基于对偶四元数的绝对定向直接解法

Close-Form Solution of Absolute Orientation Based on Dual Quaternion

绝对定向在摄影测量学中具有重要的作用,惯用的迭代解法需要比较准确的迭代初值。在简要介绍对偶四元数的基础上,利用对偶四元数描述坐标系之间的旋转与平移,通过严格的数学推导得到了一种利用对偶四元数进行绝对定向的新算法。该算法将绝对定向问题转化为最优化问题进行求解,无需迭代,直接求解。实验结果表明:同惯用迭代解法进行比较,无需设置计算的初始参数,计算速度快,求解正确,且具有很好的适应性和稳定性。

Absolute orientation is very important in photogrammetry. The algorithm for traditional absolute orientation is an iterative algorithm which needs accurate iterative initial value. Based on the introduction of dual quaternion, Dual quaternion was used to describe the rotation and translation between different coordinates system, and a new algorithm of absolute orientation based on dual quaternion by the way of strictly mathematic deduction is proposed. This new algorithm is a close-form solution, and the problem about absolute orientation was transformed into an optimal problem to solve. Comparing with the idiomatic iterative solution, initial values of absolute orientation elements are not required, and at the same time, the calculation speed is rapid, and the results are correct and highly precise. The result of experiment indicates that the arithmetic has obvious adaptability and stability.