Challis J H
Applied Physiology Research Unit, School of Sport and Exercise Sciences, University of Birmingham, Edgbaston, U.K.
J Biomech. 1995 Jun;28(6):733-7. doi: 10.1016/0021-9290(94)00116-l.
For many biomechanical applications it is necessary to determine the parameters which describe the transformation of a rigid body from one reference frame to another. These parameters are a scaling factor, an attitude matrix, and a translation vector. The paper presents a new procedure for the determination of these parameters incorporating the work of Arun et al. [IEEE Trans. Pattern Anal. Machine Intell, 9, 698-700 (1987)] but expanding their analysis to allow for the determination of a scale factor, the scalar weighting of the least-squares problem, and the problem of obtaining the incorrect determinant when determining the attitude matrix. The procedure, which requires the coordinates of three or more non-collinear points, is based around the singular value decomposition, and provides a least-squares estimate of the rigid body transformation parameters. Examples are presented of the use of this procedure for determining the attitude of a rigid body, and for osteometric scaling. When used for osteometric scaling mirror transformations are possible, therefore a right-hand specimen can be scaled to the left-hand side of another specimen.
对于许多生物力学应用而言，有必要确定描述刚体从一个参考系到另一个参考系变换的参数。这些参数是一个缩放因子、一个姿态矩阵和一个平移向量。本文提出了一种确定这些参数的新方法，该方法结合了阿伦等人的工作[《IEEE模式分析与机器智能汇刊》，9，698 - 700(1987)]，但扩展了他们的分析，以允许确定缩放因子、最小二乘问题的标量加权以及在确定姿态矩阵时获得错误行列式的问题。该方法需要三个或更多非共线点的坐标，基于奇异值分解，并提供刚体变换参数的最小二乘估计。给出了使用此方法确定刚体姿态和进行骨测量缩放的示例。当用于骨测量缩放时，镜像变换是可能的，因此右手标本可以缩放到另一个标本的左手边。
