用于相机标定的球靶标投影误差分析与校正

由于球体具有轮廓连续性好等优点，在摄像机标定,尤其是多相机标定方面获得了广泛的应用。利用球作为标定靶标可以弥补平面靶标在多相机标定中出现视角过大时畸变太大甚至于观测不到的不足，但是空间球经透视投影后成像一般并非标准圆，而是一个椭圆。椭圆几何中心与球心真实成像中心并不一致，从而影响了标定精度。造成球心成像误差的因素主要有两个，即球的相对大小及相对于相机的位置。通过分析空间球成像模型，仿真研究了各因素对球心成像误差影响的大小，寻找球心的透视投影像点与其成像椭圆几何中心之间的误差变化规律，并建立了两者之间的误差校正模型，最后通过实验验证了该校正模型的可行性和有效性。通过校正，球心投影像点定位精度可达到亚像素级。

Analysis and Correction of Projection Error of Camera Calibration Ball

As a ball has the advantage of contour continuity, it has been used widely in camera calibration, especially in multiple camera calibration. Using a ball as calibration target can make up for the shortages of plane target that it may distort or even disappear in the field of view when the viewpoint is large. However, when a ball is projected into the camera it is usually not a standard circle, but an ellipse. The calibration precision will be affected when the elliptic geometric center is not the same as the ball-center′s real image. There are two factors that determine the distortion: the relative size and position of the ball with the camera. The influence of the two factors are analyzed, and the distortion rules are studied by simulating ball′s imaging model. A correction model which is verified feasible and effective in experiment is established. Through the model, the ball center′s projection error can achieve subpixel precision.