共面点的摄像机非线性畸变校正

采用传统的Tsai两步法进行摄像机标定时,标定精度会受一阶径向畸变模型的限制。本文提出了一种同时考虑摄像机镜头径向畸变和切向畸变的摄像机模型并研究了模型求解方法来提高畸变校正精度。考虑图像中心区域畸变较小,故用中心附近点列出线性方程组计算了摄像机的部分参数;建立了综合畸变模型,将摄像机参数代入模型计算畸变参数的初始值。由于焦距和平移分量在标定板与相机平面的距离深度变化不够时难以一次性准确标定,故将其代入综合畸变模型重新计算,并运用两步迭代法逐步逼近精确解。最后,对世界坐标系进行空间几何变换、透视变换和成像变换得到的重投影图像的像素坐标并与实际测得的像素坐标值进行比较,得到校正误差。结果表明,本文的畸变校正方法平均像素误差可以达到0.114 9pixel,优于Tsai校正方法的0.367 0pixel,且重复性较好。

Camera nonlinear distortion correction based on coplanar points

When traditional Tsai two-stage technique is used to calibrate a camera, its calibration accuracy will be limited by first-order radial distortion model. Therefore, a camera imaging model considering both radial distortion and tangential distortion is proposed, and a new method to solve the model is presented to improve the distortion correction accuracy. As the center of an image has a smaller distortion, the image center points are used to give a linear equation group and to calculate a part of parameters of the camera. Then camera parameters are taken into comprehensive distortion model to derive the initial values of distortion coefficients. As focal length and matrix's translation value can not be calculated directly when the calibration board's depth variation is small, the values have to be retaken to model and to be calculated.Then the converged solution is approached by two-stage iterative computation. Finally, the world coordinate system is converted by space geometric transform, perspective transform and imaging transform to obtain the pixel coordinate of the reprojective image. The calibration error is obtained by calculating the mean difference between re-projection pixel coordinates and actual measured pixel coordinates of each point. Experimental result indicates that the calibration method can offer the accuracy of 0.1149 pixel, which is better than Tsai's 0.3670 pixel with well repeatability.