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

这项跨学科的研究旨在利用工程学、几何学和统计学的基本工具，促进对时空对称性在分析人体运动中的当前理解和利用。这项研究的更广泛的应用包括以家庭或工作场所为基础的日常活动的自我反省，促进人类运动的更高效率，以及长期管理和/或预防运动障碍。虽然对人体运动学进行全面和统计分析的需要已经有了很好的记载，但目前的测量往往局限于简单的数量，如单个肢体的速度和加速度分布。该项目将专注于肢体运动的空间和时间对称性、全身形状和完整的动力学动作，以评估从日常活动到理疗练习的各种运动。对称性在过去曾在临床生物力学中使用过，但使用的方式有限。这个项目将开发一个全面的理论，建立在几何对象的微分几何和统计分析的基本工具的基础上，根据运动的对称程度来表示、量化、分析和分类运动。对称的具体形式包括空间反射、时间反射和时空滑动对称。该公式将包括来自各种传感模式和功能的数据，包括来自运动捕获系统的点轨迹和棒状图形，以塑造从视频传感器获得的轮廓和动态纹理。项目成果还包括开发一个实时媒体系统，用于运动再培训和反映坐到站(STS)等共同行动。该提案汇集了一支强大的跨学科研究团队，他们拥有计算机视觉和动作识别(Turaga)、微分几何和统计学(Sriastava)以及躯体和运动学(Coleman)方面的专业知识。

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).