\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Calibration of a 3D laser rangefinder and a camera based on optimization solution

Abstract Full Text(HTML) Figure(13) / Table(1) Related Papers Cited by
  • The calibration of a 3D laser rangefinder (LRF) and a camera is a key technique in the field of computer vision and intelligent robots. This paper proposes a new method for the calibration of a 3D LRF and a camera based on optimization solution. The calibration is achieved by freely moving a checkerboard pattern in front of the camera and the 3D LRF. The images and the 3D point clouds of the checkerboard pattern in various poses are collected by the camera and the 3D LRF respectively. By using the images, the intrinsic parameters and the poses of the checkerboard pattern are obtained. Then, two kinds of geometric constraints, line-to-plane constraints and plane-to-plane constraints, are constructed to solve the extrinsic parameters by linear optimization. Finally, the intrinsic and extrinsic parameters are further refined by global optimization, and are used to compute the geometric mapping relationship between the 3D LRF and the camera. The proposed calibration method is evaluated with both synthetic data and real data. The experimental results show that the proposed calibration method is accurate and robust to noise.

    Mathematics Subject Classification: Primary: 53C38, 68U05; Secondary: 49K35.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • Figure 1.  Calibration board and 3D color laser ranging system

    Figure 2.  Pinhole camera model

    Figure 3.  Point cloud of the calibration board and its line point clouds

    Figure 4.  Calibration images

    Figure 5.  Normal vector $ \bar{\mathit{\boldsymbol{n}}}_{j} $ of the calibration board in $ j $th pose

    Figure 6.  Line-to-plane constraint

    Figure 7.  The plane-to-plane constraint

    Figure 8.  Synthetic data generation

    Figure 9.  Calibration results with the increasing number of poses

    Figure 10.  Calibration results with the increasing noise level

    Figure 11.  Calibration results with the number of poses 30 and the noise level 10$ mm $

    Figure 12.  3D color point cloud of the room

    Figure 13.  3D color point cloud of the housing estate

    Table 1.  RMS error analysis results (unit: pixel)

    Method Minimum Average Maximum
    Our Method 1.3571 3.6962 7.2579
    Zhang's Method 1.8495 4.7702 8.6392
    Ying's Method 1.5946 3.7866 7.4648
     | Show Table
    DownLoad: CSV
  • [1] Y. I. Abdel-Aziz and H. M. Karara, Direct linear transformation into object space coordinates in close-range photogrammetry, in Proceedings of the Symposium on Close-Range Photogrammetry, (1971), 1–18.
    [2] J.-Y. Bouguet, Camera Calibration Toolbox for Matlab, 2003.
    [3] J. Briales and J. Gonzalez-Jimenez, A minimal solution for the calibration of a 2D laser-rangefinder and a camera based on scene corners, in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, (2015), 1891–1896. doi: 10.1109/IROS.2015.7353625.
    [4] J. Y. Fan, On the levenberg-marquardt methods for convex constrained nonlinear equations, Journal of Industrial and Management Optimization, 9 (2013), 227-241.  doi: 10.3934/jimo.2013.9.227.
    [5] O. D. Faugeras and G. Toscani, Camera calibration for 3D computer vision, in Proceedings of International Workshop on Industrial Application of Machine Vision and Machine Intelligence, (1987), 240–247.
    [6] A. Geiger, F. Moosmann, Ö. Car and B. Schuster, Automatic camera and range sensor calibration using a single shot, in Proceedings of IEEE International Conference on Robotics and Automation, (2012), 3936–3943. doi: 10.1109/ICRA.2012.6224570.
    [7] R. Gomez-Ojeda, J. Briales, E. Fernandez-Moral and J. Gonzalez-Jimenez, Extrinsic calibration of a 2D laser-rangefinder and a camera based on scene corners, in Proceedings of IEEE International Conference on Robotics and Automation, (2015), 3611–3616. doi: 10.1109/ICRA.2015.7139700.
    [8] X. J. GongY. Lin and J. L. Liu, 3D LIDAR-camera extrinsic calibration using an arbitrary trihedron, Sensors, 13 (2013), 1902-1918.  doi: 10.3390/s130201902.
    [9] J. Heikkila and O. Silven, A four-step camera calibration procedure with implicit image correction, in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, (1997), 1106–1112. doi: 10.1109/CVPR.1997.609468.
    [10] Z. Z. HuY. C. LiN. Li and B. Zhao, Extrinsic calibration of 2-D laser rangefinder and camera from single shot based on minimal solution, IEEE Transactions on Instrumentation and Measurement, 65 (2016), 915-929.  doi: 10.1109/TIM.2016.2518248.
    [11] G.-M. Lee, J.-H. Lee and S.-Y. Park, Calibration of VLP-16 Lidar and multi-view cameras using a ball for 360 degree 3D color map acquisition, in Proceedings of IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems, (2017), 64–69.
    [12] Z. W. Liu, D. M. Lu, W. X. Qian, G. H. Gu, K. Ren, J. Zhang and X. F. Kong, Calibration of a single-point laser range finder and a camera, Optical and Quantum Electronics, 50 (2018), 447. doi: 10.1007/s11082-018-1702-y.
    [13] T. Melen, Geometrical modelling and calibration of video cameras for underwater navigation, Psychotherapeut, 60 (1994), 351-352. 
    [14] J. J. Moré, The Levenberg-Marquardt algorithm: Implementation and theory, LNumerical Analysis, Lecture Notes in Math., Springer, Berlin, 630 (1978), 105–116.
    [15] H. Rushmeier, J. Gomes, F. Giordano, H. E. Shishiny, K. Magerlein and F. Bernardini, Design and use of an in-museum system for artifact capture, in Proceedings of Conference on Computer Vision and Pattern Recognition Workshop, (2003), p8. doi: 10.1109/CVPRW.2003.10005.
    [16] A. R. F. Sergio, V. Fremont and P. Bonnifait, Extrinsic calibration between a multi-layer Lidar and a camera, in Proceedings of IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems, (2008), 214–219.
    [17] R. Tsai, A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses, IEEE Journal on Robotics and Automation, 3 (1987), 323-344.  doi: 10.1109/JRA.1987.1087109.
    [18] F. VasconcelosJ. P. Barreto and U. Nunes, A minimal solution for the extrinsic calibration of a camera and a laser-rangefinder, IEEE Transactions on Pattern Analysis and Machine Intelligence, 34 (2012), 2097-2107.  doi: 10.1109/TPAMI.2012.18.
    [19] L. Wang, F. C. Wu and Z. Y. Hu, Multi-camera calibration with one-dimensional object under general motions, in Proceedings of IEEE International Conference on Computer Vision, (2007), 1–7. doi: 10.1109/ICCV.2007.4408994.
    [20] X. H. Ying, G. W. Wang, X. Mei, S. Yang, J. P. Rong and H. B. Zha, A direct method for the extrinsic calibration of a camera and a line scan LIDAR, in Proceedings of IEEE International Conference Mechatronics and Automation, (2014), 571–576. doi: 10.1109/ICMA.2014.6885760.
    [21] Q. Zhang and R. Pless, Extrinsic calibration of a camera and laser range finder (improves camera calibration), in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, (2004), 2301–2306.
    [22] Z. Zhang, A flexible new technique for camera calibration, IEEE Transactions on Pattern Analysis and Machine Intelligence, 22 (2000), 1330-1334.  doi: 10.1109/34.888718.
    [23] Z. Y. Zhang, Camera calibration with one-dimensional objects, Computer Vision-ECCV 2002, (2002), 161–174. doi: 10.1007/3-540-47979-1_11.
    [24] L. P. Zhou, A new minimal solution for the extrinsic calibration of a 2D LIDAR and a camera using three plane-line correspondences, IEEE Sensors Joural, 14 (2014), 442-454.  doi: 10.1109/JSEN.2013.2284789.
    [25] Y. ZhuangF. Yan and H. S. Hu, Automatic extrinsic self-calibration for fusing data from monocular vision and 3-D laser scanner, IEEE Transactions on Instrumentation and Measurement, 63 (2014), 1874-1876.  doi: 10.1109/TIM.2014.2307731.
  • 加载中

Figures(13)

Tables(1)

SHARE

Article Metrics

HTML views(3087) PDF downloads(558) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return