A Framework for Interpretable Full-Body Kinematic Description using Geometric and Functional Analysis.

Rapid advances in cost-effective and non-invasive depth sensors, and the development of reliable and real-time 3D skeletal data estimation algorithms, have opened up a new application area in computer vision - statistical analysis of human kinematic data for fast, automated assessment of body movements. These assessments can play important roles in sports, medical diagnosis, physical therapy, elderly monitoring and related applications. This paper develops a comprehensive geometric framework for quantification and statistical evaluation of kinematic features. The key idea is to avoid analysis of individual joints, as is the current paradigm, and represent movements as temporal evolutions, or trajectories, on shape space of full body skeletons. This allows metrics with appropriate invariance properties to be imposed on these trajectories and leads to definitions of higher-level features, such as spatial symmetry (sS), temporal symmetry (tS), action's velocity (Vl) and body's balance (Bl), during performance of an action. These features exploit skeletal symmetries in space and time, and capture motion cadence to naturally quantify motions of individual subjects. The study of these features as functional data allows us to formulate certain hypothesis tests in feature space. This, in turn, leads to validation of existing assumptions and discoveries of new relationships between kinematics and demographic factors, such as age, gender, and athletic training. We use the clinically validated K3Da kinect dataset to illustrate these ideas, and hope these tools will lead to discovery of new relationships between full body kinematic features and demographic, health, and wellness factors that are clinically relevant.