CAREER: Role of geometry in dynamical modeling of human movement: Applications to activity quality assessment across Euclidean, non-Euclidean, and function spaces

职业：几何在人体运动动态建模中的作用：在欧几里德、非欧和功能空间的活动质量评估中的应用

• 批准号: 1452163
• 负责人: Pavan Turaga
• 金额: $ 53.6万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-06-15 至 2022-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1452163&HistoricalAwards=false
• 关键词: CAREER; Role; geometry; dynamical; modeling

Human movement is a complex multi-dimensional dynamical process arising out of complex non-linear interactions between various muscles and joints as well as interactions with external forces and objects. These physical factors often impose certain analytical constraints on movement data obtained from external sensors, often with associated geometric representations. Examples of such representations abound in the area of human activity analysis, where several contemporary and emerging human shape and movement representations such as silhouettes, stick-figure sequences, orientation signals, and optical- flow have intricate signal spaces, often described in the language of Riemannian geometry. The research thrusts focus on foundational methods for extracting meaningful dynamical attributes that will dovetail into the application thrust. The application centers on computational modeling of qualities of physical activities from low-fidelity sensing infrastructure, which is an important component for technology-mediated physical rehabilitation and preventive interventions. Classical vector-valued signal processing and machine learning has had a large impact in the area of understanding and modeling human activities, but their applicability is significantly limited when it comes to signal-spaces with non-Euclidean geometry. This research project aims to advance a new class of robust, non-parametric dynamical modeling approaches, which will extend from classical vector-valued observation spaces, to finite-dimensional Riemannian manifolds, as well as to infinite-dimensional function-spaces. In order to be general enough to account for various geometric spaces as mentioned here, a framework that is free of restrictive assumptions on parametric forms of dynamics is needed. Further, integrating dynamical analysis with Riemannian geometric theory allows the analysis to extend to several feature spaces including depth maps, shape sequences, stick-figures, and orientation data, without re-defining the fundamental models for activity analysis.

人体运动是一个复杂的多维动力学过程，它是由各种肌肉和关节之间复杂的非线性相互作用以及与外力和物体的相互作用引起的。这些物理因素通常对从外部传感器获得的运动数据施加某些分析约束，通常具有相关联的几何表示。这样的表示的示例在人类活动分析的领域中比比皆是，其中若干当代和新兴的人类形状和运动表示（诸如轮廓、简笔画序列、取向信号和光流）具有复杂的信号空间，通常以黎曼几何的语言描述。 研究重点集中在基础方法提取有意义的动态属性，将衔接到应用程序的推力。该应用程序集中在低保真传感基础设施的身体活动质量的计算建模上，这是技术介导的身体康复和预防干预的重要组成部分。经典的向量值信号处理和机器学习在理解和建模人类活动方面产生了很大的影响，但当涉及到非欧几里德几何的信号空间时，它们的适用性受到了极大的限制。该研究项目旨在提出一类新的鲁棒的非参数动力学建模方法，该方法将从经典的向量值观测空间扩展到有限维黎曼流形以及无限维函数空间。为了足够一般地解释这里提到的各种几何空间，需要一个框架，该框架不受动力学参数形式的限制性假设的约束。此外，将动态分析与黎曼几何理论相结合，可以将分析扩展到几个特征空间，包括深度图、形状序列、条形图和方向数据，而无需重新定义活动分析的基本模型。