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.

This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and nonlinear methods with their respective drawbacks. A novel approach we propose is the use of descriptors of the shape of the dynamical attractor as a feature representation of nature of dynamics. The proposed framework has two main advantages over traditional approaches: a) representation of the dynamical system is derived directly from the observational data, without any inherent assumptions, and b) the proposed features show stability under different time-series lengths where traditional dynamical invariants fail. We illustrate our idea using nonlinear dynamical models such as Lorenz and Rossler systems, where our feature representations (shape distribution) support our hypothesis that the local shape of the reconstructed phase space can be used as a discriminative feature. Our experimental analyses on these models also indicate that the proposed framework show stability for different time-series lengths, which is useful when the available number of samples are small/variable. The specific applications of interest in this paper are: 1) activity recognition using motion capture and RGBD sensors, 2) activity quality assessment for applications in stroke rehabilitation, and 3) dynamical scene classification. We provide experimental validation through action and gesture recognition experiments on motion capture and Kinect datasets. In all these scenarios, we show experimental evidence of the favorable properties of the proposed representation.

In this paper, we propose a general framework for tuning component-level kinematic features using therapists' overall impressions of movement quality, in the context of a home-based adaptive mixed reality rehabilitation (HAMRR) system. We propose a linear combination of nonlinear kinematic features to model wrist movement, and propose an approach to learn feature thresholds and weights using high-level labels of overall movement quality provided by a therapist. The kinematic features are chosen such that they correlate with the quality of wrist movements to clinical assessment scores. Further, the proposed features are designed to be reliably extracted from an inexpensive and portable motion capture system using a single reflective marker on the wrist. Using a dataset collected from ten stroke survivors, we demonstrate that the framework can be reliably used for movement quality assessment in HAMRR systems. The system is currently being deployed for large-scale evaluations, and will represent an increasingly important application area of motion capture and activity analysis.

In this paper, we propose a new approach for quantification of ‘dynamical regularity’ as applied to modeling human actions. We use approximate entropy-based feature representation to model the dynamics in human movement to achieve temporal segmentation in untrimmed motion capture data and fine-grained quality assessment of diving actions in videos. The principle herein is to quantify regularity (frequency of typical patterns) in the dynamical space computed from trajectories of action data. We extend conventional ideas for modeling dynamics in human movement by introducing multivariate and cross approximate entropy features. Our experimental evaluation on theoretical models and two publicly available databases show that the proposed features can achieve state-ofthe-art results on applications such as temporal segmentation and quality assessment of actions.