Korean Journal of Applied Biomechanics (한국운동역학회지)

Korean Society of Applied Biomechanics (한국운동역학회)
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The Comparison of Sphere Fitting Methods for Estimating the Center of Rotation on a Human Joint

인체관절의 회전중심 추정을 위한 구적합법의 비교

  • Kim, Jin-Uk (Department of Physical Education & Sports, College of Natural Science, Kunsan National University)
  • 김진욱 (군산대학교 자연과학대학 체육학과)
  • Received : 2012.04.28
  • Accepted : 2013.03.06
  • Published : 2013.03.31
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Abstract

The methods of fitting a circle to measured data, geometric fit and algebraic fit, have been studied profoundly in various areas of science. However, they have not been applied exactly to a biomechanics discipline for locating the center of rotation of a human joint. The purpose of this study was to generalize the methods to fitting spheres to the points in 3-dimension, and to estimate the center of rotation of a hip joint by three of geometric fit methods(Levenberg-Marquardt, Landau, and Sp$\ddot{a}$th) and four of algebraic fit methods(Delogne-K${\aa}$sa, Pratt, Taubin, and Hyper). 1000 times of simulation experiments for flexion/extension and ad/abduction at an artificial hip joint with four levels of range of motion(10, 15, 30, and $60^{\circ}$) and three levels of angular velocity(30, 60, and $90^{\circ}$/s) were executed to analyze the responses of the estimated center of rotation. The results showed that the Sp$\ddot{a}$th estimate was very sensitive to the marker near the center of rotation. The bias of Delogne-K${\aa}$sa estimate existed in an even larger range of motion. The Levenberg-Marquardt algorithm of geometric fit and the Pratt of algebraic fit showed the best results. The combination of two methods, using the Pratt's estimate as initial values of the Levenberg-Marquardt algorithm, could be a candidate of more valid estimator.

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References

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