Fish-eye Camera Calibration Model Based on Vector Observations and Its Application

doi:10.11947/j.AGCS.2016.20150080

Abstract

Abstract: A fish-eye camera calibration model is presented, basic observations of which consist of both half angle of view and azimuth. Rodrigues matrix is introduced into the model, and three Rodrigues parameters instead of Euler angles are used to represent elements of exterior orientation in order to simplify the expressions and calculations of observation equations.The new model is compared with the existing models based on half angle of view constraint by actual star-map data processing, and the results indicate that the model is superior to control the azimuth error, while slightly inferior to constrain the error of half angle of view. It is advised that radial distortion parameters should be determined by the model based on half angle of view constraint at first, and other camera parameters should be calculated by the new model.

Key words: celestial navigation, fish-eye camera, camera calibration, Rodrigues matrix, precision estimation

CLC Number:

P231

ZHAN Yinhu, ZHENG Yong, ZHANG Chao, LUO Yabo, WANG Kai. Fish-eye Camera Calibration Model Based on Vector Observations and Its Application[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(3): 332-338.

References

[1] 侯文广, 尚涛. 鱼眼镜头在获取建筑物立面影像中的新方法[J]. 武汉大学学报(工学版), 2007, 40(1):105-109. HOU Wenguang, SHANG Tao. A New Method for Obtaining Façade Image of Building by Using Fish-eye Lens[J]. Engineering Journal of Wuhan University, 2007, 40(1):105-109.
[2] 凌飞龙, 李增元, 陈尔学, 等. 青海云杉林叶面积指数半球摄影测量方法研究[J]. 地球科学进展, 2009, 24(7):803-809. LING Feilong, LI Zengyuan, CHEN Erxue, et al. Leaf Area Index Estimation for Qinghai Spruce Forest Using Digital Hemispherical Photography[J]. Advances in Earth Science, 2009, 24(7):803-809.
[3] DEANS M C, WETTERGREEN D, VILLA D. A Sun Tracker for Planetary Analog Rovers[C]//Proceedings of the 8th International Symposium on Artificial Intelligence, Robotics and Automation in Space.Munich, Germany:[s.n.], 2005:1-7.
[4] URGALE P, ENRIGHT J, BARFOOT T. Sun Sensor Navigation for Planetary Rovers:Theory and Field Testing[J]. IEEE Transactions on Aerospace and Electronic Systems, 2011, 47(3):1631-1647.
[5] THEIN M L, QUINN D A, FOLTA D C. Celestial Navigation(CelNav):Lunar Surface Navigation[C]//Proceedings of the 2008 AIAA/AAS Astrodynamics Specialist Congress and Exposition.Honolulu, Hawaii:[s.n.], 2008:1-19.
[6] 杨鹏. 基于太阳观测图像的月球车天文导航[D]. 杭州:浙江大学, 2011. YANG Peng.Sun Observation Image Based Celestial Navigation for Lunar Rover[D]. Hangzhou:Zhejiang University, 2011.
[7] 李崇辉, 郑勇, 张超, 等. 一种无需精密整平的抗差天文定位方法[J]. 测绘学报, 2013, 42(6):810-816. LI Chonghui, ZHENG Yong, ZHANG Chao, et al. A Robust Celestial Positioning Method without Precise Leveling[J]. Acta Geodaetica et Cartographica Sinica, 2013, 42(6):810-816.
[8] ZHAN Yinhu, ZHENG Yong, ZHANG Chao. Celestial Positioning with CCD Observing the Sun[C]//SUN Jiadong, JIAO Wenhai, WU Haitao, et al.China Satellite Navigation Conference(CSNC) 2013 Proceedings. Berlin Heidelberg:Springer, 2013:697-706.
[9] SHAH S, AGGARWAL J K. Intrinsic Parameter Calibration Procedure for a(high distortion) Fish-eye Lens Camera with Distortion Model and Accuracy Estimation[J]. Pattern Recognition,1996, 29(11):1775-1788.
[10] BRAUER-BURCHARDT C, VOSS K. A New Algorithm to Correct Fish-eye and Strong Wide-Angle-Lens-Distortion from Single Images[C]//Proceedings of 2001 International Conference on Image Processing.Thessaloniki,Greece:IEEE, 2001,1:225-228.
[11] KEDZIERSKI M, FRYSKOWSKA A. Precise Method of Fish-eye Lens Calibration[C]//Proceedings of the 21th ISPRS Congress.Beijing, China:[s.n.], 2008:765-768.
[12] SCHWALBE E. Geometric Modelling and Calibration of Fisheye Lens Camera Systems[C]//Proceedings of the 2nd Panoramic Photogrammetry Workshop, International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences.Berlin, Germany:[s.n.], 2005, 36:1-6.
[13] 刘兴库, 何东坡, 李兆华. 鱼眼全景像片光束法整体平差解法[J]. 测绘学报, 1993, 22(3):218-222. LIU Xingku, HE Dongpo, LI Zhaohua. A Method of Overall Bundle Adjustment of the Panoramic Photograph by Fish Eye Lens[J]. Acta Geodaetica et Cartographica Sinica, 1993, 22(3):218-222.
[14] 贾云得, 吕宏静, 徐岸, 等. 一种鱼眼镜头成像立体视觉系统的标定方法[J]. 计算机学报, 2000, 23(11):1215-1219. JIA Yunde, LV Hongjing, XU An, et al. Fish-eye Lens Camera Calibration for Stereo Vision System[J]. Chinese Journal of Computers, 2000, 23(11):1215-1219.
[15] 英向华, 胡占义. 一种基于球面透视投影约束的鱼眼镜头校正方法[J]. 计算机学报, 2003, 26(12):1702-1708. YING Xianghua, HU Zhanyi. Fisheye Lense Distortion Correction Using Spherical Perspective Projection Constraint[J]. Chinese Journal of Computers, 2003, 26(12):1702-1708.
[16] 原玉磊. 鱼眼相机恒星法检校技术研究[D].郑州:信息工程大学, 2012. YUAN Yulei. Research on Fish-Eye Camera Stellar Calibration Technology[D].Zhengzhou:The PLA Information Engineering University, 2012.
[17] 曾文宪, 陶本藻. 三维坐标转换的非线性模型[J]. 武汉大学学报(信息科学版), 2003, 28(5):566-568. ZENG Wenxian, TAO Benzao. Non-linear Adjustment Model of Three-Dimensional Coordinate Transformation[J]. Geomatics and Information Science of Wuhan University, 2003, 28(5):566-568.
[18] 姚吉利, 韩保民, 杨元喜. 罗德里格矩阵在三维坐标转换严密解算中的应用[J]. 武汉大学学报(信息科学版), 2006, 31(12):1094-1096. YAO Jili, HAN Baomin, YANG Yuanxi. Applications of Lodrigues Matrix in 3D Coordinate Transformation[J]. Geomatics and Information Science of Wuhan University, 2006, 31(12):1094-1096.
[19] 隋立芬, 宋力杰. 误差理论与测量平差基础[M]. 北京:解放军出版社, 2003. SUI Lifen, SONG Lijie. Basis of Error Theory and Surveying Adjustment[M]. Beijing:PLA Press, 2003.
[20] APOGEE. U9000 High Light[R/OL].(2006-10-16)[2014-12-05] Apogee Instruments, 2006. http://www.Apogee.com.