基于投影矩阵的摄像机标定新方法

A New Camera Calibration Method Based on Projection Matrix

摘要:

提出一种基于投影矩阵的摄像机标定新方法。该算法根据旋转矩阵的单位正交性结合Cholesky分解，由投影矩阵直接估算内参数矩阵; 然后由旋转矩阵行列式约束排除误解，获得摄像机位置和方位矩阵，并以最小化反投影残差为代价函数对估计参数实现优化。该标定方法在针孔相机模型下进行，整个过程无需求解非线性方程，简单可靠。模拟数据和真实图像实验均证明了此算法的可行性与鲁棒性。通过误差分析得出结论,随着已知空间点数量的增加和拍摄距离的减小，标定精度能进一步得到提高。

Abstract:

A new calibration algorithm based on projection matrix is proposed. This algorithm can directly estimate intrinsic parameter matrix from the obtained projection matrix by combining unitary orthogonality of rotation matrix and Cholesky decomposition. Then camera location and orientation matrix can be ultimately obtained when false solutions are excluded by the constraints of rotation matrix, and the estimated parameters of the camera are optimized by regarding the minimum error of reprojection residual as the cost function. A pinhole camera model is taken in this algorithm which is simple and reliable with no need for solving non-linear equation during the execution. Both simulation and true image experiments prove the feasibility and robustness of this algorithm. In addition, its error analysis indicates a further improvement on the accuracy of the calibration algorithm along with the increased known number of space points and the decreased photographic distance.