基于反对称矩阵分解的计算刚体三维运动旋转参数的线性算法

本文根据正交矩阵的反对称阵分解性质,提出了一个计算刚体三维运动参数的线性算法,把旋转参数计算中通常的9个未知量简化为3个未知量,因而大大减低了算法的复杂程度,提高了算法的可靠性。算法的主要计算过程都是针对线性超定方程组的解算,具有未知量少、计算简便的特点。模拟实验表明,当对图象致据截尾到整数使得中间参数矩阵的计算产生50％左右的误差时,由本算法计算旋转矩阵的误差为5％左右。

The Algorithm for Determining 3-D Motion Parameters Based on Skew-Symmetric Decomposition

On the basis of the skew-symmetric decomposition of an orthonormal matrix, this paper proposes a linear algorithm for determining 3-D motion parameters of a rigid body in monocular case. Since the computation for rotation parameters is simplified from nine variables to three variables in the algorithm, the complexity of the computation is reduced so greatly that the reliability and the stability are improved apparently. The translation up to a positive scale factor and three independent variables of rotation can be derived uniquely through- solving a series of overdetermined linear equations. Simulation experiments show that the relative error of rotation matrix is up to 5%, while the relative error of the intermediate parameters is about 50% caused by truncation error of image data.