To realize accurate self-calibration of pan-tilt camera with nonideal structure, an accurate pan-tilt camera model is built, and a self-calibration method for intrinsic camera parameters and pan-tilt structural parameters is proposed based on self-constraint characteristics in rotation. Firstly, according to the structural feature of the system, an accurate pan-tilt camera model, different from the ideal model, is built to describe the relative orientation and position offset among pan axes, tilt axes and the camera. Secondly, fixed entities in rotation are calculated by taking advantage of the self-constraint characteristics in rotation, and then combining with the polarizing constraint, the constraint equations of the image for an absolute conic are established and computed to obtain the intrinsic camera parameters by Cholesky's factorization. Finally, based on the intrinsic matrix of the camera, the pan-tilt structural parameters are solved by using the projection characteristics of the rotation axes and cross sections. Experimental results indicate that, for 0.5 pixel noise level, the calibration errors in focal length are less than 0.73% and in principle points are less than 0.52%, and mean error in reprojection of real images is 2.38, all of which are better than those by self-calibration method based on ideal model. The whole calibration process only utilizes the geometric constraint in active rotation of pan-tilt camera, without the information of outside scene or calibration object.
 杨浩,张峰,叶军涛.摄像机和惯性测量单元的相对位姿标定方法[J].机器人,2011,33(4):419-426. Yang H, Zhang F, Ye J T. A camera-IMU relative pose calibration method[J]. Robot, 2011, 33(4): 419-426. 谭海曙,周富强,张伟,等.摄像机标定中特征点的一种自动对应方法[J].光电子. 激光,2011,22(5):736-739. Tan H S, Zhou F Q, Zhang W, et al. Automatic correspondence approach for feature points in camera calibration[J]. Journal of Optoelectronics . Laser, 2011, 22(5): 736-739. 吴刚,唐振民.单目式自主机器人视觉导航中的测距研究[J].机器人,2010,32(6):828-832. Wu G, Tang Z M. Distance measurement in visual navigation of monocular autonomous robots[J]. Robot, 2010, 32(6): 828-832. Kim H, Hong K. A practical self-calibration method of rotating and zooming cameras[C]//IEEE International Conference on Pattern Recognition. Piscataway, NJ, USA: IEEE, 2000: 354-357. De Agapito L, Hayman E, Reid I. Self-calibration of rotating and zooming cameras[J]. International Journal of Computer Vision, 2001, 45(2): 107-127.  Basu A, Ravi K. Active camera calibration using pan, tilt and roll[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 1997, 27(3): 559-566.  Sinha S N, Pollefeys M. Pan-tilt-zoom camera calibration and high-resolution mosaic generation[J]. Computer Vision and Image Understanding, 2006, 103(3): 170-183.  Davis J, Chen X. Calibrating pan-tilt cameras in wide-area surveillance networks[C]//IEEE International Conference on Computer Vision. Piscataway, NJ, USA: IEEE, 2003: 144-149. Shih SW, Hung Y P, LinWS. Calibration of an active binocular head[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans, 1998, 28(4): 426-442.  Kwon H, Park J, Kak A C. A new approach for active stereo camera calibration[C]//IEEE International Conference on Robotics and Automation. Piscataway, NJ, USA: IEEE, 2007: 3180-3185. Semple J G, Kneebone G T. Algebraic projective geometry[M]. Oxford, UK: Oxford University Press, 1979. Colombo C, Del Bimbo A, Pernici F. Metric 3D reconstruction and texture acquisition of surfaces of revolution from a single uncalibrated view[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(1): 99-114.  Hartley R, Zisserman A. Multiple view geometry in computer vision[M]. 2nd ed. Cambridge, UK: Cambridge University Press, 2004.