针对多视图三维重建中畸变影像的相对姿态估计问题, 提出了一种高精度的鲁棒性估计方法.根据对极几何关系, 推导了畸变中心未知时的畸变基础矩阵表达模型.在系数矩阵中引入加权矩阵, 控制参与估计的匹配对应点, 通过奇异值分解估计畸变基础矩阵.根据加权矩阵更新准则对加权矩阵进行更新, 然后进行迭代计算, 比较前后两次估计得到的内点数目及平均极线距离, 得到畸变基础矩阵的最优解, 并判断是否需要继续迭代.在得到最优畸变基础矩阵后, 再分别对畸变中心、畸变参数以及焦距进行估计.仿真和真实实验表明该方法能有效提高相对姿态鲁棒估计速度, 在噪声均方差为2.5时, 畸变参数误差均值小于2%, 焦距估计误差小于3.5%.

To estimate a relative pose for uncalibrated cameras with unknown distortion in multi-view 3D reconstruction, a robust method with high precision was proposed. Based on the epipolar geometry relationship, the radial fundamental matrix with unknown center of distortion is deduced. The weighted matrix is introduced into the coefficient matrix to control the correspondences using to estimate the radial fundamental matrix by singular value decomposition. Then the weighted matrix is updated according to the proposed criterion, and the calculation is performed iteratively. By comparing number of inliers and average distance to epipolar line, the optimal result of the radial fundamental matrix is obtained, determining whether to continue the iterative calculation. After iterative optimization, the final radial fundamental matrix can be used to estimate the center of distortion, distortion parameters and focal length. Experimental results show the efficiency, high precision and numerical stability of the proposed solution and when the mean variance of the noise is 2.5, the mean of distortion parameter error is less than 2% and the focal length estimation error is less than 3.5%.