Journal of Information Processing Systems

Korea Information Processing Society (한국정보처리학회)
권호 표지
DOI QR코드

DOI QR Code

Research on the Basic Rodrigues Rotation in the Conversion of Point Clouds Coordinate System

  • Xu, Maolin (School of Civil Engineering, University of Science and Technology Liaoning) ;
  • Wei, Jiaxing (School of Civil Engineering, University of Science and Technology Liaoning) ;
  • Xiu, Hongling (School of Civil Engineering, University of Science and Technology Liaoning)
  • Received : 2018.06.26
  • Accepted : 2018.12.14
  • Published : 2020.02.29
Download PDF
⟨ Previous Next ⟩

Abstract

In order to solve the problem of point clouds coordinate conversion of non-directional scanners, this paper proposes a basic Rodrigues rotation method. Specifically, we convert the 6 degree-of-freedom (6-DOF) rotation and translation matrix into the uniaxial rotation matrix, and establish the equation of objective vector conversion based on the basic Rodrigues rotation scheme. We demonstrate the applicability of the new method by using a bar-shaped emboss point clouds as experimental input, the three-axis error and three-term error as validate indicators. The results suggest that the new method does not need linearization and is suitable for optional rotation angle. Meanwhile, the new method achieves the seamless splicing of point clouds. Furthermore, the coordinate conversion scheme proposed in this paper performs superiority by comparing with the iterative closest point (ICP) conversion method. Therefore, the basic Rodrigues rotation method is not only regarded as a suitable tool to achieve the conversion of point clouds, but also provides certain reference and guidance for similar projects.

Keywords

References

  1. V. Carbone, M. Carocci, E. Savio, G. Sansoni, and L. De Chiffre, "Combination of a vision system and a coordinate measuring machine for the reverse engineering of freeform surfaces," The International Journal of Advanced Manufacturing Technology, vol. 17, no. 4, pp. 263-271, 2001. https://doi.org/10.1007/s001700170179
  2. N. Haala, M. Peter, J. Kremer, and G. Hunter, "Mobile LiDAR mapping for 3D point cloud collection in urban areas: a performance test," in Proceedings of the 21st ISPRS Congress, Beijing, China, 2008, pp. 1119-1127.
  3. M. Olano and T. Greer, "Triangle scan conversion using 2D homogeneous coordinates," in Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Workshop on Graphics Hardware, Los Angeles, CA, 1997, pp. 89-95.
  4. N. J. Mitra, N. Gelfand, H. Pottmann, and L. Guibas, "Registration of point cloud data from a geometric optimization perspective," in Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, Nice, France, 2004, pp. 22-31.
  5. S. Shepperd, "Quaternion from rotation matrix," Journal of Guidance and Control, vol. 1, no. 3, pp. 223-224, 1978. https://doi.org/10.2514/3.55767b
  6. A. W Lohmann, "Image rotation, Wigner rotation, and the fractional Fourier transform," Journal of the Optical Society of America A, vol. 10, no. 10, pp. 2181-2186, 1993. https://doi.org/10.1364/JOSAA.10.002181
  7. C. Gosselin, "Determination of the workspace of 6-dof parallel manipulators," Journal of Mechanical Design, vol. 112, no. 3, pp. 331-336, 1990. https://doi.org/10.1115/1.2912612
  8. L. M. Paz, P. Pinies, J. D. Tardos, and J. Neira, "Large-scale 6-DOF SLAM with stereo-in-hand," IEEE Transactions on Robotics, vol. 24, no. 5, pp. 946-957, 2008. https://doi.org/10.1109/TRO.2008.2004637
  9. I. Bonev and J. Ryu, "A new approach to orientation workspace analysis of 6-DOF parallel manipulators," Mechanism and Machine Theory, vol. 36, no. 1, pp. 15-28, 2001. https://doi.org/10.1016/S0094-114X(00)00032-X
  10. H. Lim, S. N. Sinha, M. F. Cohen, M. Uyttendaele, and H. J. Kim, "Real-time monocular image-based 6-DOF localization," The International Journal of Robotics Research, vol. 34, no. 4-5, pp. 476-492, 2015. https://doi.org/10.1177/0278364914561101
  11. H. Kim, S. Leutenegger, and A. Davison, "Real-time 3D reconstruction and 6-DOF tracking with an event camera," in Computer Vision - ECCV 2016. Cham: Springer, 2016 pp. 349-364.
  12. J. S. Dai, "Euler-Rodrigues formula variations, quaternion conjugation and intrinsic connections," Mechanism and Machine Theory, vol. 92, pp. 144-152, 2015. https://doi.org/10.1016/j.mechmachtheory.2015.03.004
  13. G. Gallego and Y. Anthony, "A compact formula for the derivative of a 3-D rotation in exponential coordinates," Journal of Mathematical Imaging and Vision, vol. 51, no. 3, pp. 378-384, 2015. https://doi.org/10.1007/s10851-014-0528-x
  14. Y. Bo and W. Xuan, "Extraction method of structure deformation parameters based on Rodrigue matrix," Geospatial Information, vol. 2016, no. 9, pp. 26-28, 2016.
  15. B. Bellekens, V. Spruyt, R. Berkvens, and M. Weyn, "A survey of rigid 3d pointcloud registration algorithms," in Proceedings of the 4th International Conference on Ambient Computing, Applications, Services and Technologies (AMBIENT), Rome, Italy, 2014, pp. 8-13.
  16. Y. Li, N. Snavely, D. Huttenlocher, and P. Fua, "Worldwide pose estimation using 3D point clouds," in Computer Vision - ECCV 2012. Heidelberg: Springer, 2012, pp. 15-29.
  17. R. C. Luo, V. W. Ee, and C. K. Hsieh, "3D point cloud based indoor mobile robot in 6-DoF pose localization using Fast Scene Recognition and Alignment approach," in Proceedings of 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI), Baden-Baden, Germany, 2016, pp. 470-475.
  18. A. Kendall, M. Grimes, and R. Cipolla, "PoseNet: a convolutional network for real-time 6-dof camera relocalization," in Proceedings of the IEEE International Conference on Computer Vision, Santiago, Chile, 2015, pp. 2938-2946.
  19. D. Jia, Y. Su, and C. Li, "Deep convolutional neural network for 6-dof image localization," 2016; https://arxiv.org/abs/1611.02776.
  20. J. Shao, W. Zhang, Y. Zhu, and A. Shen, "Fast registration of terrestrial LiDAR point cloud and sequence images," in Proceedings of the International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Wuhan, China, 2017, pp. 875-879.
  21. B. Bercovici and J. W. McMahon, "Point-cloud processing using modified Rodrigues parameters for relative navigation," Journal of Guidance, Control, and Dynamics, vol. 40, no. 12, pp. 3167-3179, 2017. https://doi.org/10.2514/1.G002787
  22. G. Pandey, S. Giri, and J. R. Mcbride, "Alignment of 3D point clouds with a dominant ground plane," in Proceedings of 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, Canada, 2017, pp. 2143-2150.
  23. W. Sun and J. R. Cooperstock, "An empirical evaluation of factors influencing camera calibration accuracy using three publicly available techniques," Machine Vision and Applications, vol. 17, no. 1, pp. 51-67, 2006. https://doi.org/10.1007/s00138-006-0014-6
  24. S. J. Buckley, J. A. Howell, H. D. Enge, and T. H. Kurz, "Terrestrial laser scanning in geology: data acquisition, processing and accuracy considerations," Journal of the Geological Society, vol. 165, no. 3, pp. 625-638, 2008. https://doi.org/10.1144/0016-76492007-100
  25. S. Harwin and A. Lucieer, "Assessing the accuracy of georeferenced point clouds produced via multi-view stereopsis from unmanned aerial vehicle (UAV) imagery," Remote Sensing, vol. 4, no. 6, pp. 1573-1599, 2012. https://doi.org/10.3390/rs4061573