基于正交Procrustes分析的绝对定向闭合解法

Absolute Orientation Closure Solution Based on Orthogonal Procrustes Analysis

绝对定向是指在多余控制条件下确定尺度、平移和旋转参数,传统解法通常用欧拉角表示旋转矩阵,在给定待求参数初值的前提下迭代求解。其缺点之一是某些情况下初值难以确定,其二是由于三角函数的多值性导致计算复杂乃至错误收敛。而基于正交Procrustes分析的绝对定向解法不需要将旋转矩阵参数化,直接以旋转矩阵的正交条件为约束条件求最目标函数的最小二乘解,只需将一个特征方程进行分解,解算过程极为简便,且能达到传统迭代方法的精度。

Absolute orientation is the determination of scale,translation and rotation parameters under superfluous control conditions.The traditional solution widely used in photogrammetry is the iterative solution under the premise of the given initial values of unknown parameters,and the rotation matrix is parameterized with three Euler angles.One of its disadvantages is hard to get initial values in certain conditions,second are the calculation complex and even errors convergence because of the multivalues of trigonometric function.Whereas the orthogonal Procrustes analysis method is a closed-form solution,it applies the orthogonal conditions of rotation matrix as the constraints for solving the least squares of objective function without parametric rotation matrix,just needs to decompose a matrix,the solving procedures are very simple,and it can achieve the precision of the traditional iterative solution.