基于平面运动约束的摄像机自标定方法
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摘要
当摄像机在某个平面作平面运动,即平移平行于该平面而旋转平行于该平面的法线,那么该平面的圆环点的像即为由该平面诱导的图像单应变换的复特征向量。根据所推导出的此结论,提出了一种基于平面运动约束的线性自标定算法。该算法只需摄像机在某个平面上作两次以上姿态不同的平面运动,每次平面运动前后采集该平面的两幅图像,计算它们的单应变换并对其进行特征值分解,所得到的复特征向量即为一对复共轭圆环点的像。通过不同平面运动得到的圆环点的像就能拟合出绝对二次曲线的像,最后通过Cholesky分解绝对二次曲线的像并能计算出摄像机内参数。模拟图像实验和实拍图像实验表明,本文所提出的自标定算法具有较高的精度和较强的鲁棒性。
In this paper it is proved that if the camera undergoes planar motion on some plane, i.e. the translation is parallel to the plane and the rotation is parallel to the plane normal, the images of the plane′s circular points are the complex eigenvectors of the homography induced by the plane. According to this conclusion, a linear self-calibration algorithm based on planar motion constraint is proposed. The proposed algorithm only requires the camera to perform two or more planar motions at different attitudes in a certain plane. For each planar motion, two images of the plane are taken before and after this motion, and then their homography is calculated. By conducting eigenvalue decomposition on the homography matrix, its complex eigenvectors are a pair of conjugate circular points. The image of the absolute curve can be fitted by the images of the circular points obtained from different plane motions. The intrinsic parameters of the camera can be easily calculated by Cholesky decomposing the image of the absolute curve. Experimental results with simulation images and real images show that the proposed self-calibration algorithm has high calibration accuracy and strong robustness.
In this paper it is proved that if the camera undergoes planar motion on some plane, i.e. the translation is parallel to the plane and the rotation is parallel to the plane normal, the images of the plane′s circular points are the complex eigenvectors of the homography induced by the plane. According to this conclusion, a linear self-calibration algorithm based on planar motion constraint is proposed. The proposed algorithm only requires the camera to perform two or more planar motions at different attitudes in a certain plane. For each planar motion, two images of the plane are taken before and after this motion, and then their homography is calculated. By conducting eigenvalue decomposition on the homography matrix, its complex eigenvectors are a pair of conjugate circular points. The image of the absolute curve can be fitted by the images of the circular points obtained from different plane motions. The intrinsic parameters of the camera can be easily calculated by Cholesky decomposing the image of the absolute curve. Experimental results with simulation images and real images show that the proposed self-calibration algorithm has high calibration accuracy and strong robustness.
引文
[1] 马健翔,任安虎,牛孝通. 基于机器视觉的车辆排队长度检测[J]. 国外电子测量技术, 2018,37(8):86- 89.MA J X, REN AN H, NIU X T. Vehicle queue length detection based on machine vision[J]. Foreign Electronic Measurement Technology, 2018,37(8):86- 89.
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[7] 吴玉香, 王超, 冼颖宪. 基于稀疏直接法和图优化的移动机器人SLAM[J]. 仪器仪表学报, 2018,39(4):257- 263.WU Y X, WANG CH, XIAN Y X. SLAM based on sparse direct method and graph optimization for mobile robot[J]. Chinese Journal of Scientific Instrument, 2018, 39(4): 257- 263.
[8] 李秀智, 李尚宇, 贾松敏, 等. 实时的移动机器人语义地图构建系统[J]. 仪器仪表学报, 2017, 38(11): 2769- 2778.LI X ZH, LI SH Y, JIA S M, et al. System of real time mobile robot semantic map building[J]. Chinese Journal of Scientific Instrument, 2017, 38(11): 2769- 2778.
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[10] ZHANG Z. A flexible new technique for camera calibration[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22(11): 1330-1334
[11] 傅思勇, 吴禄慎, 陈华伟, 等. 综合多畸变因素的摄像机标定[J]. 仪器仪表学报, 2018, 39(2):248- 256.FU S Y, WU L SH, CHENG H W, et al. Camera calibration based on multiple distortion factors[J]. Chinese Journal of Scientific Instrument, 2018, 39(2):248- 256.
[12] 邹建成, 田楠楠. 简易高精度的平面五点摄像机标定方法[J]. 光学精密工程, 2017, 25(3):786-791.ZOU J CH, TIAN N N. An easy and high-precision camera calibration method based on planar five points [J]. Optics and Precision Engineering, 2017, 25(3):786-791.
[13] 任亮,邱天爽. 一种基于三正交约束的摄像机标定方法[J]. 电子学报, 2014, 42(10): 2050- 2054.REN L, QIU T SH. Camera calibration method based on three orthogonal constraints[J]. Acta Electronica Sinica, 2014, 42(10): 2050- 2054.
[14] MAYBANK S J, FAUGERAS O D. A theory of self-calibration of a moving camera[J]. International Journal of Computer Vision, 1992, 8(2):123-151.
[15] DONG Q, SHU M, CUI H, etc. Learning stratified 3D reconstruction[J]. Science China Information Sciences, 2018, 61(2): 023101.
[16] 许华荣. 关于分层三维重建中模约束的一点讨论[J]. 计算机辅助设计与图形学学报, 2016, 28(2):310-313.XU H R. A note on the modulus constraint in stratified 3D reconstruction[J]. Journal of Computer-Aided Design & Computer Graphics, 2016, 28(2):310-313.
[17] 孙凤梅, 吴福朝, 胡占义. 由平行平面的投影确定无穷远平面的单应矩阵[J]. 软件学报, 2003, 14(5):66-76.SUN F M, WU F CH, HU ZH Y. Determination of the infinite homography through scene parallel planes[J]. Journal of Software, 2003, 14(5):66-76.
[18] KIM J S, KWEON I S. Camera calibration based on arbitrary parallelograms[J]. Computer Vision and Image Understanding, 2009, 113(1):1-10.
[19] WANG G, TSUI H T, HU ZH Y, et al. Camera calibration and 3D reconstruction from a single view based on scene constraints[J]. Image and Vision Computing, 2005, 23(3): 311-323.
[20] H?DLMOSER M, MICUSIK B, KAMPEL M. Camera auto-calibration using pedestrians and zebra-crossings[C]. Proceedings of the IEEE International Conference on Computer Vision Workshops, 2011: 1697-1704.
[21] 霍炬, 杨卫, 杨明. 基于消隐点几何特性的摄像机自标定方法[J]. 光学学报, 2010, 30(2):465- 472.HUO J, YANG W, YANG M. A self-calibration technique based on the geometry property of the vanish Point [J]. Acta Optica Sinica, 2010, 30(2):465- 472.
[22] 徐小泉, 杨奇, 李超, 等. 鲁棒的三正交灭点摄像机自标定算法[J]. 电子测量与仪器学报, 2018,32(4):65-73XU X Q, YANG Q, LI CH, et al. Robust camera calibration algorithm with three-orthogonal vanishing point [J]. Journal of Electronic Measurement and Instrumentation, 2018,32(4):65-73.
[23] 陈爱华, 高诚辉, 何炳蔚. 基于正交消失点对的摄像机标定方法[J]. 仪器仪表学报, 2012,33 (1): 161-166.CHENG AI H, GAO CH H, HE B H. Camera calibration method based on orthogonal vanishing point pair [J]. Chinese Journal of Scientific Instrument, 2012, 33(1): 161-166.
[24] WILDENAUER H, HANBURY A. Robust camera self-calibration from monocular images of Manhattan worlds[C]. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2012: 2831- 2838.
[25] WANG Y, LU X, LING Z, et al. A method to calibrate vehicle-mounted cameras under urban traffic scenes[J]. IEEE Transactions on Intelligent Transportation Systems, 2015, 16(6): 3270-3279.
[26] FISCHLER M A, BOLLES R C. Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartogramphy[J]. Communications of the ACM, 1981, 24(6): 381-395.
[27] BAY H, ESS A, TUYTELAARS T, et al. Speeded-up robust features (SURF)[J]. Computer vision and image understanding, 2008, 110(3): 346-359.
[28] HARTLEY R, ZISSERMAN A. Multiple View Geometry in Computer Vision[M]. 2nd ed. Cambridge: Cambridge University Press, 2004.
[2] 王陈园. 基于自顶向下方法的建筑物三维重建[J]. 国外电子测量技术, 2017, 36(2):95-99.WANG CH Y. Building reconstruction based on top-down method [J]. Foreign Electronic Measurement Technology, 2017,36(2):95-99.
[3] 吕丽平, 张西芝, 张玉宏. 基于中心线引导的主动视觉导航方法研究[J]. 电子测量与仪器学报, 2018, 32(3): 18- 25.LV L P, ZHANG X ZH, ZHANG Y H. Research of active vision navigation based on centerline guidance[J]. Journal of Electronic Measurement and Instrumentation, 2018, 32(3):18- 25.
[4] 关闯, 魏朗, 乔洁, 等. 一种基于消隐点的单目视觉车辆测距方法[J]. 电子测量技术, 2018,41(11):83- 87.GUANG CH, WEI L, QIAO J, et al. A vehicle distance measurement method with monocular vision based on vanishing point[J]. Electronic Measurement Technology, 2018, 41(11):83- 87.
[5] 李帅鑫, 李广云, 周阳林, 等. 改进的单目视觉实时定位与测图方法[J]. 仪器仪表学报, 2017,38(11):2849- 2857.LI SH X, LI G Y, ZHOU Y L, et al. Improved monocular simultaneous localization and mapping solution[J]. Chinese Journal of Scientific Instrument, 2017, 38(11): 2849- 2857.
[6] 高如新, 朱烜甫. 基于ORB算法的双目视觉定位[J]. 电子测量技术, 2017, 40 (4):142-145.GAO R X, ZHU X F. Based on the ORB algorithm of binocular vision positioning[J]. Electronic Measurement Technology, 2017, 40 (4):142-145.
[7] 吴玉香, 王超, 冼颖宪. 基于稀疏直接法和图优化的移动机器人SLAM[J]. 仪器仪表学报, 2018,39(4):257- 263.WU Y X, WANG CH, XIAN Y X. SLAM based on sparse direct method and graph optimization for mobile robot[J]. Chinese Journal of Scientific Instrument, 2018, 39(4): 257- 263.
[8] 李秀智, 李尚宇, 贾松敏, 等. 实时的移动机器人语义地图构建系统[J]. 仪器仪表学报, 2017, 38(11): 2769- 2778.LI X ZH, LI SH Y, JIA S M, et al. System of real time mobile robot semantic map building[J]. Chinese Journal of Scientific Instrument, 2017, 38(11): 2769- 2778.
[9] 孟晓桥,胡占义.摄像机自标定方法的研究与进展[J].自动化学报, 2003, 29(1):110-124.MENG X Q, HU ZH Y. Recent progress in camera self-calibration[J]. Acta Automatica Sinica, 2003, 29(1): 110-124.
[10] ZHANG Z. A flexible new technique for camera calibration[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22(11): 1330-1334
[11] 傅思勇, 吴禄慎, 陈华伟, 等. 综合多畸变因素的摄像机标定[J]. 仪器仪表学报, 2018, 39(2):248- 256.FU S Y, WU L SH, CHENG H W, et al. Camera calibration based on multiple distortion factors[J]. Chinese Journal of Scientific Instrument, 2018, 39(2):248- 256.
[12] 邹建成, 田楠楠. 简易高精度的平面五点摄像机标定方法[J]. 光学精密工程, 2017, 25(3):786-791.ZOU J CH, TIAN N N. An easy and high-precision camera calibration method based on planar five points [J]. Optics and Precision Engineering, 2017, 25(3):786-791.
[13] 任亮,邱天爽. 一种基于三正交约束的摄像机标定方法[J]. 电子学报, 2014, 42(10): 2050- 2054.REN L, QIU T SH. Camera calibration method based on three orthogonal constraints[J]. Acta Electronica Sinica, 2014, 42(10): 2050- 2054.
[14] MAYBANK S J, FAUGERAS O D. A theory of self-calibration of a moving camera[J]. International Journal of Computer Vision, 1992, 8(2):123-151.
[15] DONG Q, SHU M, CUI H, etc. Learning stratified 3D reconstruction[J]. Science China Information Sciences, 2018, 61(2): 023101.
[16] 许华荣. 关于分层三维重建中模约束的一点讨论[J]. 计算机辅助设计与图形学学报, 2016, 28(2):310-313.XU H R. A note on the modulus constraint in stratified 3D reconstruction[J]. Journal of Computer-Aided Design & Computer Graphics, 2016, 28(2):310-313.
[17] 孙凤梅, 吴福朝, 胡占义. 由平行平面的投影确定无穷远平面的单应矩阵[J]. 软件学报, 2003, 14(5):66-76.SUN F M, WU F CH, HU ZH Y. Determination of the infinite homography through scene parallel planes[J]. Journal of Software, 2003, 14(5):66-76.
[18] KIM J S, KWEON I S. Camera calibration based on arbitrary parallelograms[J]. Computer Vision and Image Understanding, 2009, 113(1):1-10.
[19] WANG G, TSUI H T, HU ZH Y, et al. Camera calibration and 3D reconstruction from a single view based on scene constraints[J]. Image and Vision Computing, 2005, 23(3): 311-323.
[20] H?DLMOSER M, MICUSIK B, KAMPEL M. Camera auto-calibration using pedestrians and zebra-crossings[C]. Proceedings of the IEEE International Conference on Computer Vision Workshops, 2011: 1697-1704.
[21] 霍炬, 杨卫, 杨明. 基于消隐点几何特性的摄像机自标定方法[J]. 光学学报, 2010, 30(2):465- 472.HUO J, YANG W, YANG M. A self-calibration technique based on the geometry property of the vanish Point [J]. Acta Optica Sinica, 2010, 30(2):465- 472.
[22] 徐小泉, 杨奇, 李超, 等. 鲁棒的三正交灭点摄像机自标定算法[J]. 电子测量与仪器学报, 2018,32(4):65-73XU X Q, YANG Q, LI CH, et al. Robust camera calibration algorithm with three-orthogonal vanishing point [J]. Journal of Electronic Measurement and Instrumentation, 2018,32(4):65-73.
[23] 陈爱华, 高诚辉, 何炳蔚. 基于正交消失点对的摄像机标定方法[J]. 仪器仪表学报, 2012,33 (1): 161-166.CHENG AI H, GAO CH H, HE B H. Camera calibration method based on orthogonal vanishing point pair [J]. Chinese Journal of Scientific Instrument, 2012, 33(1): 161-166.
[24] WILDENAUER H, HANBURY A. Robust camera self-calibration from monocular images of Manhattan worlds[C]. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2012: 2831- 2838.
[25] WANG Y, LU X, LING Z, et al. A method to calibrate vehicle-mounted cameras under urban traffic scenes[J]. IEEE Transactions on Intelligent Transportation Systems, 2015, 16(6): 3270-3279.
[26] FISCHLER M A, BOLLES R C. Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartogramphy[J]. Communications of the ACM, 1981, 24(6): 381-395.
[27] BAY H, ESS A, TUYTELAARS T, et al. Speeded-up robust features (SURF)[J]. Computer vision and image understanding, 2008, 110(3): 346-359.
[28] HARTLEY R, ZISSERMAN A. Multiple View Geometry in Computer Vision[M]. 2nd ed. Cambridge: Cambridge University Press, 2004.