CIF: Small: Collaborative Research: Geometrical and Statistical Modeling of Space-Time symmetries for Human Action Analysis and Retraining

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This interdisciplinary research aims to advance current understanding and utilization of space-time symmetries in analyzing human movements, using fundamental tools from engineering, geometry, and statistics. Broader applications of this research include home or workplace-based self-reflection of daily activities, promotion of higher efficiency of human movements, and long-term management and/or prevention of movement disorders. While the need for comprehensively and statistically analyzing human kinematics is well chronicled, the current measures are often limited to simplistic quantities such as speeds and acceleration profiles of individual limbs. This project will focus on both spatial and temporal symmetries of limb movements, full body shapes, and complete dynamical actions, for assessment of movements ranging from daily activities to physiotherapeutic exercises. Symmetry has been used in the past, in clinical biomechanics, but in a limited way. This project will develop a comprehensive theory, built on fundamental tools from differential geometry and statistical analysis of geometric objects, to represent, quantify, analyze, and classify motions according to their level of symmetry. The specific forms of symmetry will include spatial reflection, temporal reflection, and space-time glide symmetries. This formulation will incorporate data from various sensing modalities and features, including point trajectories and stick figures from motion capture systems, to shape silhouettes and dynamic textures obtained from video sensors. The project outcomes also include the development of a real-time media-system for movement re-training and reflection of common actions, such as sitting to standing (STS). The proposal brings together a strong and inter-disciplinary team of researchers with expertise in computer vision and action recognition (Turaga), differential geometry and statistics (Srivastava), and somatics and kinesiology (Coleman).