Söderkvist I, Wedin P A
Department of Computing Science, University of Umeå, Sweden.
J Biomech. 1993 Dec;26(12):1473-7. doi: 10.1016/0021-9290(93)90098-y.
The problem of determining skeletal movements in three dimensions by using a number of landmarks is treated. We present a method that determines the motion of a rigid body by using the positions of the landmarks in least-squares sense. The method uses the singular value decomposition of a matrix derived from the positions of the landmarks. We show how one can use this method to express movement of skeleton segments relative to each other. As many others have pointed out, the movement can be very ill determined if the landmarks are badly configured. We present a condition number for the problem with good geometrical properties. The condition number depends on the configuration of the landmarks and indicates how to distribute the landmarks in a suitable way.
本文探讨了通过使用多个地标来确定三维骨骼运动的问题。我们提出了一种方法，该方法通过在最小二乘意义上使用地标位置来确定刚体的运动。该方法使用从地标位置导出的矩阵的奇异值分解。我们展示了如何使用此方法来表示骨骼段相对于彼此的运动。正如许多人所指出的，如果地标配置不当，运动可能很难确定。我们给出了一个具有良好几何性质的问题条件数。条件数取决于地标的配置，并指示如何以合适的方式分布地标。
