FU Luhua1,2， REN Zeguang1， WANG Peng1,2， SUN Changku1,2， ZHANG Baoshang2
（1. State Key Laboratory of Precision Measurement Technology and Instruments， Tianjin University， Tianjin 300072， China；2. Science and Technology on ElectroOptic Control Laboratory， Luoyang Institute of ElectroOptic Equipment， Aviation Industry Corporation of China, Ltd.， Luoyang 471009， China）
Abstract： The ability to build an imaging process is crucial to vision measurement. The nonparametric imaging model describes an imaging process as a pixel cluster, in which each pixel is related to a spatial ray originated from an object point. However, a nonparametric model requires a sophisticated calculation process or highcost devices to obtain a massive quantity of parameters. These disadvantages limit the application of camera models. Therefore, we propose a novel camera model calibration method based on a singleaxis rotational target. The rotational vision target offers 3D control points with no need for detailed information of poses of the rotational target. Radial basis function (RBF) network is introduced to map 3D coordinates to 2D image coordinates. We subsequently derive the optimization formulization of imaging model parameters and compute the parameter from the given control points. The model is extended to adapt the stereo camera that is widely used in vision measurement. Experiments have been done to evaluate the performance of the proposed camera calibration method. The results show that the proposed method has superiority in accuracy and effectiveness in comparison with the traditional methods.
Key words： camera calibration； rotational target； nonparametric model
References
［1］TSAI R. A versatile camera calibration technique for highaccuracy 3D machine vision metrology using offtheshelf TV cameras and lenses. IEEE Journal on Robotics and Automation, 1987, 3(4): 323344.
［2］LI W, GEE T, FRIEDRICH H, et al. A practical comparison between Zhang’s and Tsai’s calibration approaches//The 29th International Conference on Image and Vision Computing, Nov. 19, 2014, Hamilton, New Zealand. New York: ACM, 2014: 166171.
［3］FITZGIBBON A W. Simultaneous linear estimation of multiple view geometry and lens distortion//Conference on Computer Vision and Pattern Recognition, Dec. 84, 2001, Kauai, HI, USA. New York: IEEE, 2001: 127132.
［4］LOPEZ M, MARI R, GARGALLO P, et al. Deep single image camera calibration with radial distortion//Conference on Computer Vision and Pattern Recognition, Jun. 1520, Long Beach, CA, USA. New York: IEEE, 2019: 1181711825.
［5］L B, LI L, YAN C. Threedimensional laser scanning under the pinhole camera with lens distortion. Machine Vision and Applications, 2017, 28(7): 737742.
［6］XIONG P, WANG S, WANG W, et al. Modelindependent lens distortion correction based on subpixel phase encoding. Sensors, 2021, 21(22): 7465.
［7］BERGAMASCO F, ALBARELLI A, RODOL E, et al. Can a fully unconstrained imaging model be applied effectively to central cameras//Conference on Computer Vision and Pattern Recognition, Jun. 2328, Portland, OR, USA. New York: IEEE, 2013: 13911398.
［8］PETER S. A generic concept for camera calibration. Lecture Notes in Computer Science, 2004, 3022: 113.
［9］HARTLEY R, KANG S B. Parameterfree radial distortion correction with center of distortion estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29(8): 13091321.
［10］BERGAMASCO F, COSMO L, GASPARETTO A, et al. Parameterfree lens distortion calibration of central cameras//International Conference on Computer Vision, Oct. 2229, Venice, Italy. New York: IEEE, 2017: 38473855.
［11］SUN C, DONG H, ZHANG B, et al. An orthogonal iteration pose estimation algorithm based on an incident ray tracking model. Measurement Science and Technology, 2018, 29(9): 095402.
［12］MONGILLO M. Choosing basis functions and shape parameters for radial basis function methods. SIAM Undergraduate Research Online, 2011, 4(4): 190209.
［13］DEBNATH R, TAKAHASHI H. Learning capability: classical RBF network vs. SVM with gaussian kernel//International Conference on Industrial and Engineering, Application of Artificial Intelligence and Experts Systems, Jun. 1720, Cairns, Austrialia. Berlin: Springer, 2002: 293302.
［14］MICHALIKOVA M, PRAUZEK M, KOZIOREK J. Impact of the radial basis function spread factor onto image reconstruction in electrical impedance tomography. IFACPapersOnLine, 2015, 48(4): 230233.
［15］CARR J C, BEATSON R K, CHERRIE J B, et al. Reconstruction and representation of 3D objects with radial basis functions//The 28th Annual Conference on Computer Graphics and Interactive Techniques, Aug. 1217, 2001, Los Angeles, CA, USA. New York: ACM, 2001: 6776.
［16］SARRA S A. Radial basis function approximation methods with extended precision floating point arithmetic. Engineering Analysis with Boundary Elements, 2011, 35(1): 6876.
［17］MAIDI M, DIDIER JY, ABABSA F, et al. A performance study for camera pose estimation using visual marker based tracking. Machine Vision and Applications, 2010, 21(3): 365376.
［18］PRATT V. Direct leastsquares fitting of algebraic surfaces. ACM Siggraph Computer Graphics, 1987, 21(4): 145152.
［19］FRANASZEK M, CHEOK G S, SAIDI K S, et al. Fitting spheres to range data from 3D imaging systems. IEEE Transactions on Instrumentation and Measurement, 2009, 58(10): 35443553.
［20］FENG J, SONG L, YANG X, et al. Sub clustering KSVD: size variable dictionary learning for sparse representations//The 16th IEEE International Conference on Image Processing, Nov. 710, 2009, Cairo, Egypt. New York: IEEE, 2009: 21492152.
［21］HAARBACH A, BIRDAL T, ILIC S. Survey of higher order rigid body motion interpolation methods for keyframe animation and continuoustime trajectory estimation//International Conference on 3D Vision, Sept. 58, 2018, Verona, Italy. New York: IEEE, 2018: 381389.
［22］BARFOOT T D. State estimation for robotics. Cambridge: Cambridge University Press, 2017.
［23］HARTLEY R, TRUMPF J, DAI Y, et al. Rotation averaging. International Journal of Computer Vision, 2013, 103(3): 267305.
基于单轴旋转靶标的非参数相机标定方法
付鲁华1,2, 任泽光1, 王鹏1,2, 孙长库1,2, 张宝尚2
（1. 天津大学 精密测试技术及仪器国家重点实验室， 天津 300072； 2. 中国航空工业集团有限公司洛阳电光设备研究所 光电控制技术重点实验室， 河南 洛阳 471009）
摘要:建立成像过程的能力对于视觉测量至关重要。 非参数相机模型将图像形成过程描述为与来自物体的空间射线对应的像素集合。 然而， 非参数模型需要复杂的计算或高成本的装置来获取大量参数， 这限制了该模型的应用。 为此， 提出了一种基于单轴旋转靶标的非参数成像模型标定方法。 旋转靶标提供三维控制点， 并引入径向基神经网络将三维坐标映射到二维图像坐标。 该方法无需旋转靶标的详细位姿信息， 从而避免了额外的角度测量设备。 随后， 推导出成像模型参数的目标函数， 给出了优化步骤， 进而计算出模型参数。 在获得单个相机中的光线轨迹后， 该模型被迁移于双目立体相机应用。 最后， 通过实验对所提出方法的性能进行了评估， 结果表明， 与传统方法相比该方法优势明显。
关键词:相机标定； 旋转靶标； 非参数模型
引用格式：FU Luhua, REN Zeguang, WANG Peng, et al． Nonparametric camera calibration method using singleaxis rotational target． Journal of Measurement Science and Instrumentation， 2022， 13（1）： 111. DOI： 10．3969／j．issn．1674-8042．2022．01．001
[full text view]
