Accuracy of an optical active-marker system to track the relative motion of rigid bodies

Abstract

The measurement of relative motion between two moving bones is commonly accomplished for in vitro studies by attaching to each bone a series of either passive or active markers in a fixed orientation to create a rigid body (RB). This work determined the accuracy of motion between two RBs using an Optotrak optical motion capture system with active infrared LEDs. The stationary noise in the system was quantified by recording the apparent change in position with the RBs stationary and found to be 0.04° and 0.03 mm. Incremental 10° rotations and 10-mm translations were made using a more precise tool than the Optotrak. Increasing camera distance decreased the precision or increased the range of values observed for a set motion and increased the error in rotation or bias between the measured and actual rotation. The relative positions of the RBs with respect to the camera-viewing plane had a minimal effect on the kinematics and, therefore, for a given distance in the volume less than or close to the precalibrated camera distance, any motion was similarly reliable. For a typical operating set-up, a 10° rotation showed a bias of 0.05° and a 95% repeatability limit of 0.67°. A 10-mm translation showed a bias of 0.03 mm and a 95% repeatability limit of 0.29 mm. To achieve a high level of accuracy it is important to keep the distance between the cameras and the markers near the distance the cameras are focused to during calibration.

Introduction

Kinematics of human joints are commonly described by measuring the motion of rigid bodies (RBs) attached to bones and using a sequence of transformation matrices to describe the relative motion (Wu and Cavanagh, 1995). There are many different methods to measure the relative motion of two bones including goniometers, video cameras, electromagnetic sensors, optical devices, and fluoroscopy to name a few. Common electromagnetic kinematic measurement systems are where the position and orientation of a receiver is described relative to a transmitter. At an optimal set-up, translational errors of between 0.2% and 2.0% of step size with a resolution of 0.25 mm, and 0.8% to 2.0% of rotational increment with 0.1° resolution can be obtained (Milne et al., 1996; Bull et al., 1998; Day et al., 1998; Schuler et al., 2005). Metal in the measurement area cause field distortion that decreases the accuracy (Day et al., 1998; Perie et al., 2002) and both the noise increases and the signal quality decreases as the distance between the sensor and transmitter increases beyond the suggested range (Day et al., 1998; Schuler et al., 2005). Optical systems using passive markers typically have a series of cameras that triangulate the position of a retroreflective ball in space. Accuracy values are often cited for markers at fixed distances from each other moving in the viewing volume (Kidder et al., 1996; Ehara et al., 1997; Richards, 1999), for fixed-marker arrays (Zavatsky et al., 2004), and also in vivo configurations (Selfe, 1998). The accuracies of the systems have been shown to be dependent on factors such as the location of the cameras relative to each other (calibration field), the distance from the cameras to the markers, as well as the position within the field and the motion of the markers in the viewing volume (Kidder et al., 1996; Dabnichki et al., 1997). Active marker optical systems use infrared light-emitting diodes (IRED) that are triangulated in space using a set of cameras, typically in a fixed orientation to each other. The accuracy of a single marker position is affected by many parameters such as the distance and the angle from the camera to the marker. RBs are defined from multiple markers in a fixed relationship to each other. Researchers have examined the accuracy of active-marker RBs and found the RMS error to be minimal (States and Pappas, 2006), with values of 0.233 mm and 0.362° (Wiles et al., 2004).

In this study, an Optotrak® 3020 (Northern Digital Inc., Waterloo, Ontario) active-marker optical system was used. As reported by the manufacturer, the RMS accuracy of the system for each individual IRED at 2.25 m was 0.1 mm for the viewing plane of the cameras and 0.15 mm directed towards the cameras (manufacturer's information). The cameras were prefocused by the manufacturer to a predetermined distance and the positional accuracy of the IREDs in the viewing plane of the cameras was reported to be higher than in the direction towards the cameras. The objectives of this study were to quantify how two variables in the experimental set-up influenced the rotational and translational accuracy of the relative position between two RBs: (a) the distance between the cameras and the RBs and (b) the motion of the RBs relative to the cameras.