In the last two decades, numerous human movement scientists faced the problem of the in vivo and non-invasive reconstruction of the skeletal movement from measures of the 3D position of points located on the human body surface. To this purpose, the estimation of the pose (position and orientation) of skeletal bones is required. In order to determine the pose of a bone, the definition of a reference frame (RF) attached to it, typically an orthogonal RF defined by bone anatomical landmarks (ALs), is required (anatomical RF). In order to gain more freedom in positioning the markers on the body segment, a technical RF is often identified from the position of the markers attached to the body segment. In this case, the rigid body transformation parameters between the two systems of axes can be obtained with a calibration procedure of the bone ALs .
Three sources of errors typically affect the in vivo estimation of the pose of a skeletal bone when non invasive techniques are used: instrumental errors, soft tissues artifacts and AL mislocation. Reviews of such sources of errors and their effect on joint kinematics were recently published [2–5]. Numerous techniques have been proposed to reduce the effect of one or more of these sources of error. Some of them were based on marker attachment devices , others were based on computational methods. The latest motion capture technology allows the positioning of a high number of markers on all sides of the surface of each body segment, thus facilitating the use of redundant markers attached directly to the subject skin, which renders in some cases the use of attachment devices obsolete. The same consensus has not been reached yet in the determination of an "optimal" computational method for the determination of the bone pose when the above mentioned sources of error are present.
Skeletal bone pose has been determined from marker positions using various methods including geometrical and optimal. Usually the geometrical pose estimators do not make use of redundant information included in the marker position. Typically, an axis of the RF is defined as the oriented line passing through two of the markers attached to the body segment, a second is defined as the axis perpendicular to the first and lying on the plane identified by the three markers, and the third one is obtained from the cross product of the unit vectors of the two axes already defined. Anatomical RFs are normally identified by the relevant AL positions using geometrical methods with few exceptions . The optimal pose estimators derive the rigid body transformation parameters using least squares methods to solve the difference equation by using either the matrix characteristic equation , the singular value decomposition (SVD) [9–13] or iterative methods . In some cases, non-least squares method are used .
All the above mentioned pose estimators have pros and cons the importance of which is difficult to determine with in vivo experiments without using invasive techniques. In fact, while the estimation of instrumental errors is not problematic, the in vivo quantification of soft tissue artifacts and their effect on the determination of the bone pose is still an open issue. Recently, several attempts have been made to this respect using various approaches [16, 17]. Simulation studies have also been proposed with the limitation of imposing error time histories not generated from experimental observations .
Some studies compared the pose estimators mentioned above [13, 19]. In the latter study the goal was to test the examined pose estimators' performance in the case of ill-conditioned marker distribution, since some of the optimal pose estimators are very sensitive to highly symmetric spatial distribution of the marker cluster.
Some of the mentioned studies focused their attention on a specific joint, the knee, or a specific segment, the thigh, since soft tissues artifacts have great effects on the determination of the thigh kinematics, which is of particular relevance in gait analysis.
In this study, we evaluated the performance of various pose estimators by implementing a four-bar linkage (FBL) model of the knee attached to rigid models of the tibia end the femur and relevant ALs. The latter bone was equipped with virtual markers the trajectories of which, during simulated FBL movement, were corrupted by both instrumental noise and soft tissue artifacts. By including AL mislocation information in the model, an evaluation of the performance of the selected pose estimators was obtained.