Surface-marker cluster design criteria for 3-D bone movement reconstruction

When three-dimensional (3-D) human or animal movement is recorded using a photogrammetric system, bone-embedded frame positions and orientations are estimated from reconstructed surface marker trajectories using either nonoptimal or optimal algorithms. The effectiveness of these mathematical procedures in accommodating for both photogrammetric errors and skin movement artifacts depends on the number of markers associated with a given bone as well as on the size and shape characteristics of the relevant cluster. One objective of this paper deals with the identification of marker cluster design criteria aimed at the minimization of error propagation from marker coordinates to bone-embedded frame position and orientation. Findings allow for the quantitative estimation of these errors for any given cluster configuration and suggest the following main design criteria. A cluster made up of four markers represents a good practical compromise. Planar clusters are acceptable, provided in quasi-isotropic distribution. The root mean square distance of the markers from their centroid should be greater than ten times the standard deviation of the marker position error. The second objective of this paper deals with the identification of the optimal cluster position and orientation on the limb aimed at the minimization of error propagation to anatomical landmark laboratory coordinates. Cluster position should be selected to minimize skin movement artifacts. The longest principal axis of the marker distribution should be oriented toward the relevant anatomical landmark position.