A framework for measuring TRE at the tip of an optically tracked pointing stylus

Abstract

We describe a framework for measuring TRE at the tip of an optically tracked pointing stylus. Our approach relied on a robotic manipulator equipped with a spherical wrist to collect large amounts of tracking data from well defined paths. Fitting the tracking data to planes, circles, and spheres allowed us to derive estimates of FLE and precisely localize target locations. A preliminary analysis of our data suggested that there was bias in the registered pointer tip location that depended on the tilt angle of the coordinate reference frame with respect to the tracking system. 1. PURPOSE The purpose of our work is to develop a framework for empirically determining the precision of an optical tracking system in terms of fiducial localization error (FLE) and target registration error (TRE) 1 so that theoretical models of the behavior of TRE 2‐7 can be validated or refuted. In this report, we are primarily interested in describing the framework, reporting on the consistency of the measurements, and reporting the results of measuring TRE as a function of the angle between a tracked coordinate reference frame (CRF) and the viewing direction of the tracking system. Our approach is designed to measure FLE of markers on a CRF and TRE at the tip of a tracked and calibrated pointing stylus; TRE models have previously been used to model such errors. 7, 8 FLE is present in the tracking system measurements of the CRF attached to the pointing device, which induces a TRE at the tip of the pointing device when the calibrated tip location is transformed into the tracking system coordinate frame. If FLE is anisotropic with the largest component oriented along the viewing direction of the tracking system, then the predicted RMS TRE decreases as the CRF is tilted towards and away from the tracking cameras; 7 this is contrary to most users’ expectations, and one empirical study of TRE suggest that TRE at the tip of a pointer is smallest when “the largest possible surface area of the pointer’s reflecting ball is directed toward the camera”. 9