Static and Dynamic Accuracy Determination of a Three Dimensional Motion Analysis System
ABSTRACT: Video motion analysis techniques are used in various applications to determine the three-dimensional kinematics of objects in motion. The typical procedure first determines the position of the cameras and the coefficients for the Direct Linear Transformation (DLT) method of Abdel-Aziz and Karara, (1971) using images of control points with known positions. Then the digitized images of a tracked target from multiple cameras are reconstructed with the DLT to obtain three-dimensional space coordinates. The purpose of this study was to determine the accuracy of this procedure for a four-camera video motion analysis system and to investigate the possible causes of any systematic errors in the process. Sixteen control points enclosing a three-dimensional control volume of 8m x 6m x 3m were surveyed to an accuracy of 2.1 mm and were used to determine the positions of the four cameras. As a measure of static accuracy, some of the same control points were digitized at 60 Hz and compared statistically to the known survey results. A dynamic accuracy study was conducted by comparing the theoretical trajectory of a spherical pendulum moving in various types of motion to experimental 60 Hz digitized data. Studies were carried out in various lighting conditions and with different threshold values for the digitization. In the static tests the known "model" was that the objects were motionless. In the dynamic tests, a spherical pendulum was chosen for its fully three-dimensional, yet highly precisely known, motion. Its dynamic model included the effects of aerodynamic drag on both the bob and suspending wire, an accurate determination of gravity, the rotational effects of the earth, and accurately measured physical properties of the bob and wire. The initial conditions and other imprecisely known quantities were determined using the parameter estimation techniques of Hubbard and Alaways (1989). The results of the study show that great care must be taken, not only in data collection, but also in determining control point locations, lighting conditions and threshold values.