考虑圆形特征边缘模糊和偏心误差修正的高精度相机标定方法

针对立体视觉系统采用圆形特征点标定时存在的空间圆形投影边缘模糊和偏心现象问题，利用改进Zernike矩和偏心误差修正进行圆心的高精度定位，以此提高相机参数的标定精度。首先考虑了由于立体视觉成像系统的标定场景光照强度不均匀引起的圆形特征投影图像边缘模糊的问题，引入高斯误差函数对边缘过渡段的灰度分布进行描述，建立了高斯边缘模型，并基于该模型计算投影图像的Zernike矩，然后利用改进Zernike矩实现高精度的圆形特征投影边缘像素坐标定位。此外，分析了影响圆形特征中心投影点和拟合圆心间偏差大小的因素，基于该分析对迭代拟合圆心进行偏差补偿使之逼近真实的圆心投影，最后通过所提算法对99圆形标志点进行圆心坐标提取并用于相机参数的标定。仿真实验表明，文中算法对投影图像边缘定位的精度以及圆心拟合的精度均高于传统的算法；实测实验中，基于圆心高精度坐标得到的相机标定参数对标准杆进行三维重建，长度测量精度比传统算法提高了30%。

High-precision camera calibration method considering projected circular edge blur and eccentricity error

In order to improve the calibration accuracy of camera parameters, the improved Zernike moment and eccentricity error correction were used to locate the center of the circle with high accuracy for the problem of blurred edges and eccentricity of spatial circular projection when calibrating with circular feature points in stereo vision system. The problem of blurred edges of circular feature projection image caused by uneven illumination intensity at the calibration site of stereo vision imaging system was firstly considered, and the Gaussian error function was introduced to describe the grayscale distribution of the edge transition section. The Gaussian edge model was established, and Zernike moments of the projection image were calculated based on this model, and then the improved Zernike moments were used to achieve high-precision circular feature projection edge pixel coordinate positioning. In addition, the factors that affecting the deviation between the projection point of the circular feature and the fitted circle center were analyzed, and the deviation compensation of the iterative fitted circle center was made based on this analysis to make it close to the real circle center projection, and lastly the circle centers of 99 circular marker points were extracted and used for the calibration of the camera parameters by the proposed algorithm. The simulation experiments show that the accuracy of the algorithm for edge positioning of the projected image and the accuracy of the circle center fitting are higher than those of the traditional algorithm; In the practical measurement experiments, it turns out that the length measurement accuracy of standard rod based on the proposed method is improved by 30% compared with traditional methods.