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，几何和统计学的基本工具，促进当前对时空对称性的理解和利用，以分析人类运动。这项研究的更广泛应用包括基于家庭或工作场所的日常活动的自我反思，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。虽然需要全面和统计分析人体运动学是很好的编年史，目前的措施往往限于简单的数量，如速度和加速度曲线的个别肢体。该项目将侧重于肢体运动的空间和时间对称性，完整的身体形状和完整的动态动作，用于评估从日常活动到体能锻炼的运动。对称性在过去曾被用于临床生物力学，但以有限的方式。该项目将开发一个全面的理论，建立在微分几何和几何对象的统计分析的基础工具上，根据它们的对称性水平来表示，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。该公式将结合来自各种传感模式和特征的数据，包括来自运动捕捉系统的点轨迹和简笔画，以形成从视频传感器获得的轮廓和动态纹理。该项目的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共同行动，如从坐到站（STS）。该提案汇集了一个强大的跨学科研究人员团队，他们在计算机视觉和动作识别（Turaga），微分几何和统计学（Srivastava）以及体细胞学和运动学（科尔曼）方面具有专业知识。

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).