Accuracy of Three-Dimensional Linear and Angular Estimates Obtained With the Ariel Performance Analysis System

Penelope J. Klein, Ed.D., PT, James J. DeHaven, Ph.D.

cpy 1995 by the American Congress of Rehabilitation Medicine and the American Academy of Physical Medicine and Rehabilitation

Table of Contents

1. Introduction
   • Abstract
   • Background
2. Method
   • Instrumentation
   • Procedures
3. Results
4. Discussion
   • Conclusion
   • Acknowledgment
   • References
   • Suppliers

List Of Tables/Figures

Because results of validation studies conducted on one system do not necessarily generalize to other systems, the ideal accuracy of each system requires definition. Studies describing the accuracy of the Ariel Performance Analysis System have been comparatively rare(10). The purpose of the current work is to report determinations of the accuracy and consistency of linear and angular measures obtained using the Ariel Performance Analysis System.

Antonsson and Mann(7) have reported a high-bandwidth, active marker, optoelectronic system for making real-time measurements of position and rotational trajectories of use in both biomechanical and industrial contexts. The researchers described an extensive mapping of nonlinearities in the lenses, detectors, and electronics which, along with careful camera positioning on precision optical benches, allowed the system to meet its original design goals of 1mm positional and 20 milliradians rotational resolution at 3m range, for 10 bodies, sampled at 300Hz. The authors also extensively documented the mathematical procedures used to extract trajectory data in real time, and discussed the advantages of affixing the coordinate system to the segments whose trajectories are to be studied. The overall performance of the system in three dimensions was evaluated by measuring the motion of a pendulum.

Vander Linden and colleagues(6) reported the accuracy of angular and linear measurements obtained under static and dynamic conditions with the Motion Analysis Expert Vision' video system. Two cameras 2.37m apart were placed 1.80m from a calibrated field 1.63m wide x 0.72m deep X 1.27cm high. The authors assessed system accuracy of linear estimates using a protocol similar to the one described by Haggard and Wing.(4) A rigid wooden bar, to which two spherical passive markers were affixed 178.5mm apart, was systematically and then unsystematically moved through the calibrated field. Within-trial variability (defined as the standard deviation) ranged from 1.39mm to 3.04mm. Using a protocol similar to Scholz(5), they assessed 17 angles in 10 deg increments from 20 deg to 180 deg and found that average-within trial variability was less than +/-O.4 deg.

Scholz(5) evaluated the accuracy and consistency of the Watsmart system applied to angular and dynamic measurements. Two wall-mounted cameras were positioned 2m apart and 4m from a measurement field approximately 1.2m wide x 1.2m deep x 1.8m high. Using a standard goniometer, Scholz assessed 12 angles in five-degree increments from 45 deg to 100 deg and found that the 95% confidence interval for each angle was less than +/-0.5 deg. The author noted that reliability and accuracy decreased somewhat as the object was rotated away from the plane of the cameras.

Haggard and Wing 4 studied the accuracy of the Northern Digital's Watsmart optical tracking system applied to linear measurements. The context of their assessment was a reaching activity, and their study included reconstruction and quantitative measures of accuracy. A data acquisition region of 66cm by 66cm in the horizontal or xy-plane was defined. This region was subdivided into nine equal-sized cells. By measuring a 1Ocm rigid bar marked with two miniature infrared emitting diodes (IREDs), the authors assessed the consistency of the estimates generated by the system. The authors reported the standard deviation of the length of the bar to be between 2.1 and 3.4mm and reasonably independent of location. Their proposed methods for assessing accuracy using known reference models are relatively simple to implement, and are applicable to both film and video-based systems.

Previous research 4-9 has described system-specific tests of validity. Parameters of interest have included absolute and relative point estimations, linear, and angular estimations, consistency of measurement throughout a defined data acquisition region, the ability of a system to track a moving object, and estimations of linkage dynamics.

Computer-assisted motion analysis is a method of evaluating human kinematics that offers promise in both research and clinical applications. Because this is a relatively new technology, validation of measurement is fundamental to its use in these areas. Validity is a complex concept. Measurement validity reflects the extent to which an instrument measures what it is intended to measure.(1-3) Although measurement validity is context-specific, the definition of the upper limits of accuracy of a particular measurement instrument provides the researcher or clinician with critical information to assist in making judgments regarding the degree to which inferences can be drawn from measurement data.

Computer-assisted video motion analysis is a method of evaluating human kinematics that offers promise both for research and for clinical application. This study determined the upper limits of accuracy and consistency of linear and angular measures obtained using the Ariel Performance Analysis System. Reference standards included a meter stick and a universal 360 deg goniometer. Average mean error observed for reconstruction of absolute point estimates was found to be less than 3.5mm. Mean error estimate for three-dimensional (3D) reconstruction of a linear standard was found to be 1.4mm (SD 0.30). Average mean angular error observed for 3D reconstruction of goniometer settings 10 deg to 170 deg was found to be 0.26 deg (mean SD 0.21). System users are cautioned that some increased error associated with software derivation of joint angles exists as angles approach 180 deg, use of wide-angle lens accessories introduces a systematic field-dependent bias; and planar rotation introduces some (less than 2 deg) random error.

ABSTRACT. Klein Pj, DeHaven Jj. Accuracy of three-dimensional linear and angular estimates obtained with the Ariel performance analysis system. Arch Phys Med Rehabil 1995;76:183-9.