基于最小二乘配置的光学镜头畸变校正方法
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摘要
针对靶场使用的光学镜头畸变校正方法错误地将似系统误差当作偶然误差处理,并且只能在局部区域对畸变值曲面进行拟合,无法用一个曲面函数精确描述畸变值整体变化特征等问题,提出了一种基于多面函数的最小二乘配置法,该方法首先用多面函数拟合最小二乘配置的趋势项,然后,利用拟合后残差求得经验协方差函数的未知参数,进而得到协方差矩阵,最后,通过配置法求解待校正点的修正值。通过使用本文方法和传统方法分别对炸点坐标测试系统的光学经纬仪进行畸变校正,证明本文方法的有效性和可行性。实验结果表明:相比于传统方法,本文方法能从整体上反映畸变值的整体连续变化趋势,去除趋势项后得到的随机变化部分也较平稳;校正精度在水平和垂直方向上分别提高了19.6"和10.9",达到11.7"和7.7"。通过对实验数据的分析与验证,证明了本文方法能有效提高光学测试设备的测角精度,可为靶场大视场光学镜头的畸变校正提供参考依据。
The optical lens distortion correction method used in shooting range treats Quasi systematic error as the accidental error,and can only fit distorted curve in the local region,can not use a curved surface function to describe the problems such as the whole change characteristics of distortion accurately.To solve this problem,a method of least square collocation based on polyhedral function was proposed.Firstly,the method used polyhedral function to fit the trend term of the least squares collocation.Then,the unknown parameters of the empirical covariance function were obtained through the fitted residuals,and the covariance matrix was obtained.Finally,the correction value of the points to be corrected was solved by the collocation method.By using this method and traditional method to do the distortion correction of optical theodolite in the burst point coordinate test system partly,the results prove the effectiveness and feasibility of this method.The experimental results show that,compared with the traditional method,the proposed method can reflect the overall continuous change trend of the distortion value by using polyhedral function on a whole.The correction accuracy is in-creased by 19.6 "and 10.9" in the horizontal and vertical directions,respectively,to 11.7 "and 7.7".Through the analysis and verification of the experimental data,which proved that this method can effectively improve the measurement accuracy of optical testing equipment,to provide reference for correcting the distortion of wide field optical lens in shooting range.
The optical lens distortion correction method used in shooting range treats Quasi systematic error as the accidental error,and can only fit distorted curve in the local region,can not use a curved surface function to describe the problems such as the whole change characteristics of distortion accurately.To solve this problem,a method of least square collocation based on polyhedral function was proposed.Firstly,the method used polyhedral function to fit the trend term of the least squares collocation.Then,the unknown parameters of the empirical covariance function were obtained through the fitted residuals,and the covariance matrix was obtained.Finally,the correction value of the points to be corrected was solved by the collocation method.By using this method and traditional method to do the distortion correction of optical theodolite in the burst point coordinate test system partly,the results prove the effectiveness and feasibility of this method.The experimental results show that,compared with the traditional method,the proposed method can reflect the overall continuous change trend of the distortion value by using polyhedral function on a whole.The correction accuracy is in-creased by 19.6 "and 10.9" in the horizontal and vertical directions,respectively,to 11.7 "and 7.7".Through the analysis and verification of the experimental data,which proved that this method can effectively improve the measurement accuracy of optical testing equipment,to provide reference for correcting the distortion of wide field optical lens in shooting range.
引文
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[2]王虎,苗兴华,惠彬.短焦矩大视场光学系统的畸变校正[J].光子学报,2001,30(11):1409-1412.WANG H,MIAO X H,HUI B.The distortion correct of short focus wide-angle optical system[J].Acta Photonica Sinica,2001,30(11):1409-1412.(in Chinese)
[3]于国栋.靶场光学镜头畸变校正方法研究[J].液晶与显示,2017,32(3):227-233.YU G D.Distortion correction method for optical lens of the range[J].Chinese Journal of Liquid Crystals and Displays,2017,32(3):227-233.(in Chinese)
[4]叶峰,王敏,陈剑东,等.共面点的摄像机非线性畸变校正[J].光学精密工程,2015,23(10):2962-2970.YE F,WANG M,CHEN J D,et al.Camera nonlinear distortion correction based on coplanar points[J].Optics and Precision Engineering,2015,23(10):2962-2970.(in Chinese)
[5]周子卿,赵鹏,李勃,等.基于共线向量的非量测镜头畸变校正[J].光学学报,2014,34(10):101500.ZHOU Z Q,ZHAO P,LI B,et al.Nonmetric lens distortion calibration based on collinear vectors[J].Acta Optica Sinica,2014,34(10):101500.(in Chinese)
[6]乔彦峰,高峰端,王志乾.基于三次拟合方程畸变校正的光电测量系统[J].光电工程,2008,35(6):28-31,129.QIAO Y F,GAO F D,WANG Z Q.Distortion correction for the photoelectricity measuring system based on the cubic fitting equation[J].Opto-Electronic Engineering,2008,35(6):28-31,129.(in Chinese)
[7]张敏,金龙旭,李国宁,等.基于直线特征的摄像机镜头畸变标定方法[J].光学学报,2015,35(6):061500.ZHANG M,JIN L X,LI G N,et al.Camera distortion calibration method based on straight line characteristics[J].Acta Optica Sinica,2015,35(6):061500.(in Chinese)
[8]徐嵩,孙秀霞,刘树光.摄像机畸变标定的模型参考逼近方法[J].光学学报,2013,33(7):071500.XU S,SUN X X,LIU S G.Model reference approaching method of camera distortion calibration[J].Acta Optica Sinica,2013,33(7):071500.(in Chinese)
[9]张靖,朱大勇,张志勇.摄像机镜头畸变的一种非量测校正方法[J].光学学报,2008,28(8):1552-1557.ZHANG J,ZHU D Y,ZHANG Z Y.Nonmetric calibration of camera lens distortion[J].Acta Optica Sinica,2008,28(8):1552-1557.(in Chinese)
[10]刘炼雄,胡昌华,何川,等.一种改进的基于直线特征的非量测畸变校正方法[J].光学学报,2017,37(9):0915001.LIU L X,HU C H,HE C,et al.An improved non-metric distortion calibration method based on straight line characteristics[J].Acta Optica Sinica,2017,37(9):0915001.(in Chinese)
[11]王海栋,柴洪洲,赵东明.基于抗差最小二乘配置的海底地形生成研究[J].系统仿真学报,2010,22(9):2091-2094,2099.WANG H D,CHAI H Z,ZHAO D M.Research on seabed terrain generation based on robust least-squares collocation[J].Journal of System Simulation,2010,22(9):2091-2094,2099.(in Chinese)
[12]王宇谱,吕志平,王宁,等.顾及卫星钟随机特性的抗差最小二乘配置钟差预报算法[J].测绘学报,2016,45(6):646-655.WANG Y P,LZ P,WANG N,et al.Prediction of navigation satellite clock bias considering clock's stochastic variation behavior with robust least square collocation[J].Acta Geodaetica et Cartographica Sinica,2016,45(6):646-655.(in Chinese)
[13]HARDY R L.Multiquadric equations of topography and other irregular surfaces[J].Journal of Geophysical Research,1971,76(8):1905-1915.
[14]HARDY R L.The application of Multiquadric equations and point mass anomaly models to crustal movement studies[R].NOAA Technical Report NGS 76,NGS 11.Washington,DC:Report National Research Council.National Academy of Science,1978.