基于矢量差分的未标定摄像机P5P问题的求解

针对PnP问题的方程建立与求解, 提出一种基于矢量差分的未标定摄像机P5P问题的线性求解算法. 将5个控制点组成非共面的4点集合, 按照成像过程, 通过两个集合间的控制点矢量差分逐步构建摄像机姿态及相机矩阵的线性约束方程. 再依据线性理论与旋转阵 R 的正交性化简约束方程, 利用矢量积运算给出未标定P5P问题摄像机姿态及相机矩阵的解析解. 模拟和真实实验都验证了该方法的有效性.

Solution to the P5P Problem with Un-calibrated Camera Based on Vector Difference

The establishment and solution of a PnP problem are investigated here, and a vector difference based solution algorithm for linear P5P problem with an un-calibrated camera is proposed. Five control points are divided into collections containing four points of non-planar. According to the process of image formation, the constraint equations are set up between two collections of vector differences of control points. Then, these equations are simplified and determined in terms of linear theory and the orthogonal relation of rotation R. As a result, the analytic solutions of camera pose and intrinsic parameter matrix are obtained via vector cross or inner product operation. Simulated and real experiments illustrate that the proposed algorithm is effective.