基于圆形标记点的平面靶标被广泛应用于摄像机标定与视觉测量中。针对该平面靶标, 为得到圆形标记点在像面上的圆心投影, 提高摄像机的标定精度, 本文提出了一种基于对偶二次曲线几何特性的圆心提取算法。该算法的核心是平面内一个标记点A像面投影二次曲线对应的对偶矩阵C*A, 相对于平面内另外一个标记点B的对偶矩阵C*B的一个广义特征向量, 穿过这两个标记点的圆心投影。因此, 在获取标记点亚像素级边缘点, 拟合椭圆得到椭圆二次曲线方程后, 通过任意两个标记点的对偶矩阵, 均可得到一条穿过这两个圆心投影的向量。经过同一个圆心投影的多个向量叉乘标准化后的结果就是该标记点的圆心投影。为测试本文方法提取圆心像点的精度, 本文在像面与靶标平面夹角40°的姿态下, 对直径为90 mm的超大标记点提取圆心投影, 圆心投影误差为0.1~1 pixel。并以此方法得到的圆心投影对手持式扫描仪进行摄像机标定, 进而对已知坐标的平面靶标及3D工件上的标记点进行扫描, 最大误差不超过0.2 mm。通过实验证明了本文提取的圆心投影比采用椭圆圆心的精度高, 而且提高了摄像机的标定精度。

Planar targets with circular marked points are widely used in camera calibration and visual measurement. To obtain the real circular center in the image of a planar target and improve calibration precision, a circular center extraction method based on dual conic geometric characteristics was proposed. The key to this method was that the dual conic matrix C*A of the marked point A in the image has a generalized eigenvector associated with the dual conic matrix C*B of the marked point B in the image, and this generalized eigenvector passed through the two center projections of both points A and B. As a result, after obtaining the subpixel edge points and fitting the ellipse conic function, a vector linking the two center projections could be computed by using the dual conic matrices of the two marked points, and the standardized interpoint of the eigenvectors would be the center projection. To test the extraction accuracy of center projection with the proposed method, the center projection of a huge marked point with a diameter of 90 mm is extracted when the relative angle between the charge-coupled device and the target plane is 40°, and the errors are found to be within 0.1 to 1 pixel. The camera parameters of a handheld scanner are calibrated with these center projections. A three-dimensional workpiece and a planar target with known marked points are scanned with the handheld scanner, and distance errors are within 0.2 mm. The extraction accuracy of this proposed method is higher than that of the elliptical center method and is superior to the precision of camera calibration.