摄影测量共线方程的单位四元数描述

Unit quaternion based description of collinearity equations

为探讨四元数在摄影测量共线方程严密解算中的应用问题,从四元数的基本理论出发,详细推导以单位四元数矩阵表达的共线方程的严密线性化公式,该线性化公式无须对旋转矩阵进行微分。以单像后方交会和光束法平差为例采用模拟数据和实际数据实验。结果表明,推导的以四元数矩阵为基础的线性化共线方程具有形式简单、初值无关性和收敛速度快的优点。具有一定的实用价值。

Collinearity equations play a very important role in photogrammetry and computer vision. It established the relationship between three points, that is, the camera projective center, an object point and its corresponding image point. In collinearity equations, a rotation matrix is usually used to describe the attitude of an image traditionally a rotation matrix is always represented by three Euler angles because of its vivid describing of the relationships between three axes. However, since the unit quarternion was presented by Hamilton in 1843, its use has extended into many application fields such as signal processing, mechanics, and aerospace. In order to discuss the application problem of unit quaternion in photogrammetry, research was carried out in this paper systemically into rigorous solution of eollinearity equations by using unit quarternion based rotation matrices. Starting from the basic theories and its operations of unit quaternion, rigorous linearized expression of unit quaternion based eollinearity equations are derived in detail and there is no need to derive the rotation matrix. Tests by using both simulated data and real image data indicate that linearized collineafity equations have many merits such as having a very simple form, being independent of initial values, and having a high convergent speed compared to two other rotation matrices orthe Euler angle based rotation matrix. So, unit quatemion based rotation matrix should be used widely in practical application.