针对摄像机一维(1D)标定的问题, 将世界坐标系建立在1D标定物上, 提出新的数学模型, 给出了一种新的标定方法。一般地, 假设1D标定物与世界坐标系的X轴重合, 定义了1D标定点与其对应投影图像点之间的1D单应矩阵。从单幅视图出发, 推导了1D摄像机标定的基本约束方程。根据基本约束方程采用线性最小二乘估计摄像机的初值, 并以标定点的反投影误差最小为目标函数进行非线性优化得到最终的标定结果。通过仿真实验和真实实验证明了该算法的正确性和可行性。实验结果表明, 与传统的方法相比, 所提出的方法线性初值估计精度高, 且对于固定点不可见的情况, 无需估计固定点的图像投影坐标。

Aiming at camera calibration with one dimensional (1D) objects, a new mathematical model of a novel method for camera calibration is proposed, in which the world coordinate system is established with the 1D object. Generally, assuming that the 1D calibration object is located along the X-axis of the world coordinate system and the 1D homography matrix between 1D calibration object and its image plane is defined. The basic constraint for 1D camera calibration from a single image is derived. The closed-form solution is estimated by linear least-square method based on the basic constraint equations and the final calibration results are obtained by minimizing the projection error of the points. Simulation results with real experiment show that the proposed method is valid and feasible. The experimental results indicate that compared with traditional method, the proposed novel method has the characteristic of higher closed-form solution precision and the image coordinates of the fixed point are not needed to be estimated when the fixed point is invisible.