基于单位四元数描述的单像空间后方交会算法

A unit quaternion based approach for single image space resection

针对基于旋转矩阵描述的单像空间后方交会算法在线性化过程中因舍弃高阶项而导致的对于相似变换参数初值选取要求较高的问题,立足于中心投影的构像方程(共线方程),利用单位四元数实现空间旋转变换的描述与表达,基于矩阵微分的方式实现了共线方程的微分,进而实现其线性化表达;给出了基于单位四元数描述的单向空间后方交会的详细实现思路,并对算法实现过程中所涉及的公式进行了详细推导;最后,通过实验对算法的可行性与有效性进行了论证.实验表明,基于单位四元数描述的单像空间后方交会算法有效地避免了共线方程的线性化所导致的相似变换初值选取问题,降低了其对于迭代初值的选择要求,且基于单位四元数的旋转变换表达方式还具备形式简单,易于编程实现的特点.

The results of traditional matrix based single image space resection depends heavily on initial estimates of similarity transformation parameters, which is mainly caused by the dis- carding of higher order terms in linearization of collinear equation. Based on the collinear equa- tion, unit quaternion is employed to express rotation matrix, and the differential of collinear e- quation is realized by differential of rotation matrix. Advantages of this approach lie in that there＇s no discarding for higher order terms contrasting to traditional methods, and so there is no loss of accuracy. Main ideas and deduction of each equation are all given in detail. Three ex- periments are carried out to verify the correctness and effectiveness of the algorithm, and re- sults show that no matter what initial estimates of similarity transformation parameters are used, the results are the same. However, if good initial estimates are given, the running time of the algorithm will be greatly decreased. Most important of all, using unit quaternion to ex- press spatial rotation, only four parameters are needed, which is less than the nine of rotation matrix, and so programming of it will become easy.