8 2014年8月
文章编号
1004-924X(2014)08-2267-07
光学精密工程
Optics and Precision Engineering
Vol. 22No. 8
Aug.2014
利用圆心不对称投影精确标定工业相机
朱伟东*，曹良洪，梅标，李江雄，封璞加（1.浙江大学机械工程学院系，浙江杭州310027；
2.中国航空工业集团公司陕西飞机工业（集团）有限公司，陕西汉中723213）
摘要：工业相机常采用基于圆形控制点的方法进行标定，但该方法存在不对称投影同题，极易产生标定误差。为了避免引人不对称投影误差并能以选代方式修正这一误差，本文提出了一种利用圆心不对称投影所莲含信息的相机标定方法。首先，推导了平面模板上的阅形控制点投影成为椭圆之后的理论坐标；然后，提取每一幅标定板图像中实际椭圆的中心坐标，通过最小二乘算法求得该幅图像对应的精确投影变换矩阵；最后，利用所有的投影变换矩阵求出相机内参数。实验结果表明：采用本文提出的标定方法，标定结果的重投影误差降到了1/50pixel。该方法可一次完成标定，计算简单，标定精度高，适用于工业相机的标定，
关键调：工业相机；相机标定；不对称投影；投影变换矩阵；重投影误差
中图分类号：TP391;TB853
文献标识码：A
doi:10. 3788/OPE. 20142208.2267
Calibration of industrial cameras using asymmetric circle center projection
ZHU Wei-dong'',CAO Liang-hong',MEIBiao',LI Jiang-xiong,'Feng Pu-jia
(l.DepartmentofMechanicalEngineering,ZhejiangUniversity,Hangzhou310027,China;
2.Shanri Aireraft Industry(Group)Company Ltd.,AviationIndustry
CorporationofChina,Hanzhong723213,China） Corresponding author,E-mail;wdzhuzju.edu.cn
Abstract: The calibration of industrial cameras usually uses circular points as control points. Howev er, there is asymmetric projection in the calibration, so that the calibration results have errors, In or-der to avoid the introduction of asymmetric projection error and to correct the error in an iteration form , this paper proposes a new camera calibration method by utilizing the asymmetric projection of circular centers. Firstly, the theoretical coordinate of the projection ellipse center from a circular point on the planar pattern was deduced , then the center coordinate of actual ellipse for the image of a cali-bration board was extracted and the projective transformation matrix was obtained by using nonlinear least square method, Finally, the camera intrinsic parameters were obtained by using all projective transformation matrixes, Experimental result reveals that the re-projection error of the calibration re-sult of Baumer TXG12 industrial camera is just about 1/5o pixels by using proposed method.The method can complete the calibration at a time and is able to meet the precision requirement of industri al measurement in simpler calculation and higher accuracy .
收稿日期：2013-11-29；修订日期：2014-01-04.
基金项目：国家自然科学基金资助项目（No.51205352）