Please wait a minute...
浙江大学学报(工学版)
J4  2013, Vol. 47 Issue (8): 1500-1507    DOI: 10.3785/j.issn.1008-973X.2013.08.026
    
Calibration of fisheye cameras based on the viewing sphere
LIN Ying, GONG Xiao-jin, LIU Ji-lin
Department of Information Science and Electronic Engineering, Zhejiang University,Hangzhou 310027, China
Download:   PDF(0KB) HTML
Export: BibTeX | EndNote (RIS)      

Abstract  

With respect to the large field of view (FOV) of a fisheye camera, a new calibration method was proposed, This method takes advantage of two mutually orthogonal sets of parallel lines. The intrinsic parameters could be initialized by the field of view (FOV) and imaging boundary, and corners extracted in the image plane could be back-projected to a viewing sphere. Two geometric properties of the two line sets on the viewing sphere provided a closed-form solution for extrinsic parameters. Finally, all the parameters were optimized according to the re-projection errors of the corners. Three commonly used fisheye projection models are simulated with respect to the image number and noise level. The simulation shows that, within meaningful noise, the method can achieve high accuracy when the image number is larger than 5. A fisheye camera with 185°FOV is also calibrated, and a geometry-known trihedral object is further tested to validate the estimation of extrinsic parameters. The experiments compared to the popular fisheye calibration toolbox from Caltech prove that with a lower uncertainty, the proposed method is more accurate than Caltech’s toolbox.

Published: 01 August 2013
CLC:  TP 242.6  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Cite this article:

LIN Ying, GONG Xiao-jin, LIU Ji-lin. Calibration of fisheye cameras based on the viewing sphere. J4, 2013, 47(8): 1500-1507.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2013.08.026     OR     http://www.zjujournals.com/eng/Y2013/V47/I8/1500


基于单位视球的鱼眼相机标定方法

针对鱼眼镜头的大范围视场,提出一种新的鱼眼相机标定方法.利用2组相互垂直的平行线来进行鱼眼相机标定.依据相机视场和成像边缘得到内部参数的估计值后,将图像平面上提取的角点反投影到单位视球（viewing sphere）上,2组平行线在单位球面上的2种几何特性提供外部参数估计的解析解.利用角点在图像平面的重投影误差来,得到优化后的所有参数.对3种常见的鱼眼投影模型分别进行关于标定图像数量和噪声水平的仿真实验.从仿真结果来看,在合理的噪声范围内,当用于标定的图像大于5张时,可以得到精度较高的标定结果.利用视场角185°的鱼眼相机来进行标定,并进一步的利用已知结构的立方体模板来验证外参估计方法.与加州理工学院提供的标定工具箱相比较，结果表明该算法不确定度较低,提供更为准确的标定结果.

［1］ GLAVIN M, HUGHES C. Equidistant fish-eye calibration and rectification by vanishing point extraction ［J］. IEEE Transaction on Pattern Analysis and Machine Intelligence, 2010, 32(12): 2289-2296.

［2］ SCARAMUZZA D, MARTINELLI A, SIEGWART R. A flexible technique for accurate omnidirectional camera calibration and structure from motion ［C］∥ Proceedings of IEEE International Conference on Computer Vision Systems. New York: IEEE, 2006: 4552.

［3］ HO T H, DAVIS C C, MILNER S D. Using geometric constraints for fisheye camera calibration ［C］∥ Proceeding of Workshop on Omnidirectional Vision, 2005.

［4］ YING Xiang-hua, HU Zhan-yi. Catadioptric camera calibration using geometric invariants ［J］. IEEE Transaction on Pattern Analysis and Machine Intelligence, 2004, 26(10): 1260-1271.

［5］ GEYER C, DANIILIDIS K. Catadioptric camera calibration ［C］∥Proceeding of IEEE International Conference on Computer Vision. Kerkyra: IEEE, 1999, 1: 398-404.

［6］ 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.

［7］ SWAMINATHAN R, NAYAR S K. Nonmetric calibration of wide-angle lenses and polycameras ［J］. IEEE Transaction on Pattern Analysis and Machine Intelligence, 2000, 22(10): 1172-1178.

［8］ ZHU H, YANG J, LIU Z. Fisheye camera calibration with two pairs of vanishing points ［C］∥International conference on information technology and computer science. Kiev: IEEE, 2009: 321-324.

［9］ GALLAGHER A C. Using vanishing points to correct camera rotation in images ［C］∥ Proceeding Second Canadian Conf. Computer and Robot Vision. Canada: IEEE, 2005, 1: 460-467.

［10］ LI Shi-gang. Binocular spherical stereo ［J］. IEEE transactions on Intelligent Transportation Systems, 2008, 9(4): 589-600.

［11］ KANNALA J, BRANDT S S. A generic camera model and calibration method for conventional, wide-angle, and fish-eye lenses ［J］. IEEE Transaction on Pattern Analysis and Machine Intelligence, 2006, 28(8): 1335-1340.

［12］ ZHANG Zheng-you. A flexible new technique for camera calibration ［J］. IEEE Transaction on Pattern Analysis and Machine Intelligence, 2000, 22(11): 1330-1334.

［13］ YING Xiang-hua, HU Zhan-yi. Fisheye lenses calibration using straight-line spherical perspective projection constraint ［C］∥Proceeding of Asian Conference on Computer Vision. India: Springer, 2006, 2: 61-70.

［14］ GEYER C, DANIILIDIS K. A unifying theory for central panoramic systems and practical implications ［C］.∥Proceeding of European Conference on Computer Vision. Dublin: Springer, 2000: 445-461.

［15］YING Xiang-hua, HU Zhan-yi. Can we consider central catadioptric cameras and fisheye cameras within a unified imaging model ［C］∥Proceeding of European Conference on Computer Vision. Prague: Springer, 2004: 442-455.

［16］ BASU A, LICARDIE S. Alternative models for fisheye lenses ［J］. Pattern Recognition Letters, 1995, 16(4): 433-441.

［17］ GENNERY D B. Generalized camera calibration including fish-eye lenses ［J］. International Journal of Computer Vision, 2006, 68(3): 239-266.

［18］ FREK M M. Perspective projection: the wrong imaging models ［R］. University of Iowa: Department. of Computer Science, 1995.

［19］ HUGHES C, DENNY P, JONES E, et al. Accuracy of fish-eye lens models ［J］. Applied Optics, 2010, 49(17): 3338-3347.

［20］ WENG J, COHEN P, HERNIOU M. Camera calibration with distortion models and accuracy evaluation ［J］. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1992: 965-980.

［21］ BOUGUET J-Y. Camera Calibration Toolbox for Matlab［EB/OL］.［2010-09-05］. http:∥www.vision.caltech.edu/bouguetj/cali_ doc/.
[1] CHEN Ming-ya, XIANG Zhi-yu, LIU Ji-lin. Assistance localization method for mobile robot based on
monocular natural visual landmarks[J]. J4, 2014, 48(2): 285-291.
[2] WANG Hui-fang, ZHU Shi-qiang, WU Wen-xiang. Improved adaptive robust control of servo system with harmonic drive[J]. J4, 2012, 46(10): 1757-1763.
[3] OUYANG Liu, XU Jin, GONG Xiao-jin, LIU Ji-lin. Optimization of visual odometry based on uncertainty analysis[J]. J4, 2012, 46(9): 1572-1579.
[4] MA Li-sha, ZHOU Wen-hui, GONG Xiao-jin, LIU Ji-lin. Motion constrained generalized Field D* path planning[J]. J4, 2012, 46(8): 1546-1552.
[5] XU Jin, SHEN Min-yi, YANG Li, WANG Wei-qiang, LIU Ji-lin. Binocular bundle adjustment based localization
and terrain stitching for robot[J]. J4, 2011, 45(7): 1141-1146.
[6] CHEN Jia-qian, LIUYu-tian, HE Yan, JIANG Jing-ping. Novel dynamic mapping method based on occupancy grid
model and sample sets[J]. J4, 2011, 45(5): 794-798.
[7] CHEN Jia-Gan, HE Yan, JIANG Jing-Ping. Improved FastSLAM algorithm based on importance weight smoothing[J]. J4, 2010, 44(8): 1454-1459.
[8] MEI Gong, ZHANG Zhi-Feng, LAI Huan-Huan. Continuoustime based optimized scheduling of production process[J]. J4, 2010, 44(7): 1423-1427.
[9] XU Sheng-Lin, LIU Yan-Na. Modeling of biped robot by SimMechanics[J]. J4, 2010, 44(7): 1361-1367.
[10] BO Hua-Dong, WANG Ji-Cong, XIE Bin, HU Shi-Fang, LIU Ji-Lin. Data processing method of time-of-flight 3D imaging camera[J]. J4, 2010, 44(6): 1049-1056.
[11] WANG Li, XIONG Rong, CHU Jian, et al. Fuzzy evaluation based exploring planning for map building in unknown environment[J]. J4, 2010, 44(2): 253-258.
[12] CHEN Shao-Bin, JIANG Jing-Ping. Optimal state feedback control for trajectory tracking of four-wheel mobile robot[J]. J4, 2009, 43(12): 2186-2190.