Impact of Dynamics on Subspace Embedding and Tracking of Sequences

In this paper we study the role of dynamics in dimensionality reduction problems applied to sequences. We propose a new family of marginal auto-regressive (MAR) models that describe the space of all stable auto-regressive sequences, regardless of their specific dynamics. We apply the MAR class of models as sequence priors in probabilistic sequence subspace embedding problems. In particular, we consider a Gaussian process latent variable approach to dimensionality reduction and show that the use of MAR priors may lead to better estimates of sequence subspaces than the ones obtained by traditional non-sequential priors. We then propose a learning method for estimating nonlinear dynamic system (NDS) models that utilizes the new MAR priors. The utility of the proposed methods is demonstrated on several synthetic datasets as well as on the task of tracking 3D articulated figures in monocular image sequences.

[1]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[2]  David Barber,et al.  Bayesian Classification With Gaussian Processes , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Aaron Hertzmann,et al.  Style-based inverse kinematics , 2004, SIGGRAPH 2004.

[4]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[5]  Aaron Hertzmann,et al.  Style-based inverse kinematics , 2004, ACM Trans. Graph..

[6]  Cristian Sminchisescu,et al.  Conditional Visual Tracking in Kernel Space , 2005, NIPS.

[7]  David J. Fleet,et al.  Priors for people tracking from small training sets , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[8]  Rómer Rosales,et al.  Specialized mappings and the estimation of human body pose from a single image , 2000, Proceedings Workshop on Human Motion.

[9]  Cristian Sminchisescu,et al.  Discriminative density propagation for 3D human motion estimation , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[10]  David J. Fleet,et al.  Gaussian Process Dynamical Models , 2005, NIPS.

[11]  Neil D. Lawrence,et al.  Gaussian Process Latent Variable Models for Visualisation of High Dimensional Data , 2003, NIPS.

[12]  A. Elgammal,et al.  Inferring 3D body pose from silhouettes using activity manifold learning , 2004, CVPR 2004.

[13]  Rui Li,et al.  Articulated Pose Estimation in a Learned Smooth Space of Feasible Solutions , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Workshops.

[14]  B. Triggs,et al.  3D human pose from silhouettes by relevance vector regression , 2004, CVPR 2004.

[15]  Mikhail Belkin,et al.  Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.

[16]  Matthew Brand,et al.  Shadow puppetry , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[17]  Cristian Sminchisescu,et al.  Generative modeling for continuous non-linearly embedded visual inference , 2004, ICML.

[18]  David J. Fleet,et al.  This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE Gaussian Process Dynamical Model , 2007 .

[19]  Qiang Wang,et al.  Learning object intrinsic structure for robust visual tracking , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[20]  Ankur Agarwal,et al.  3D human pose from silhouettes by relevance vector regression , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..