Optimization and smoothing techniques in movement analysis

This paper deals with accurate estimation of the degrees of freedom (DOF) of a body segment, starting from the trajectories of clusters of markers acquired with a suitable measurement system. The most commonly employed estimation procedures involve two sequential steps, a trajectory smoothing algorithm and a DOF reconstruction routine. Three optimized smoothing and reconstruction schemes are described, analyzed and tested and their performances are compared with each other and with those of a more traditional technique which contains no optimization criteria. All three schemes include an iterative, weighted-least-squares DOF reconstruction routine and a self-tuning, zero-phase-shift, 4th-order Butterworth filter. Both routines are extensively described and validated on the basis of numerically-simulated marker trajectories. Test results, analyzed on a statistical basis, show that the use of an optimization routine provides a visible improvement in DOF reconstruction. This performance has also been confirmed using stereophotogrammetric data collected on a subject wearing an external fracture fixation device which provides reference values for the bone DOF. Angular DOF estimated applying the optimized method to skin technical clusters are much closer to the reference values than the non-optimized values. Smoothing of data further improves the reconstruction accuracy while a far less crucial role is played by the order in which smoothing and reconstruction routines are applied.