摄像机线性三步定标方法研究

A Linear Three-step Approach for Camera Calibration

计算机视觉中,在对景物进行定量分析或对物体进行精确定位时,都需要进行摄像机标定,即准确确定摄像机的内部参数和外部参数。由于真实的摄像机光学模型存在很多类型的畸变,因而导致透视投影关系是非线性的。为了解决标定过程的非线性最优化问题,针对常用的带有一阶径向畸变的摄像机模型,提出了一种新的线性三步摄像机定标方法,即首先通过径向排列约束计算摄像机参数的旋转矩阵、x轴平移向量和y轴平移向量;然后根据透视投影的交比不变性解算一阶径向畸变参数;最后利用求得的摄像机参数建立有效焦距和z轴平移向量的线性方程,采用最小二乘法来得到线性解。实验表明,该方法简单快捷,不仅具有较高的标定精度,而且解决了原有算法采用非线性搜索寻优可能存在的解不稳定的问题。

Camera calibration, which is to calculate the intrinsic and extrinsic parameters of a camera in viewing, is one of the basic tasks for analyzing the geometry of a scene and determining the shapes and locations of objects in vision. Since the optical system of a real camera has many types of distortions, and these distortions must be taken into account in three dimensional geometry reconstruction when high precision is needed, this will cause the relation of perspective transformation to be nonlinear. Many efforts have been made to solve the nonlinear calibration problem. A new linear three-step approach for camera calibration was proposed to deal with camera model of one order radial distortion. In the first stage all extrinsic parameters except those for translation vector in Z-axis are computed by using the Radial Parallelism Constraint（RAC）. In the second stage the one order radial distortion parameter is computed by using cross ratio invariability. In the third stage all the missing parameters are computed by the least square method. Experiments with simulated data as well as real image show that the new approach is efficient, robust and accurate. And the approach eliminates the nonlinear iterative calculation processes.