling and shape recovery based on ideas developed by Osher & Sethian for interface motion. In this framework, shapes are represented by propagating fronts, whose motion is governed by a “Hamilton-Jacobi” type equation. This equation is written for a function in which the interface is a particular level set. Unknown shapes are modeled by making the front adhere to the object boundary of interest under the influence of a synthesized halting criterion. The resulting equation of motion is solved using a narrow-band algorithm designed for rapid front advancement. Our techniques can be applied to model arbitrarily complex shapes, which include shapes with significant protrusions, and to situations where no a priori assumption about the object's topology can be made. We demonstrate the scheme via examples of shape recovery in 2D and 3D from synthetic and low contrast medical image data.

Keywords

Shape Modeling Object Boundary Shape Recovery Front Propagation Deformable 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.

References

  1. 1.
    D. Adalsteinsson and J. A. Sethian, “A fast level set method for propagating interfaces,” submitted for publication, Journal of Computational Physics, 1994.Google Scholar
  2. 2.
    R. M. Bolle and B. C. Vemuri, “On three-dimensional surface reconstruction methods,” IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. PAMI 13, No. 1, pp. 1–13, 1991.Google Scholar
  3. 3.
    T.E. Boult and J.R. Kender, “Visual surface reconstruction using sparse depth data,” in Proc. IEEE Conf. on Computer Vision and Pattern Recognition, June 1986, pp. 68–76.Google Scholar
  4. 4.
    A. Blake and A. Zisserman, Visual Reconstruction, MIT Press, Cambridge, MA.Google Scholar
  5. 5.
    L. D. Cohen, “On Active Contour Models and Balloons,” Computer Vision, Graphics, and Image Processing, Vol. 53, No. 2, pp. 211–218, March 1991.Google Scholar
  6. 6.
    H. Delingette, M. Hebert, and K. Ikeuchi, “Shape representation and image segmentation using deformable models,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pp. 467–472, Maui Hawaii, June 1991.Google Scholar
  7. 7.
    W. T. Freeman and E. H. Adelson, “Steerable filters for early vision, image analysis, and wavelet decomposition,” in Proceedings of ICCV, pp. 406–415, Osaka, Japan, 1990.Google Scholar
  8. 8.
    M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active Contour Models,” International Journal of Computer Vision, pp. 321–331, 1988.Google Scholar
  9. 9.
    D. Lee and T. Pavlidis, “One-dimensional regularization with discontinuities,” IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. PAMI 10, pp. 822–829, 1986.Google Scholar
  10. 10.
    R. Malladi, J. A. Sethian, and B. C. Vemuri, “Shape modeling with front propagation: A level set approach,” to appear in IEEE Trans. on Pattern Analysis and Machine Intelligence.Google Scholar
  11. 11.
    R. Malladi, J. A. Sethian, and B. C. Vemuri, “A fast level set based algorithm for topology-independent shape modeling,” to appear in the Journal of Mathematical Imaging & Vision, special issue on Topology & Geometry in Computer Vision.Google Scholar
  12. 12.
    S. Osher and J. A. Sethian, “Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulation,” Journal of Computational Physics, Vol. 79, pp. 12–49, 1988.Google Scholar
  13. 13.
    L.L. Schumaker, “Fitting Surfaces to Scattered data,” in Approximation Theory II, G.G. Lorentz, C.K. Chui, and L.L. Schumaker, (eds.). New York: Academic Press, 1976, pp. 203–267.Google Scholar
  14. 14.
    J. A. Sethian, “Curvature and the evolution of fronts,” Commun. in Mathematical Physics, Vol. 101, pp. 487–499, 1985.Google Scholar
  15. 15.
    J. A. Sethian, “Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws,” Journal of Differential Geometry, Vol. 31, pp. 131–161, 1990.Google Scholar
  16. 16.
    R. Szeliski and D. Tonnesen, “Surface modeling with oriented particle systems,” Computer Graphics SIGGRAPH, Vol. 26, No. 2, pp. 185–194, July 1992.Google Scholar
  17. 17.
    D. Terzopoulos, “Regularization of inverse visual problems involving discontinuities,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. PAMI 8, No. 2, pp. 413–424, 1986.Google Scholar
  18. 18.
    D. Terzopoulos, A. Witkin, and M. Kass, “Constraints on deformable models: Recovering 3D shape and nonrigid motion,” Artificial Intelligence, 36, pp. 91–123, 1988.Google Scholar
  19. 19.
    B. C. Vemuri and R. Malladi, “Intrinsic Parameters for Surface Representation using Deformable Models,” in IEEE Trans. on Systems, Man & Cybernetics, Vol. 23, No. 2, pp. 614–623, March/April 1993.Google Scholar
  20. 20.
    B. C. Vemuri and R. Malladi, “Constructing intrinsic parameters with active models for invariant surface reconstruction,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 15, No. 7, pp. 668–681, July 1993.Google Scholar
  21. 21.
    B. C. Vemuri, A. Mitiche, and J. K. Aggarwal, “Curvature-based representation of objects from range data,” Int. Journal of Image and Vision Computing, 4, pp. 107–114, 1986.Google Scholar
  22. 22.
    Y. F. Wang and J. F. Wang, “Surface reconstruction using deformable models with interior and boundary constraints,” in Proceedings of ICCV, pp. 300–303, Osaka, Japan, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • R. Malladi
    • 1
  • J. A. Sethian
    • 1
  • B. C. Vemuri
    • 2
  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.University of FloridaGainesvilleUSA

Personalised recommendations