一种新型的本质矩阵解析分解算法

为了由本质矩阵分解出两摄像机的相对位姿，提出了一种新型的本质矩阵解析分解算法。首先，利用本质矩阵秩2的属性求出两摄像机间的平移量；然后，利用求解旋转矩阵方程组的方法求出两摄像机间的旋转量；最后，利用直接求取空间3D点成像深度的方法快速从四组分解结果中确定出满足空间3D点可见性约束的惟一正确解。实验结果表明，本文提出的分解算法不仅避免了对本质矩阵进行复杂耗时的奇异值分解运算，而且分解出的四组解析解具有直观且明确的几何意义，同时因为完全避免了景物结构的3D重建，大大简化了惟一解确定过程，降低了惟一解确定难度。

A novel analytical essential matrix decomposition algorithm

For purpose of acquiring the pose and position information of two cameras from essential matrix decomposi-tion efficiently, a novel analytical essential matrix decomposition method is proposed. Firstly, by taking essential ma-trix’ s rank 2 property into account, the position information of the two cameras corresponding to two views respectively is acquired. Secondly, the pose information is obtained through solving rotation matrix equations. Finally, in order to distinguish the unique solution that satisfies the reference-point visibility constraint quickly, the 3D point’ s imaging depths are obtained directly. The experimental results show that, the proposed method not only avoids the time consu-ming singular value decomposition operation, but also acquires four analytical solutions that have intuitive and explicit geometric meanings, meanwhile because of the avoidance of the scene structure’ s 3D reconstruction, the process of unique solution determination is simplified greatly.