How Fast Is Your Body Motion? Determining a Sufficient Frame Rate for an Optical Motion Tracking System Using Passive Markers

This paper addresses how to determine a sufficient frame (sampling) rate for an optical motion tracking system using passive reflective markers. When using passive markers for the optical motion tracking, avoiding identity confusion between the markers becomes a problem as the speed of motion increases, necessitating a higher frame rate to avoid a failure of the motion tracking caused by marker confusions and/or dropouts. Initially, one might believe that the Nyquist-Shannon sampling rate estimated from the assumed maximal temporal variation of a motion (i.e. a sampling rate at least twice that of the maximum motion frequency) could be the complete solution to the problem. However, this paper shows that also the spatial distance between the markers should be taken into account in determining the suitable frame rate of an optical motion tracking with passive markers. In this paper, a frame rate criterion for the optical tracking using passive markers is theoretically derived and also experimentally verified using a high-quality optical motion tracking system. Both the theoretical and the experimental results showed that the minimum frame rate is proportional to the ratio between the maximum speed of the motion and the minimum spacing between markers, and may also be predicted precisely if the proportional constant is known in advance. The inverse of the proportional constant is here defined as the tracking efficiency constant and it can be easily determined with some test measurements. Moreover, this newly defined constant can provide a new way of evaluating the tracking algorithm performance of an optical tracking system.本文探讨了如何为采用被动反射标记点（passive reflective markers）的光学运动捕捉系统确定足够的帧率（采样率）。在使用被动反射标记点进行光学运动捕捉时，随着运动速度提升，避免标记点间的身份混淆会成为一项难题，此时需要更高的帧率以避免因标记点混淆和/或丢失导致的运动捕捉失败。起初，研究者或许会认为，基于假设的运动最大时间变化量估算得到的奈奎斯特-香农采样率（Nyquist-Shannon sampling rate，即采样率至少需为最大运动频率的两倍）可彻底解决该问题。然而本文表明，在确定被动反射标记点光学运动捕捉系统的合适帧率时，还需考虑标记点间的空间间距。本文从理论层面推导了被动反射标记点光学追踪的帧率判定准则，并借助高精度光学运动捕捉系统完成了实验验证。理论与实验结果均显示，最小帧率与运动最大速度和标记点最小间距的比值呈正比；若提前获知该比例常数，还可精准预测最小帧率。本文将该比例常数的倒数定义为追踪效率常数（tracking efficiency constant），仅需少量测试测量即可轻松确定该常数。此外，这一新定义的常数可为评估光学追踪系统的追踪算法性能提供全新思路。