视觉标定中圆心投影点精确定位

Accurate Location of Projected Circular Center in Visual Calibration

根据射影变换中的交比不变性原理以及几何约束条件提出一种能够独立从单个圆的投影图像中精确定位圆心投影点的方法。任取圆上的割线,由调和共轭和交比不变的性质得到割线中点与无穷远点在图像中对应的投影点之间的关系。根据几何约束建立包含割线中点参量的方程组求解割线中点,进而得到圆心投影点的位置。相比在图像中直接将投影椭圆中心作为圆心投影点,该方法不存在投影误差。仿真实验结果表明该方法的精度与稳定性均优于椭圆中心法。实际实验结果表明该方法提取的圆心位置与利用多个圆之间关系提取的圆心位置一致,最大位置误差不超过0.8 pixel。该方法能够独立定位单个投影圆的圆心,适用范围更加广泛。

A method to accurately locate projected center point from single circle image is proposed based on cross- ratio invariance principle and geometric constraint conditions in projective transformation. Take arbitrary circle secants, the relationship between the secant midpoint and the point at infinity is clear according to the harmonic conjugates and cross-ratio invariance. The equations which contain parameters of secant midpoints are established for solving secant midpoints based on the geometric constraints. Then the position of projected circular center is calculated. Compared with taking the center of projected ellipse as the center point directly, the proposed method does not have projection error. Simulation experiment results show that the accuracy and stability of the method is superior to the method of extracting ellipse＇s center. The results of actual experiment show that the circular center positions are consistent with the positions extracted from the relationship among multiple circles, and the maximum position error does not exceed 0.8 pixel. The proposed method can locate the center of a single projected circle independently, which is suitable for wider applications.