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.

中文翻译：

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使用几何和功能分析的可解释全身运动学描述框架

具有成本效益和非侵入性的深度传感器的快速进步，以及可靠和实时 3D 骨骼数据估计算法的开发，开辟了计算机视觉的新应用领域——人体运动数据的统计分析，用于快速、自动评估的身体动作。这些评估可以在运动、医疗诊断、物理治疗、老年人监测和相关应用中发挥重要作用。本文开发了一个全面的几何框架，用于运动学特征的量化和统计评估。关键思想是避免像当前范式那样分析单个关节，并将运动表示为全身骨骼形状空间上的时间演变或轨迹。这允许将具有适当不变性属性的度量强加到这些轨迹上，并导致定义更高级别的特征，例如空间对称性 (sS)、时间对称性 (tS)、动作速度 (Vl) 和身体平衡 (Bl)。一个动作的表现。这些功能利用了空间和时间的骨架对称性，并捕捉运动节奏来自然地量化单个对象的运动。将这些特征作为功能数据进行研究使我们能够在特征空间中制定某些假设检验。这反过来又会导致对现有假设的验证以及运动学与人口统计因素（例如年龄、性别和运动训练）之间新关系的发现。我们使用经过临床验证的 K3Da kinect 数据集来说明这些想法，