In this paper, we propose a novel framework for dynamical analysis of human actions from 3D motion capture data using topological data analysis. We model human actions using the topological features of the attractor of the dynamical system. We reconstruct the phase-space of time series corresponding to actions using time-delay embedding, and compute the persistent homology of the phase-space reconstruction. In order to better represent the topological properties of the phase-space, we incorporate the temporal adjacency information when computing the homology groups. The persistence of these homology groups encoded using persistence diagrams are used as features for the actions. Our experiments with action recognition using these features demonstrate that the proposed approach outperforms other baseline methods.
In section , we introduce the theoretical concepts of phase-space reconstruction and persistent homology. The feature which encodes the temporal evolution information in the persistence diagrams will be introduced in section . In section , we present our experimental results on the motion capture dataset @cite_28 .
@cite_28
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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.