Advertisement

A Unified Algebraic Approach to 2-D and 3-D Motion Segmentation

  • René Vidal
  • Yi Ma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3021)

Abstract

We present an analytic solution to the problem of estimating multiple 2-D and 3-D motion models from two-view correspondences or optical flow. The key to our approach is to view the estimation of multiple motion models as the estimation of a single multibody motion model. This is possible thanks to two important algebraic facts. First, we show that all the image measurements, regardless of their associated motion model, can be fit with a real or complex polynomial. Second, we show that the parameters of the motion model associated with an image measurement can be obtained from the derivatives of the polynomial at the measurement. This leads to a novel motion segmentation algorithm that applies to most of the two-view motion models adopted in computer vision. Our experiments show that the proposed algorithm outperforms existing algebraic methods in terms of efficiency and robustness, and provides a good initialization for iterative techniques, such as EM, which is strongly dependent on correct initialization.

Keywords

Expectation Maximization Motion Model Image Pair Image Measurement Algebraic Approach 
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.
    Darrel, T., Pentland, A.: Robust estimation of a multi-layered motion representation. In: IEEE Workshop on Visual Motion, pp. 173–178 (1991)Google Scholar
  2. 2.
    Jepson, A., Black, M.: Mixture models for optical flow computation. In: CVPR, pp. 760–761 (1993)Google Scholar
  3. 3.
    Ayer, S., Sawhney, H.: Layered representation of motion video using robust maximum-likelihood estimation of mixture models and MDL encoding. In: ICCV, pp. 777–785 (1995)Google Scholar
  4. 4.
    Weiss, Y.: Smoothness in layers: Motion segmentation using nonparametric mixture estimation. In: CVPR, pp. 520–526 (1997)Google Scholar
  5. 5.
    Shi, J., Malik, J.: Motion segmentation and tracking using normalized cuts. In: ICCV, pp. 1154–1160 (1998)Google Scholar
  6. 6.
    Torr, P., Szeliski, R., Anandan, P.: An integrated Bayesian approach to layer extraction from image sequences. IEEE Transactions on Pattern Analysis and Machine Intelligence 23, 297–303 (2001)CrossRefGoogle Scholar
  7. 7.
    Wang, J., Adelson, E.: Layered representation for motion analysis. In: CVPR, pp. 361–366 (1993)Google Scholar
  8. 8.
    Feng, X., Perona, P.: Scene segmentation from 3D motion. In: CVPR, pp. 225–231 (1998)Google Scholar
  9. 9.
    Vidal, R., Sastry, S.: Segmentation of dynamic scenes from image intensities. In: IEEE Workshop on Vision and Motion Computing, pp. 44–49 (2002)Google Scholar
  10. 10.
    Costeira, J., Kanade, T.: Multi-body factorization methods for motion analysis. In: ICCV, pp. 1071–1076 (1995)Google Scholar
  11. 11.
    Kanatani, K.: Motion segmentation by subspace separation and model selection. In: ICCV, pp. 586–591 (2001)Google Scholar
  12. 12.
    Vidal, R., Ma, Y., Sastry, S.: Generalized principal component analysis (GPCA). In: CVPR, pp. 621–628 (2003)Google Scholar
  13. 13.
    Wolf, L., Shashua, A.: Two-body segmentation from two perspective views. In: CVPR, pp. 263–270 (2001)Google Scholar
  14. 14.
    Vidal, R., Ma, Y., Soatto, S., Sastry, S.: Two-view multibody structure from motion. To appear in International Journal of Computer Vision (2004)Google Scholar
  15. 15.
    Vidal, R., Ma, Y., Piazzi, J.: A new GPCA algorithm for clustering subspaces by itting, differentiating and dividing polynomials. In: CVPR (2004)Google Scholar
  16. 16.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • René Vidal
    • 1
    • 2
  • Yi Ma
    • 3
  1. 1.Center for Imaging ScienceJohns Hopkins UniversityBaltimoreUSA
  2. 2.National ICT AustraliaCanberraAustralia
  3. 3.Dept. of Elect. and Comp. Eng.UIUCUrbanaUSA

Personalised recommendations