Journal of Sensor Science and Technology (센서학회지)

The Korean Sensors Society (한국센서학회)
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Verification of Two Least-Squares Methods for Estimating Center of Rotation Using Optical Marker Trajectory

  • Received : 2017.11.20
  • Accepted : 2017.11.25
  • Published : 2017.11.30
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Abstract

An accurate and robust estimation of center of rotation (CoR) using optical marker trajectory is crucial in human biomechanics. In this regard, the performances of the two prevailing least-squares methods, the Gamage and Lasenby (GL) method, and the Chang and Pollard (CP) method, are verified in this paper. While both methods are sphere-fitting approaches in closed form and require no tuning parameters, they have not been thoroughly verified by comparison of their estimation accuracies. Furthermore, while for both methods, results for stationary CoR locations are presented, cases for perturbed CoR locations have not been investigated for any of them. In this paper, the estimation performances of the GL method and CP method are investigated by varying the range of motion (RoM) and noise amount, for both stationary and perturbed CoR locations. The difference in the estimation performance according to the variation in the amount of noise and RoM was clearly shown for both methods. However, the CP method outperformed the GL method, as seen in results from both the simulated and the experimental data. Particularly, when the RoM is small, the GL method failed to estimate the appropriate CoR while the CP method reasonably maintained the accuracy. In addition, the CP method showed a considerably better predictability in CoR estimation for the perturbed CoR location data than the GL method. Accordingly, it may be concluded that the CP method is more suitable than the GL method for CoR estimation when RoM is limited and CoR location is perturbed.

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References

  1. A. Filippeschi, N. Schmitz, M. Miezal, G. Bleser, E. Ruffaldi, and D. Stricker, "Survey of motion tracking methods based on inertial Sensors: a focus on upper limb human motion", Sensors, Vol. 17, 1257, 2017. https://doi.org/10.3390/s17061257
  2. C. Canton-Ferrer, J. R. Casas, M. Pardas, "Human motion capture using scalable body models," Comput. Vis. Image Underst., Vol. 115, pp. 1363-1374, 2011. https://doi.org/10.1016/j.cviu.2011.06.001
  3. T. Seel, J. Raisch, and T. Schauer, "IMU-based joint angle measurement for gait analysis," Sensors, Vol. 14, pp.6891-6909, 2014. https://doi.org/10.3390/s140406891
  4. N. B. Figueroa, F. Schmidt, H. Ali, N. Mavridis, "Joint origin identification of articulated robots with marker-based multi-camera optical tracking systems," Rob. Auton. Syst., Vol. 61, pp. 580-592, 2013. https://doi.org/10.1016/j.robot.2013.02.008
  5. P. Cerveri, N. Lopomo, A. Pedotti, G. Ferrigno, "Derivation of centers and axes of rotation for wrist and fingers in a hand kinematic model: methods and reliability results," Ann. Biomed. Eng., Vol. 33, pp. 402-412, 2005. https://doi.org/10.1007/s10439-005-1743-9
  6. A. Aristidou and J. Lasenby, "Real-time marker prediction and CoR estimation in optical motion capture," Visual Computer, Vol. 29, pp. 7-26, 2013. https://doi.org/10.1007/s00371-011-0671-y
  7. M. Sangeux, H. Pillet, W. Skalli, "Which method of hip joint centre localisation should be used in gait analysis?," Gait Posture, Vol. 40, pp. 20-25, 2014. https://doi.org/10.1016/j.gaitpost.2014.01.024
  8. L. Y. Chang and N. S. Pollard, "Constrained least-squares optimization for robust estimation of center of rotation", J. Biomech., Vol. 40, pp. 1392-1400, 2007. https://doi.org/10.1016/j.jbiomech.2006.05.010
  9. K. Halvorsen, "Bias compensated least squares estimate of the center of rotation", J. Biomech., Vol. 36, pp. 999-1008, 2003 https://doi.org/10.1016/S0021-9290(03)00070-8
  10. M. Silaghi, R. Plaenkers, R. Boulic, P. Fua, D. Thalmann, "Local and global skeleton fitting techniques for optical motion capture", Modelling and Motion Capture Techniques for Virtual Environments, Lecture Notes in Artificial Intelligence, No. 1537. Springer, Berlin, pp. 26-40, 1998.
  11. K. Halvorsen, M. Lesser, A. Lundberg, A new method for estimating the axis of rotation and the center of rotation," J. Biomech., Vol. 32, pp. 1221-1227, 1999. https://doi.org/10.1016/S0021-9290(99)00120-7
  12. S. Gamage and J. Lasenby, "New least squares solutions for estimating the average center of rotation and the axis of rotation", J. Biomech., Vol. 35, pp. 87-93, 2001
  13. V. Pratt, "Direct least-squares fitting of algebraic surfaces", Computer Graphics, Vol. 21, pp. 145-152, 1987.
  14. C. B. Moler and G. W. Stewart, "An algorithm for generalized matrix eigenvalue problems," SIAM J. Numerical Analysis, Vol. 10, pp. 241-256, 1973. https://doi.org/10.1137/0710024