Circular features are very common in geometric camera calibration. The projection of a circular feature is generally a deformed ellipse, not a true ellipse, due to the presence of lens distortion. The center of the deformed ellipse, obtained by fitting the boundary points with an ellipse, does not necessarily coincide with the distorted point corresponding to the center of the undistorted projection of the circular feature. An eccentricity error will be introduced if the two points are considered to be coincident. In this study three main factors that affect the amount of the eccentricity error are discussed, including the form and amount of lens distortion, the size of the circular feature and the tilt of the supporting plane. Then, an effective geometric camera calibration method is proposed where the eccentricity error is compensated by establishing the correspondence between the estimated model position and the real position of the fitted center of the deformed ellipse. Both simulation and measurement data verify the existence of the eccentricity error and the effectiveness of the proposed method.

中文翻译：

---

基于圆形特征的几何相机标定偏心误差补偿

圆形特征在几何相机标定中非常常见。由于透镜畸变的存在，圆形特征的投影通常是变形的椭圆，而不是真正的椭圆。边界点与椭圆拟合得到的变形椭圆的中心不一定与圆形特征的未畸变投影中心对应的畸变点重合。如果认为两点重合，则会引入偏心误差。本研究讨论了影响偏心误差量的三个主要因素，包括透镜畸变的形式和量、圆形特征的大小和支撑平面的倾斜。然后，提出了一种有效的几何相机标定方法，通过建立估计模型位置与变形椭圆拟合中心的真实位置之间的对应关系来补偿偏心误差。仿真和测量数据均验证了偏心误差的存在和所提方法的有效性。