基于前方交会的5点相对定向

Five-Point Relative Orientation Based on Forward Intersection

5点相对定向是摄影测量与机器视觉的经典问题,传统的5点相对定向方法采用多项式求解技术,导致了解的多样性。为此,研究了基于前方交会约束的5点相对定向方法,建立包含前方交会约束的同名像点共面条件方程,推导求解5点相对定向问题的最优化目标函数,并采用最小二乘广义逆法求解。非量测相机Nikon D80的8组5点相对定向实验结果表明,该方法仅利用5个同名像点即可获得两张像片的相对位置(相对定向)立体模型,在测量长度为0.92 m的标尺三维(3D)长度时,其误差的标准不确定度为0.28±0.24 mm,与现有的5点算法相比,该方法无需排解即可确保5对同名射线对对相交,并且求解精度高,稳健性好,有实用价值。

The algorithm of five- point relative orientation is a classical problem for photogrammetry and computer vision. The polynomial is used by the traditional method of five- point relative pose, which causes the polysemia. Therefore, a new method of five-point relative orientation based on the forward intersection is presented, the coplanar equations with forward intersection constraints are set up, whose optimization function is derived, and the least square generalized inverse method is employed to achieve relative orientation parameters with five homologous points. This method has been demonstrated by 8 groups of experiments which use nonmetric camera Nikon D80, the relative three dimensional（3D） model successfully only with 5homologous points of two images with different view angles, and the standard uncertainty of measured errors for the two given rules（0.92 m） is 0.28±0.24 mm. Compared with the existing five-point algorithm, this method can ensure the intersections for the five homologous rays without polysemia, its accuracy and robustness is good, and has practical value.