采用射影几何的圆阵靶标中心像点快速提取

圆阵靶标广泛应用于三维测量和相机标定。在相机的透视投影作用下，靶标上圆形标记点退化成椭圆。然而，椭圆的几何中心并非圆形标记点在像面上的圆心投影。为此，本文利用射影变换下共点、共线等几何不变性质，提出了一种基于射影几何的圆阵靶标中心像点快速提取算法。首先，经过边缘检测、形状滤波及亚像素边缘提取，拟合椭圆得到一般方程；其次，通过射影变换矩阵计算靶标坐标轴方向上的两个消隐点坐标；最后，利用透视不变性原理将消隐点与椭圆一般方程联立解出椭圆的两组公切点坐标，两组切点连线的交点即为圆形标记点在像面上的圆心投影。实验结果表明：与传统搜索公切点方法相比，本文提取中心像点的重建平均距离降低了32.34%，实现了圆形标记点的精确定位，并大幅简化求解过程，具有较强的实用性。基金项目 国家自然科学基金（62173127，61973104，61803146）、中原科技创新领军人才资助项目（224200510008）、河南省优秀青年科学基金（212300410036）、河南省高校科技创新人才支持计划（21HASTIT029）、河南省高等学校青年骨干教师培养计划（2019GGJS089）、河南省科技攻关项目（212102210169，212102210086）、郑州市协同创新专项（21ZZXTCX06）、河南工业大学自科创新基金支持计划（2020ZKCJ06）、河南工业大学青年骨干教师培育计划（21420080）、粮食信息处理与控制教育部重点实验室开放基金（KFJJ2020107，KFJJ2020111，KFJJ2020114）。]

Rapid extraction of circular array target center image points using projective geometry

Circular array targets are widely used in 3D measurement and camera calibration. Under the perspective projection of the camera, the circular marker on the target will degenerate into an ellipse. However, the geometric center of the ellipse is not the central projection of the circular marker on the image plane. Therefore, a fast image point extraction algorithm based on projective geometry is proposed by using the geometric invariance of collinear and common points under projective transformation. Firstly, the general equation is obtained by fitting the ellipse after edge detection, shape filtering, and sub-pixel edge extraction. Secondly, the coordinates of two vanishing points along the coordinate axis of the plane target are got by projective transformation matrix. Finally, using the principle of perspective invariance, the vanishing points and the ellipse general equation are used to solve the two sets of common tangent point coordinates of the ellipse image. The intersection of two sets of tangent lines is the center projection of the circular marker on the image plane. The experimental results show that compared with the traditional method of searching common tangent points, the reconstructed average distance of the extracted center image points is reduced by 32.34%, and the precise location of the circular markers is realized, and the solving process is greatly simplified, which has strong practicability.