确定摄像机内参和外参的方法研究
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摘要
从二维图像获得三维空间信息的过程中,摄像机标定是必不可少的环节。自1992年, Hartley和Faugeras首次提出摄像机自标定的思想后,摄像机自标定方法便成为计算机视觉领域的研究热点之一。虽然现在较多的文献介绍了自标定的方法,但这些方法总的来说都需解一个非线性方程组或相应的非线性规划问题,导致最后的结果对在噪声情况下和所给的初始值都非常敏感。而本文提出了三种精确并且鲁棒性较高的线性算法求解摄像机内参数和外参数。
其中第三章和第四章为本文的研究内容和创新之处。第三章是基于单视图约束确定摄像机内参数和外参数的方法,包含:外相离圆确定摄像机内参和外参数的线性方法,和同心圆求解的内参和外参数的线性方法。而第四章是对于第三章中难以进行单视图线性约束情况提供一种方法补充,其中包含两视图中基于单应矩阵方法,线性的确定摄像机的内参和外参。除了理论上的探讨,我们还进行了大量的数值模拟实验和真实图像实验。实验结果验证了本文提出的算法的可靠性和有效性。
Camera calibration is a necessary step for obtaining the 3D information from the 2D images. Since 1992, Hartley and Faugeras firstly proposed the idea of camera self-calibration, camera self-calibration has become one of the active research topic in computer vision areas. Though self-calibration methods were introduced by many literatures to solve nonlinear equations or relevant of non-linear programming questions. The final result is very sensitive to the initial value under the noise. This thesis demonstrates three kind algorithms of the robustness and the accuracy determining the camera intrinsic parameters and external parameters.
Of which, the third chapter and fourth chapter of the research are main content for this paper. The third chapter is based on single-view constraints determining camera internal parameters and external parameters method, include: outward from the circles determining the camera intrinsic parameters and external parameters by linear methods, and the concentric circles determining the camera intrinsic parameters by linear methods, and determining the extrinsic parameters by also the linear methods. The fourth chapter added the third chapter methods of the third chapter not determining the camera intrinsic parameters and extrinsic parameters based on single-view constraints. This contains homographic matrix base on two-view, determining camera internal parameters and external parameters by linear methods. In addition to theoretical discussion, we also conducted a large number of numerical simulations and real image experiments.Experimental results demonstrate that the proposed reliability and validity of the algorithm.
其中第三章和第四章为本文的研究内容和创新之处。第三章是基于单视图约束确定摄像机内参数和外参数的方法,包含:外相离圆确定摄像机内参和外参数的线性方法,和同心圆求解的内参和外参数的线性方法。而第四章是对于第三章中难以进行单视图线性约束情况提供一种方法补充,其中包含两视图中基于单应矩阵方法,线性的确定摄像机的内参和外参。除了理论上的探讨,我们还进行了大量的数值模拟实验和真实图像实验。实验结果验证了本文提出的算法的可靠性和有效性。
Camera calibration is a necessary step for obtaining the 3D information from the 2D images. Since 1992, Hartley and Faugeras firstly proposed the idea of camera self-calibration, camera self-calibration has become one of the active research topic in computer vision areas. Though self-calibration methods were introduced by many literatures to solve nonlinear equations or relevant of non-linear programming questions. The final result is very sensitive to the initial value under the noise. This thesis demonstrates three kind algorithms of the robustness and the accuracy determining the camera intrinsic parameters and external parameters.
Of which, the third chapter and fourth chapter of the research are main content for this paper. The third chapter is based on single-view constraints determining camera internal parameters and external parameters method, include: outward from the circles determining the camera intrinsic parameters and external parameters by linear methods, and the concentric circles determining the camera intrinsic parameters by linear methods, and determining the extrinsic parameters by also the linear methods. The fourth chapter added the third chapter methods of the third chapter not determining the camera intrinsic parameters and extrinsic parameters based on single-view constraints. This contains homographic matrix base on two-view, determining camera internal parameters and external parameters by linear methods. In addition to theoretical discussion, we also conducted a large number of numerical simulations and real image experiments.Experimental results demonstrate that the proposed reliability and validity of the algorithm.
引文
[1] Z. Zhang, A flexible new technique for camera calibration, IEEE Trans. Pattern Anal. Mach. Intell., vol. 22, no. 11, Nov. 2000, pp. 1330–1334.
[2] P. Sturm, S. Maybany, On Plane-Based Camera Calibration: A General Algorithm, Singularities, Applications, IEEE Conf. On Computer Vision and Pattern Recognition, 1999, pp. 432–437.
[3] B. Triggs, Autocalibration from Planar Scenes, Proc. Fifth European Conf. On Computer Vision, 1998, pp. 89–105.
[4] Meng XQ, Li H, Hu ZY, A new easy camera calibration technique based on circular points, Mirmehdi M, Thomas B, eds, Proceedings of the British Machine Vision Conf. On Bristol: ILES Central Press, 2000, pp. 496–501.
[5] Ma S D. A self-calibration technique for active vision system [J].IEEE Trans Robotics and Automation, 1996: 114一120.
[6]马颂德,张正友.计算机视觉一计算理论与算法基础[M].北京:科学出版社1998.
[7] Basu A. Active calibration : alternative strategy and analysis[C] Proceedings of CVPR 93. New York : [ s. n. ] 1993 : 405– 500
[8] Du F , Brady M. Self-calibration of the intrinsic parameters of cameras for active vision systems[ C] Proceedings of CVPR 93. New York : [ s. n. ] , 1993 : 477 - 482
[9]杨长江,汪威,胡占义.一种基于主动视觉的摄像机内参数自标定方法[J].计算机学报,1998,21(5):428 -43
[10] Li H , Zhang Huaifeng , Wu F C , Li H , Zhang Huaifeng , Wu F C , et al. A new linear camera self2calibration technique[C]∥Proceedings of the 5th Asian Conference on Computer Vision. Melbourne , Australia : [ s. n. ] , 2002 : 676– 681
[11] Li H , Wang G H , Lei C , et al. A new self-calibration technique via epipoles[C] Proceedings of the 5th Asian Conference on Computer Vision. Melbourne , Australia : [ s. n. ] , 2002 : 670 - 675.
[12] Hartley R, Estimation of relative camera positions for uncalibrated cameras, Sandini G, ed. Proceedings of the European Conf. on Computer Vision, NLCS 588, Springer-Verlag, 1992, pp. 579–387.
[13] Maybank SJ, Faugeras OD, A theory of self-calibration of a moving camera, International Journal of Computer Vision 8(2), pp. 123–151 (1992).
[14] Hartley R, Self-Calibration of stationary cameras, International Journal of Computer Vision 22(1) , pp. 5–23 (1997).
[15] Dron L, Dynamic camera self-calibration of from controlled motion sequences, Proceedings of the IEEE Conf. on Computer Vision and Pattern Recognition, IEEE Computer Society Press, 1993, pp. 501–506.
[16] Du F, Brady M, Self-Calibration of the intrinsic parameters of cameras for active vision systems, Proceedings of the IEEE Conf. on Computer Vision and Pattern Recognition, New York: IEEE Computer Society Press, 1993, pp. 477–482.
[17] Pollefeys M, Koch R, Gool LV, Self-Calibration and metric reconstruction in spite of varying and unknown internal camera parameters, Proceedings of the International Conf. on Computer Vision, Bombay, 1998, pp. 90–95.
[18] SturmP, Critical motion sequences for monocular self-calibration and uncalibrated Euclidean reconstruction, Proceedings of the IEEE Conf .on Computer Vision and Pattern Recognition, Pureto Rico, IEEE CS Press, 1997, pp. 1100–1105.
[19] Hartley R., Zisserman A, Multiple View Geometry in Computer Vision, Cambridge, University Press, 2004.
[20] B Zhang, YF Li, FC Wu, Planar pattern for automatic camera calibration, Optical Engineering 42, pp. 1542 (2003).
[21] Wu F C, Wang G H, Hu Z Y , A linear approach for determining intrinsic parameters and pose of camera from rectangles, Journal of oftware 14(3), pp. 703–712 (2003).
[22] Faugeras O , Luong Q T , Maybank S. Camera self-calibration : Theory and experiments. In : Proceedings of the 2nd European Con2ference on Computer Vision , Italy , 1992. 321～334.
[23] Maybank S , Faugeras O. A theory of self2calibration of a moving camera. International Journal of Computer Vision, 1992, 8 (2):123～151
[24] Hartley R,Zisserman A. Multiple View Geometry in Computer Vision. Cambridge: University Press, 2000
[25] Wu FC, Li H, Hu ZY. A study on active vision based camera self-calibration. Chinese Journal of Automation, 2001,27(6):736~746(in Chinese with English Abstract)
[26] Triggs B. Auto-calibration and absolute quadric[J].In Proceedings of Computer Vision and Pattern Recognition, 1997: 604-614.
[27] Caprile B, Torre V. Using vanishing International Journal of Computer Vision. points for camera calibration[J].1990, 4(2): 127-140
[28] Triggs B. Auto-calibration and absolute quadric[J].In Proceedings of Computer Vision and Pattern Recognition, 1997: 604-614
[29] B Zhang, Y F Li, F C Wu, Planar pattern for automatic camera calibration,Optical Engineering 42, pp.1542 (2003)
[30] E.Guillou, D.Meneveaux, E.Maisel etc. Using Calibration and Coarse 3D Reconstruction from Computer, 2000, 16, pp: 396-410.Vanishing Points for Cameraa Single Image[J].
[31] Criminisi A., Reid L, Zisserman A. Single View Metrology[C].Proceedings of the 7th International Conference on Computer Vision, 1999: 434-442.
[32] Taehee Lee, Brynjar Gretarrson CS290I Disital Imasin. Winter 3D Models from a Single View Image[C]. Quarter, 2006: 1-12.
[33] Guiuanghui Wang , Jonathan Wua, Zhengqiao Ji. Single view based on estimation circle or parallel lines, Pattern Recognition Letters,2008,pp.977-985.
[34] Yinqiang Zheng ,Yuncai Liu, The Projective Equation of a Circle and Its Application in Camera Calibration , Proc. 19th IEEE. Conf. on Pattern Recognition, 2008, pp. 1-4.
[35] J .Y. Bouguet, Camera Calibration Toolbox for Matlab http://www.vision.caltech.edu/bouguetj/calib_doc/, Public Domain Internet Software.
[36] K. Kanatani, N. Ohta. Accuracy bounds and optimal computation of homography for imagemosaicing applications, Proc. 7th IEEE Internat. Conf. on Computer Vision, 1999, pp. 73-78.
[37] H. Zeng, X. Meng and Z. Hu, A new normalized method on line-based homography estimation, Pattern Recognition Letters, Volume 29, Issue 9, July 2008, pp. 1236-1244.
[38] A. Agarwal, C. Jawahar, P. Narayanan, A Survey of Planar Homography Estimation Techniques, Technical Reports, 2005, International Institute of Information Technology, Hyderabad, Deemed University.
[39] J. Weng, T. Huang, and N. Ahuja, Motion and structure from two perspective views: Algorithms, error analysis and error estimation, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 11, No. 5, 1989, pp. 451–476.
[2] P. Sturm, S. Maybany, On Plane-Based Camera Calibration: A General Algorithm, Singularities, Applications, IEEE Conf. On Computer Vision and Pattern Recognition, 1999, pp. 432–437.
[3] B. Triggs, Autocalibration from Planar Scenes, Proc. Fifth European Conf. On Computer Vision, 1998, pp. 89–105.
[4] Meng XQ, Li H, Hu ZY, A new easy camera calibration technique based on circular points, Mirmehdi M, Thomas B, eds, Proceedings of the British Machine Vision Conf. On Bristol: ILES Central Press, 2000, pp. 496–501.
[5] Ma S D. A self-calibration technique for active vision system [J].IEEE Trans Robotics and Automation, 1996: 114一120.
[6]马颂德,张正友.计算机视觉一计算理论与算法基础[M].北京:科学出版社1998.
[7] Basu A. Active calibration : alternative strategy and analysis[C] Proceedings of CVPR 93. New York : [ s. n. ] 1993 : 405– 500
[8] Du F , Brady M. Self-calibration of the intrinsic parameters of cameras for active vision systems[ C] Proceedings of CVPR 93. New York : [ s. n. ] , 1993 : 477 - 482
[9]杨长江,汪威,胡占义.一种基于主动视觉的摄像机内参数自标定方法[J].计算机学报,1998,21(5):428 -43
[10] Li H , Zhang Huaifeng , Wu F C , Li H , Zhang Huaifeng , Wu F C , et al. A new linear camera self2calibration technique[C]∥Proceedings of the 5th Asian Conference on Computer Vision. Melbourne , Australia : [ s. n. ] , 2002 : 676– 681
[11] Li H , Wang G H , Lei C , et al. A new self-calibration technique via epipoles[C] Proceedings of the 5th Asian Conference on Computer Vision. Melbourne , Australia : [ s. n. ] , 2002 : 670 - 675.
[12] Hartley R, Estimation of relative camera positions for uncalibrated cameras, Sandini G, ed. Proceedings of the European Conf. on Computer Vision, NLCS 588, Springer-Verlag, 1992, pp. 579–387.
[13] Maybank SJ, Faugeras OD, A theory of self-calibration of a moving camera, International Journal of Computer Vision 8(2), pp. 123–151 (1992).
[14] Hartley R, Self-Calibration of stationary cameras, International Journal of Computer Vision 22(1) , pp. 5–23 (1997).
[15] Dron L, Dynamic camera self-calibration of from controlled motion sequences, Proceedings of the IEEE Conf. on Computer Vision and Pattern Recognition, IEEE Computer Society Press, 1993, pp. 501–506.
[16] Du F, Brady M, Self-Calibration of the intrinsic parameters of cameras for active vision systems, Proceedings of the IEEE Conf. on Computer Vision and Pattern Recognition, New York: IEEE Computer Society Press, 1993, pp. 477–482.
[17] Pollefeys M, Koch R, Gool LV, Self-Calibration and metric reconstruction in spite of varying and unknown internal camera parameters, Proceedings of the International Conf. on Computer Vision, Bombay, 1998, pp. 90–95.
[18] SturmP, Critical motion sequences for monocular self-calibration and uncalibrated Euclidean reconstruction, Proceedings of the IEEE Conf .on Computer Vision and Pattern Recognition, Pureto Rico, IEEE CS Press, 1997, pp. 1100–1105.
[19] Hartley R., Zisserman A, Multiple View Geometry in Computer Vision, Cambridge, University Press, 2004.
[20] B Zhang, YF Li, FC Wu, Planar pattern for automatic camera calibration, Optical Engineering 42, pp. 1542 (2003).
[21] Wu F C, Wang G H, Hu Z Y , A linear approach for determining intrinsic parameters and pose of camera from rectangles, Journal of oftware 14(3), pp. 703–712 (2003).
[22] Faugeras O , Luong Q T , Maybank S. Camera self-calibration : Theory and experiments. In : Proceedings of the 2nd European Con2ference on Computer Vision , Italy , 1992. 321～334.
[23] Maybank S , Faugeras O. A theory of self2calibration of a moving camera. International Journal of Computer Vision, 1992, 8 (2):123～151
[24] Hartley R,Zisserman A. Multiple View Geometry in Computer Vision. Cambridge: University Press, 2000
[25] Wu FC, Li H, Hu ZY. A study on active vision based camera self-calibration. Chinese Journal of Automation, 2001,27(6):736~746(in Chinese with English Abstract)
[26] Triggs B. Auto-calibration and absolute quadric[J].In Proceedings of Computer Vision and Pattern Recognition, 1997: 604-614.
[27] Caprile B, Torre V. Using vanishing International Journal of Computer Vision. points for camera calibration[J].1990, 4(2): 127-140
[28] Triggs B. Auto-calibration and absolute quadric[J].In Proceedings of Computer Vision and Pattern Recognition, 1997: 604-614
[29] B Zhang, Y F Li, F C Wu, Planar pattern for automatic camera calibration,Optical Engineering 42, pp.1542 (2003)
[30] E.Guillou, D.Meneveaux, E.Maisel etc. Using Calibration and Coarse 3D Reconstruction from Computer, 2000, 16, pp: 396-410.Vanishing Points for Cameraa Single Image[J].
[31] Criminisi A., Reid L, Zisserman A. Single View Metrology[C].Proceedings of the 7th International Conference on Computer Vision, 1999: 434-442.
[32] Taehee Lee, Brynjar Gretarrson CS290I Disital Imasin. Winter 3D Models from a Single View Image[C]. Quarter, 2006: 1-12.
[33] Guiuanghui Wang , Jonathan Wua, Zhengqiao Ji. Single view based on estimation circle or parallel lines, Pattern Recognition Letters,2008,pp.977-985.
[34] Yinqiang Zheng ,Yuncai Liu, The Projective Equation of a Circle and Its Application in Camera Calibration , Proc. 19th IEEE. Conf. on Pattern Recognition, 2008, pp. 1-4.
[35] J .Y. Bouguet, Camera Calibration Toolbox for Matlab http://www.vision.caltech.edu/bouguetj/calib_doc/, Public Domain Internet Software.
[36] K. Kanatani, N. Ohta. Accuracy bounds and optimal computation of homography for imagemosaicing applications, Proc. 7th IEEE Internat. Conf. on Computer Vision, 1999, pp. 73-78.
[37] H. Zeng, X. Meng and Z. Hu, A new normalized method on line-based homography estimation, Pattern Recognition Letters, Volume 29, Issue 9, July 2008, pp. 1236-1244.
[38] A. Agarwal, C. Jawahar, P. Narayanan, A Survey of Planar Homography Estimation Techniques, Technical Reports, 2005, International Institute of Information Technology, Hyderabad, Deemed University.
[39] J. Weng, T. Huang, and N. Ahuja, Motion and structure from two perspective views: Algorithms, error analysis and error estimation, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 11, No. 5, 1989, pp. 451–476.