A solidification procedure to facilitate kinematic analyses based on video system data

Abstract

When video-based motion analysis systems are used to measure segmental kinematics, the major source of error is the displacement of skin-fixed markers relative to the underlying skeletal structure. Such displacements cause the marker representation of the segment to deform, thereby decreasing the accuracy of subsequent three-dimensional kinematic calculations. We have developed a two-step solidification procedure to address this problem. First, the mean rigid shape is computed which best represents the time-varying marker configuration of each segment. Second, a least-squares minimization is used to replace the measured marker coordinates with those corresponding to the best-fit mean rigid shape. Rigid body theory can then be applied unambiguously to perform kinematic analyses. To evaluate this approach, we defined an unperturbed three-dimensional reference movement using kinematic data from the swing phase of gait. After perturbing the marker coordinates with artificial noise, the rotation matrix and translation vector (absolute and relative movement) between each pair of successive images were computed using (1) reference frames fixed directly to the perturbed marker coordinates, (2) a least-squares minimization procedure found in the literature, and (3) the proposed solidification procedure. The least-squares and solidification procedures produced extremely similar results which, relative to the direct calculation, reduced kinematic errors on average by 20-25% when the maximum distance between markers was small (e.g. < 15 cm). The solidification methodology therefore combines the numerical benefits of the least-squares method with the conceptual benefits of a rigid body method.