针对增量式运动结构恢复中相机内参数未标定情况下位姿估计问题,提出一种高精度的非迭代位姿求解方法。根据针孔成像模型,构建了相机内参数未标定位姿估计问题描述方程,使用单位四元数对旋转矩阵进行参数化,并根据四重轴对称现象对旋转矩阵进行分解,通过最小二乘原理构建目标函数后,利用一阶最优化条件建立了关于旋转矩阵参数的二元多项式方程组,使用Gr bner基求解该方程组得到旋转参数的闭合解,进而获得相机的位姿参数和焦距。该算法的计算复杂度为O(n),实验验证了其有效性、高精度和高数值稳定性。

The non-iterative method with high precision is proposed for the pose estimation of uncalibrated in-camera parameters in incremental motion structure recovery. Based on the pinhole camera model, the equations which describes uncalibrated cameras pose estimation problems are given. The rotation matrix is parameterized by unit-norm quaternion, and then decomposed according to the four-fold symmetry. To eliminate variables properly and build a bivariate objective function, the least square principle and first order optimal condition is adopted respectively. An efficient solver by using the Gr bner basis technique is developed, so as to obtain optimal solution of rotation matrix and focal length. The complexity of proposed method is O(n). Experimental results prove the efficiency, high precision and numerical stability of the proposed solution.