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Nonparametric Density Estimation with Adaptive, Anisotropic Kernels for Human Motion Tracking

  • Thomas Brox
  • Bodo Rosenhahn
  • Daniel Cremers
  • Hans-Peter Seidel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4814)

Abstract

In this paper, we suggest to model priors on human motion by means of nonparametric kernel densities. Kernel densities avoid assumptions on the shape of the underlying distribution and let the data speak for themselves. In general, kernel density estimators suffer from the problem known as the curse of dimensionality, i.e., the amount of data required to cover the whole input space grows exponentially with the dimension of this space. In many applications, such as human motion tracking, though, this problem turns out to be less severe, since the relevant data concentrate in a much smaller subspace than the original high-dimensional space. As we demonstrate in this paper, the concentration of human motion data on lower-dimensional manifolds, approves kernel density estimation as a transparent tool that is able to model priors on arbitrary mixtures of human motions. Further, we propose to support the ability of kernel estimators to capture distributions on low-dimensional manifolds by replacing the standard isotropic kernel by an adaptive, anisotropic one.

Keywords

Training Sample Gaussian Mixture Model Kernel Density Human Motion Previous Frame 
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.

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References

  1. 1.
    Akaike, H.: An approximation to the density function. Annals of the Institute of Statistical Mathematics 6, 127–132 (1954)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Brox, T., Rosenhahn, B., Kersting, U., Cremers, D.: Nonparametric density estimation for human pose tracking. In: Franke, K., Müller, K.R., Nickolay, B., Schäfer, R. (eds.) Pattern Recognition. LNCS, vol. 4174, pp. 546–555. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    CMU. Carnegie-Mellon Motion Capture Database. http://mocap.cs.cmu.edu
  4. 4.
    Cremers, D., Kohlberger, T., Schnörr, C.: Shape statistics in kernel space for variational image segmentation. Pattern Recognition 36(9), 1929–1943 (2003)zbMATHCrossRefGoogle Scholar
  5. 5.
    Grochow, K., Martin, S.L., Hertzmann, A., Popović, Z.: Style-based inverse kinematics. ACM Transactions on Graphics (Proc. SIGGRAPH) 23, 522–531 (2004)CrossRefGoogle Scholar
  6. 6.
    Herda, L., Urtasun, R., Fua, P.: Implicit surface joint limits to constrain video-based motion capture. In: Pajdla, T., Matas, J. (eds.) ECCV 2004. LNCS, vol. 3022, pp. 405–418. Springer, Heidelberg (2004)Google Scholar
  7. 7.
    Howe, N., Leventon, M., Freeman, W.: Bayesian reconstruction of 3D human motion from single-camera video. In: Proc. Neural Information Processing Systems, pp. 820–826 (2000)Google Scholar
  8. 8.
    Jacobs, R.A., Jordan, M.I., Nowlan, S.J., Hinton, G.E.: Adaptive mixtures of local experts. Neural Computation 3, 79–87 (1991)CrossRefGoogle Scholar
  9. 9.
    Moeslund, T.B., Hilton, A., Krüger, V.: A survey of advances in vision-based human motion capture and analysis. Computer Vision and Image Understanding 104(2), 90–126 (2006)CrossRefGoogle Scholar
  10. 10.
    Parzen, E.: On the estimation of a probability density function and the mode. Annals of Mathematical Statistics 33, 1065–1076 (1962)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Rosales, R., Sclaroff, S.: Learning body pose via specialized maps. In: Proc. Neural Information Processing Systems (2001)Google Scholar
  12. 12.
    Rosenblatt, F.: Remarks on some nonparametric estimates of a density function. Annals of Mathematical Statistics 27, 832–837 (1956)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Rosenhahn, B., Brox, T., Weickert, J.: Three-dimensional shape knowledge for joint image segmentation and pose tracking. International Journal of Computer Vision 73(3), 243–262 (2007)CrossRefGoogle Scholar
  14. 14.
    Sain, S.R.: Multivariate locally adaptive density estimation. Computational Statistics & Data Analysis 39(2), 165–186 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Scott, D.: Multivariate Density Estimation. Wiley, Chichester (1992)zbMATHGoogle Scholar
  16. 16.
    Sidenbladh, H., Black, M.J., Sigal, L.: Implicit probabilistic models of human motion for synthesis and tracking. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2353, pp. 784–800. Springer, Heidelberg (2002)Google Scholar
  17. 17.
    Sminchisescu, C., Jepson, A.: Generative modeling for continuous non-linearly embedded visual inference. In: Proc.International Conference on Machine Learning (2004)Google Scholar
  18. 18.
    Sminchisescu, C., Kanaujia, A., Metaxas, D.: Learning joint top-down and bottom-up processes for 3D visual inference. In: Proc. International Conference on Computer Vision and Pattern Recognition, pp. 1743–1752 (2006)Google Scholar
  19. 19.
    Sminchisescu, C., Triggs, B.: Estimating articulated human motion with covariance scaled sampling. International Journal of Robotics Research 22(6), 371–391 (2003)CrossRefGoogle Scholar
  20. 20.
    Urtasun, R., Fleet, D.J., Fua, P.: 3D people tracking with Gaussian process dynamical models. In: Proc. International Conference on Computer Vision and Pattern Recognition, pp. 238–245. IEEE Computer Society Press, Los Alamitos (2006)Google Scholar
  21. 21.
    Vincent, P., Bengio, Y.: Manifold parzen windows. In: Proc. Neural Information Processing Systems, vol. 15, pp. 825–832 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Thomas Brox
    • 1
  • Bodo Rosenhahn
    • 2
  • Daniel Cremers
    • 1
  • Hans-Peter Seidel
    • 2
  1. 1.Computer Vision Group, University of Bonn, Römerstr. 164, 53117 BonnGermany
  2. 2.Max Planck Center for Visual Computing and Communication, Stuhlsatzenhausweg 85, 66123 SaarbrückenGermany

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