Skip to main content
Log in

Nonlinear Dynamical Shape Priors for Level Set Segmentation

  • Published:
Journal of Scientific Computing Aims and scope Submit manuscript

Abstract

The introduction of statistical shape knowledge into level set based segmentation methods was shown to improve the segmentation of familiar structures in the presence of noise, clutter or partial occlusions. While most work has been focused on shape priors which are constant in time, it is clear that when tracking deformable shapes certain silhouettes may become more or less likely over time. In fact, the deformations of familiar objects such as the silhouettes of a walking person are often characterized by pronounced temporal correlations.

In this paper, we propose a nonlinear dynamical shape prior for level set based image segmentation. Specifically, we propose to approximate the temporal evolution of the eigenmodes of the level set function by means of a mixture of autoregressive models. We detail how such shape priors “with memory” can be integrated into a variational framework for level set segmentation. As an application, we experimentally validate that the nonlinear dynamical prior drastically improves the tracking of a person walking in different directions, despite large amounts of clutter and noise.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Agarwal, A., Triggs, B.: Tracking articulated motion using a mixture of autoregressive models. In: Europ. Conf. on Computer Vision, vol. 3, pp. 54–65 (2004)

  2. Blake, A., Isard, M.: Active Contours. Springer, Berlin (1998)

    Google Scholar 

  3. Caselles, V., Catté, F., Coll, T., Dibos, F.: A geometric model for active contours in image processing. Numer. Math. 66, 1–31 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  4. Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. In: Proc. IEEE Intl. Conf. on Comp. Vis., pp. 694–699, Boston, USA (1995)

  5. Chan, T.F., Vese, L.A.: A level set algorithm for minimizing the Mumford–Shah functional in image processing. In: IEEE Workshop on Variational and Level Set Methods, pp. 161–168, Vancouver, CA (2001)

  6. Cremers, D.: Dynamical statistical shape priors for level set based tracking. IEEE Trans. Pattern Anal. Mach. Intell. 28(8), 1262–1273 (2006)

    Article  Google Scholar 

  7. Cremers, D.: Nonlinear dynamical shape priors for level set segmentation. In: Int. Conf. on Computer Vision and Pattern Recognition (2007)

  8. Cremers, D., Osher, S.J., Soatto, S.: Kernel density estimation and intrinsic alignment for shape priors in level set segmentation. Int. J. Comput. Vis. 69(3), 335–351 (2006)

    Article  Google Scholar 

  9. Dervieux, A., Thomasset, F.: A finite element method for the simulation of Raleigh–Taylor instability. Lect. Notes Math. 771, 145–158 (1979)

    Article  MathSciNet  Google Scholar 

  10. Kantz, H., Schreiber, T.: Nonlinear Time Series Analysis. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  11. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. Int. J. Comput. Vis. 1(4), 321–331 (1988)

    Article  Google Scholar 

  12. Kichenassamy, S., Kumar, A., Olver, P.J., Tannenbaum, A., Yezzi, A.J.: Gradient flows and geometric active contour models. In: IEEE Int. Conf. on Computer Vision, pp. 810–815 (1995)

  13. Leventon, M., Grimson, W., Faugeras, O.: Statistical shape influence in geodesic active contours. In: Int. Conf. on Computer Vision and Pattern Recognition, vol. 1, pp. 316–323, Hilton Head Island, SC (2000)

  14. Ljung, L.: System Identification—Theory For the User. Prentice Hall, Englewood Cliffs (1999)

    Google Scholar 

  15. Malladi, R., Sethian, J.A., Vemuri, B.C.: A topology independent shape modeling scheme. In: SPIE Conf. on Geometric Methods in Comp. Vision II, vol. 2031, pp. 246–258 (1994)

  16. McInerney, T., Terzopoulos, D.: Topologically adaptable snakes. In: Proc. 5th Int. Conf. on Computer Vision, pp. 840–845. Los Alamitos, California, June 20–23. IEEE Comput. Soc., Los Alamitos (1995)

    Chapter  Google Scholar 

  17. Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42, 577–685 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  18. Osher, S.J., Fedkiw, R.P.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York (2002)

    Google Scholar 

  19. Osher, S.J., Sethian, J.A.: Fronts propagation with curvature dependent speed: Algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79, 12–49 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  20. Paragios, N., Deriche, R.: Geodesic active contours and level sets for the detection and tracking of moving objects. IEEE Trans. Pattern Anal. Mach. Intell. 22(3), 266–280 (2000)

    Article  Google Scholar 

  21. Rousson, M., Paragios, N., Deriche, R.: Implicit active shape models for 3D segmentation in MRI imaging. In: MICCAI. LNCS, vol. 2217, pp. 209–216. Springer, Berlin (2004)

    Google Scholar 

  22. Schwarz, G.: Estimating the dimension of a model. Ann. Stat. 6, 461–464 (1978)

    Article  MATH  Google Scholar 

  23. Sigal, L., Bhatia, S., Roth, S., Black, M., Isard, M.: Tracking loose-limbed people. In: Int. Conf. on Computer Vision and Pattern Recognition, vol. 1, pp. 421–428 (2004)

  24. Sminchisescu, C., Kanaujia, A., Li, Z., Metaxas, D.: Discriminative density propagation for 3D human motion estimation. In: Int. Conf. on Computer Vision and Pattern Recognition, vol. 1, pp. 390–397 (2005)

  25. 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: Comp. Vision Patt. Recog., pp. 463–468, Kauai, Hawaii (2001)

  26. Tsai, A., Yezzi, A.J., Willsky, A.S.: Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification. IEEE Trans. Image Process. 10(8), 1169–1186 (2001)

    Article  MATH  Google Scholar 

  27. Vidal, R., Hashambhoy, Y.: Recursive identification of switched arx models with unknown number of models and unknown orders. In: IEEE Conf. on Decision and Control, December (2005)

  28. Zhu, S.C., Yuille, A.: Region competition: Unifying snakes, region growing, and Bayes/MDL for multiband image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 18(9), 884–900 (1996)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Daniel Cremers.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cremers, D. Nonlinear Dynamical Shape Priors for Level Set Segmentation. J Sci Comput 35, 132–143 (2008). https://doi.org/10.1007/s10915-008-9220-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10915-008-9220-x

Keywords

Navigation