Chaotic Invariants for Human Action Recognition

The paper introduces an action recognition framework that uses concepts from the theory of chaotic systems to model and analyze nonlinear dynamics of human actions. Trajectories of reference joints are used as the representation of the non-linear dynamical system that is generating the action. Each trajectory is then used to reconstruct a phase space of appropriate dimension by employing a delay-embedding scheme. The properties of the reconstructed phase space are captured in terms of dynamical and metric invariants that include Lyapunov exponent, correlation integral and correlation dimension. Finally, the action is represented by a feature vector which is a combination of these invariants over all the reference trajectories. Our contributions in this paper include :1) investigation of the appropriateness of theory of chaotic systems for human action modelling and recognition, 2) a new set of features to characterize nonlinear dynamics of human actions, 3) experimental validation of the feasibility and potential merits of carrying out action recognition using methods from theory of chaotic systems.

[1]  Michael J. Black,et al.  Parameterized Modeling and Recognition of Activities , 1999, Comput. Vis. Image Underst..

[2]  Ivan Laptev,et al.  On Space-Time Interest Points , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[3]  Ronen Basri,et al.  Actions as space-time shapes , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[4]  James W. Davis,et al.  An appearance-based representation of action , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[5]  G. Williams.  Chaos theory tamed , 1997 .

[6]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[7]  Takeo Kanade,et al.  Shape-from-silhouette of articulated objects and its use for human body kinematics estimation and motion capture , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[8]  Stefano Soatto,et al.  Recognition of human gaits , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[9]  Mubarak Shah,et al.  Actions sketch: a novel action representation , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[10]  Michael Isard,et al.  Learning and Classification of Complex Dynamics , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Christoph Bregler,et al.  Learning and recognizing human dynamics in video sequences , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[12]  Rama Chellappa,et al.  View Invariance for Human Action Recognition , 2005, International Journal of Computer Vision.

[13]  Aaron F. Bobick,et al.  Recognition of human body motion using phase space constraints , 1995, Proceedings of IEEE International Conference on Computer Vision.

[14]  Eli Shechtman,et al.  Space-time behavior based correlation , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[15]  Jitendra Malik,et al.  Recognizing action at a distance , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[16]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[17]  M. Perc.  The dynamics of human gait , 2005 .

[18]  M. Rosenstein,et al.  A practical method for calculating largest Lyapunov exponents from small data sets , 1993 .

[19]  L. Cao.  Practical method for determining the minimum embedding dimension of a scalar time series , 1997 .

[20]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[21]  Vladimir Pavlovic,et al.  Impact of dynamic model learning on classification of human motion , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[22]  Jitendra Malik,et al.  Recovering human body configurations: combining segmentation and recognition , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[23]  Liva Ralaivola,et al.  Dynamical Modeling with Kernels for Nonlinear Time Series Prediction , 2003, NIPS.

[24]  Ze-Nian Li,et al.  Successive Convex Matching for Action Detection , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

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