Annals of Biomedical Engineering, Vol. 33, No. 3, March 2005 (© 2005) pp. 402–412 DOI: 10.1007/s10439-005-1743-9 Derivation of Centers and Axes of Rotation for Wrist and Fingers in a Hand Kinematic Model: Methods and Reliability Results P. CERVERI, 1,2 N. LOPOMO, 1 A. PEDOTTI, 1 and G. FERRIGNO 1 1 Bioengineering Department, Politecnico di Milano, Piazza Leonardo da Vinci, Milano, Italy; and 2 BTS Bioengineering, via Inverigo 2-20151 Milano, Italy (Received 12 March 2004; accepted 7 October 2004) Abstract—In the field of 3D reconstruction of human motion from video, model-based techniques have been proposed to in- crease the estimation accuracy and the degree of automation. The feasibility of this approach is strictly connected with the adopted biomechanical model. Particularly, the representation of the kine- matic chain and the assessment of the corresponding parameters play a relevant role for the success of the motion assessment. In this paper, the focus is on the determination of the kinematic pa- rameters of a general hand skeleton model using surface measure- ments. A novel method that integrates nonrigid sphere fitting and evolutionary optimization is proposed to estimate the centers and the functional axes of rotation of the skeletal joints. The reliability of the technique is tested using real movement data and simulated motions with known ground truth 3D measurement noise and dif- ferent ranges of motion (RoM). With respect to standard nonrigid sphere fitting techniques, the proposed method performs 10–50% better in the best condition (very low noise and wide RoM) and over 100% better with physiological artifacts and RoM. Repeata- bility in the range of a couple of millimeters, on the localization of the centers of rotation, and in the range of one degree, on the axis directions is obtained from real data experiments. Keywords—Hand kinematical model, Rotation centers, Func- tional axes, Surface markers. INTRODUCTION In recent years, significant efforts have been devoted to hand modeling and gesture analysis with the aim of link- ing finger kinematics to functional ability for biomechani- cal and clinical assessment. 3−5,11,16,17,20,25,28 Equivalently, considerable research has focused on the problem of cap- turing articulated finger pose for symbol understanding and command coding in the domains of interhuman communi- cation and human–computer interaction. 23,28 In particular, motion reconstruction techniques have provided the ability to estimate in vivo the 3D motion of finger joints from video-based surface measurements in real-time. 9,10,21,30 Address correspondence to Pietro Cerveri, Dipartimento di Bioingeg- neria, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy. Electronic-mail: cerveri@biomed.polimi.it In such an approach, the 3D position of physical mark- ers, attached to palpable bony landmarks on the hand, is measured by motion capture systems during articulated hand movements and the kinematic variables of the un- derlying skeletal structure are computed through a suit- able mapping. 18,27 This implies both a kinematic hand model, defined through a hierarchical chain constituted of mechanical joints corresponding to real articulations, and procedures to compute the joint centers (CoR) and axes of rotation (AoR). In general, the identification of the CoRs and AoRs guarantees more accurate descrip- tion of underlying bone kinematics as well as recognition of possible kinematic modification caused by pathologi- cal conditions. 4 It is important to understand that there are no methods readily available for the computation of CoR and AoR of the finger joints from hand articulated movements. Zhang et al. 30 developed an analytical method to derive the CoR from 21 markers during flexion-extension move- ments. While the presented results appears valuable, the involved optimization strategy was asserted to be computa- tionally nontrivial. In addition, effects of soft tissue artifacts and small range of motion (RoM), which were shown sig- nificantly affect the estimated kinematic variables derived from marker motion data, 1,6,22 were not explored. More- over, the variability of the results on the position of the markers at the finger surface was not investigated. General purpose procedures, based on rigid and nonrigid sphere fitting, were proposed 12,13 for the determination of the av- eraged CoR and AoR of the lower limb joints but their feasibility to the case of hand model was not assessed. In particular, such methods were recognized to be par- ticularly sensitive to measurement noise and motion arti- facts in radial direction when reduced ranges of motion are involved. 19 In this paper, we present the development of a new method for the calibration of kinematic characteristics of hand skeleton model utilizing motion data of surface mark- ers acquired during controlled articulated hand and finger movements. The performance of this method is compared 0090-6964/05/0300-0402/1 C  2005 Biomedical Engineering Society 402