Measurement errors in roentgen-stereophotogrammetric joint motion analysis

Abstract—In many biomechanical motion studies, kinematic parameters are estimated from position measurements on a number of landmarks. In the present investigation, dummy motion experiments are performed in order to study the error dependence of kinematic parameters on geometric factors (number of markers, isotropic vs anisotropic landmark distributions, landmark distribution size), on kinematic factors (rotation step magnitude, the presence of translational displacements, the distance of the landmarks' mean position to the rotation axis), and on anisotropically distributed measurement errors. The experimental results are compared with theoretical predictions of a previous error analysis assuming isotropic conditions for the measurement errors and for the spatial landmark distribution. In general, the experimental findings agree with the predictions of the error model. The kinematic parameters such as translations and rotations are well-determined by the model. In the helical motion description, the same applies for the finite rotation angle about and the finite shift along the helical axis. However, the direction and position of the helical axis are ill-determined. An anisotropic landmark distribution with relatively few markers located in the direction of the rotation axis will even aggravate the ill-posed nature of the finite helical axis estimation