基于归一化算法的一维标定物多相机标定
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摘要
为了提高多相机一维标定的精度,提出了一种基于归一化算法的分层逐步标定法,由基本矩阵获得射影投影矩阵,进而转换成度量投影矩阵。对标定物图像特征点的坐标进行归一化预处理,以提高标定精度,同时又保持线性方法快速、易实现的优点。在所提标定方法中,一维标定物可自由运动,不受场地环境约束,使用灵活。通过仿真和真实实验,验证了归一化特征点坐标可以显著提高标定结果的精度和稳健性。
In order to improve the accuracy of one-dimensional(1 D) multi-camera calibration, a gradual calibration method based on the normalization algorithm is proposed, where the projective projection matrices are first obtained from the fundamental matrices and then transformed into the metric projection matrices. The coordinates of the image feature points of the calibration object are pre-processed by normalization, improving the accuracy of calibration and simultaneously maintaining the advantages of fast and easy implementation of the linear method. In the proposed calibration method, the 1 D calibration objects can move freely without restriction of the site environment and are flexible to use as well. The simulation and real experiments demonstrate that the normalized feature point coordinates can substantially improve the accuracy and robustness of calibration results.
In order to improve the accuracy of one-dimensional(1 D) multi-camera calibration, a gradual calibration method based on the normalization algorithm is proposed, where the projective projection matrices are first obtained from the fundamental matrices and then transformed into the metric projection matrices. The coordinates of the image feature points of the calibration object are pre-processed by normalization, improving the accuracy of calibration and simultaneously maintaining the advantages of fast and easy implementation of the linear method. In the proposed calibration method, the 1 D calibration objects can move freely without restriction of the site environment and are flexible to use as well. The simulation and real experiments demonstrate that the normalized feature point coordinates can substantially improve the accuracy and robustness of calibration results.
引文
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[2] Tsai R.A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses[J].IEEE Journal on Robotics and Automation,1987,3(4):323-344.
[3] Markov B N,Khokholikov A A,Konov S G.Search for optimal disposition of markers in space in calibration of the camera of a photogrammatic measurement system[J].Measurement Techniques,2017,59(12):1260-1265.
[4] Yang D S,Bi S S,Cai Y R,et al.Wide-area monocular plane measurement based on calibration on a parallel plane using multiple targets[J].Acta Optica Sinica,2017,37(10):101500.杨东升,毕树生,蔡月日,等.基于平行面多靶标标定的单目大视场平面测量[J].光学学报,2017,37(10):101500.
[5] Cai M,Sun X X,Liu S G,et al.An accurate and real-time focal-length self-calibration method based on infinite homography between vanish points[J].Acta Optica Sinica,2014,34(5):0515003.蔡鸣,孙秀霞,刘树光,等.基于消隐点无穷单应的摄像机焦距精确自标定方法[J].光学学报,2014,34(5):0515003.
[6] 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.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.
[7] Zhang Z Y.Camera calibration with one-dimensional objects[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2004,26(7):892-899.
[8] Hammarstedt P,Sturm P,Heyden A.Degenerate cases and closed-form solutions for camera calibration with one-dimensional objects[C].IEEE International Conference on Computer Vision,2005:317-324.
[9] Fu Z L,Zhou F,Xie Y F,et al.One-dimensional multi-camera calibration based on fundamental matrix[J].Acta Optica Sinica,2013,33(6):0615003.付仲良,周凡,谢艳芳,等.基于像对基础矩阵的多像一维标定方法[J].光学学报,2013,33(6):0615003.
[10] de Fran?a J A,Stemmer M R,de M Fran?a M B,et al.A new robust algorithmic for multi-camera calibration with a 1D object under general motions without prior knowledge of any camera intrinsic parameter[J].Pattern Recognition,2012,45(10):3636-3647.
[11] Summan R,Pierce S G,MacLeod C N,et al.Spatial calibration of large volume photogrammetry based metrology systems[J].Measurement,2015,68:189-200.
[12] Wang L,Wang W W,Shen C,et al.A convex relaxation optimization algorithm for multi-camera calibration with 1D objects[J].Neurocomputing,2016,215:82-89.
[13] Shi K F,Wu F C.Optimally weighted linear algorithm for camera calibration with 1D objects[J].Journal of Computer-Aided Design & Computer Graphics,2014,26(8):1251-1257.史坤峰,吴福朝.相机一维标定的最优加权线性算法[J].计算机辅助设计与图形学学报,2014,26(8):1251-1257.
[14] Wang L,Duan F Q,Lü K.Camera calibration with one-dimensional objects based on the heteroscedastic error-in-variables model[J].Acta Automatica Sinica,2014,40(4):643-652.王亮,段福庆,吕科.基于HEIV模型的摄像机一维标定[J].自动化学报,2014,40(4):643-652.
[15] Halloran B,Premaratne P,Vial P,et al.Distributed one dimensional calibration and localisation of a camera sensor network[M].Cham:Springer International Publishing,2017:581-593.
[16] Hartley R,Zisserman A.Three-view geometry[M].Cambridge:Cambridge University Press,2000:363-364.
[17] Zheng Y Q,Sugimoto S,Okutomi M.A branch and contract algorithm for globally optimal fundamental matrix estimation[C]//IEEE Conference on Computer Vision and Pattern Recognition,June 20-25,2011,Colorado Springs,CO,USA,2000:2953-2960.
[18] Ila V,Polok L,Solony M,et al.Fast incremental bundle adjustment with covariance recovery[C].International Conference on 3D Vision,2017:175-184.
[19] Zhang Z.A flexible new technique for camera calibration[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2000,22(11):1330-1334.