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A Stable Algebraic Camera Pose Estimation for Minimal Configurations of 2D/3D Point and Line Correspondences

  • Lipu ZhouEmail author
  • Jiamin Ye
  • Michael Kaess
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11364)

Abstract

This paper proposes an algebraic solution for the problem of camera pose estimation using the minimal configurations of 2D/3D point and line correspondences, including three point correspondences, two point and one line correspondences, one point and two line correspondences, and three line correspondences. In contrast to the previous works that address these problems in specific geometric ways, this paper shows that the above four cases can be solved in a generic algebraic framework. Specifically, the orientation of the camera is computed from a polynomial equation system of four quadrics, then the translation can be solved from a linear equation system. To make our algorithm stable, the key is the polynomial solver. We significantly improve the numerical stability of the efficient three quadratic equation system solver, E3Q3 [17], with a slight computational cost. The simulation results show that the numerical stability of our algorithm is comparable to the state-of-the-art Perspective-3-Point (P3P) algorithm [14], and outperforms the state-of-the-art algorithms of the other three cases. The numerical stability of our algorithm can be further improved by a rough estimation of the rotation matrix, which is generally available in the Localization and Mapping (SLAM) or Visual Odometry (VO) system (such as the pose from the last frame). Besides, this algorithm is applicable to real-time applications.

Keywords

Minimal solution Pose estimation SLAM 

References

  1. 1.
    Arun, K.S., Huang, T.S., Blostein, S.D.: Least-squares fitting of two 3-D point sets. IEEE Trans. Pattern Anal. Mach. Intell. 5, 698–700 (1987)CrossRefGoogle Scholar
  2. 2.
    Chen, H.H.: Pose determination from line-to-plane correspondences: existence condition and closed-form solutions. IEEE Trans. Pattern Anal. Mach. Intell. 13(6), 530–541 (1991).  https://doi.org/10.1109/34.87340CrossRefGoogle Scholar
  3. 3.
    Dhome, M., Richetin, M., Lapreste, J.T., Rives, G.: Determination of the attitude of 3D objects from a single perspective view. IEEE Trans. Pattern Anal. Mach. Intell. 11(12), 1265–1278 (1989).  https://doi.org/10.1109/34.41365CrossRefGoogle Scholar
  4. 4.
    Finsterwalder, S., Scheufele, W.: Das rückwärtseinschneiden im raum. Verlag d. Bayer. Akad. d. Wiss. (1903)Google Scholar
  5. 5.
    Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24(6), 381–395 (1981)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Gao, X.S., Hou, X.R., Tang, J., Cheng, H.F.: Complete solution classification for the perspective-three-point problem. IEEE Trans. Pattern Anal. Mach. Intell. 25(8), 930–943 (2003)CrossRefGoogle Scholar
  7. 7.
    Grunert, J.A.: Das pothenotische problem in erweiterter gestalt nebst über seine anwendungen in der geodäsie. Grunerts archiv für mathematik und physik 1(238–248), 1 (1841)Google Scholar
  8. 8.
    Guennebaud, G., Jacob, B., et al.: Eigen v3 (2010). http://eigen.tuxfamily.org
  9. 9.
    Haralick, B.M., Lee, C.N., Ottenberg, K., Nölle, M.: Review and analysis of solutions of the three point perspective pose estimation problem. Int. J. Comput. Vis. 13(3), 331–356 (1994)CrossRefGoogle Scholar
  10. 10.
    Hartley, R., Li, H.: An efficient hidden variable approach to minimal-case camera motion estimation. IEEE Trans. Pattern Anal. Mach. Intell. 34(12), 2303–2314 (2012)CrossRefGoogle Scholar
  11. 11.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  12. 12.
    Horn, B.K.: Closed-form solution of absolute orientation using unit quaternions. JOSA A 4(4), 629–642 (1987)CrossRefGoogle Scholar
  13. 13.
    Jose Tarrio, J., Pedre, S.: Realtime edge-based visual odometry for a monocular camera. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 702–710 (2015)Google Scholar
  14. 14.
    Ke, T., Roumeliotis, S.I.: An efficient algebraic solution to the perspective-three-point problem. In: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 4618–4626, July 2017.  https://doi.org/10.1109/CVPR.2017.491
  15. 15.
    Kneip, L., Scaramuzza, D., Siegwart, R.: A novel parametrization of the perspective-three-point problem for a direct computation of absolute camera position and orientation. In: 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2969–2976. IEEE (2011)Google Scholar
  16. 16.
    Kuang, Y., Åström, K.: Pose estimation with unknown focal length using points, directions and lines. In: ICCV, pp. 529–536 (2013)Google Scholar
  17. 17.
    Kukelova, Z., Heller, J., Fitzgibbon, A.: Efficient intersection of three quadrics and applications in computer vision. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1799–1808 (2016)Google Scholar
  18. 18.
    Linnainmaa, S., Harwood, D., Davis, L.S.: Pose determination of a three-dimensional object using triangle pairs. IEEE Trans. Pattern Anal. Mach. Intell. 10(5), 634–647 (1988)CrossRefGoogle Scholar
  19. 19.
    Little, J.B., O’Shea, D.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer, New York (2007).  https://doi.org/10.1007/978-0-387-35651-8CrossRefzbMATHGoogle Scholar
  20. 20.
    Lu, Y., Song, D.: Robust RGB-D odometry using point and line features. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 3934–3942 (2015)Google Scholar
  21. 21.
    Masselli, A., Zell, A.: A new geometric approach for faster solving the perspective-three-point problem. In: 2014 22nd International Conference on Pattern Recognition (ICPR), pp. 2119–2124. IEEE (2014)Google Scholar
  22. 22.
    Merritt, E.: Explicit three-point resection in space. Photogram. Eng. 15(4), 649–655 (1949)Google Scholar
  23. 23.
    Mur-Artal, R., Montiel, J.M.M., Tardos, J.D.: ORB-SLAM: a versatile and accurate monocular slam system. IEEE Trans. Robot. 31(5), 1147–1163 (2015)CrossRefGoogle Scholar
  24. 24.
    OpenCV: Open source computer vision library (2017). https://github.com/itseez/opencv
  25. 25.
    Proença, P.F., Gao, Y.: SPLODE: Semi-probabilistic point and line odometry with depth estimation from RGB-D camera motion. arXiv preprint arXiv:1708.02837 (2017)
  26. 26.
    Pumarola, A., Vakhitov, A., Agudo, A., Sanfeliu, A., Moreno-Noguer, F.: PL-SLAM: real-time monocular visual SLAM with points and lines. In: 2017 IEEE International Conference on Robotics and Automation (ICRA), pp. 4503–4508. IEEE (2017)Google Scholar
  27. 27.
    Quan, L., Lan, Z.: Linear N-point camera pose determination. IEEE Trans. Pattern Anal. Mach. Intell. 21(8), 774–780 (1999)CrossRefGoogle Scholar
  28. 28.
    Ramalingam, S., Bouaziz, S., Sturm, P.: Pose estimation using both points and lines for geo-localization. In: 2011 IEEE International Conference on Robotics and Automation (ICRA), pp. 4716–4723. IEEE (2011)Google Scholar
  29. 29.
    Sola, J., Vidal-Calleja, T., Civera, J., Montiel, J.M.M.: Impact of landmark parametrization on monocular EKF-SLAM with points and lines. Int. J. Comput. Vis. 97(3), 339–368 (2012)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Taylor, C.J., Kriegman, D.J.: Structure and motion from line segments in multiple images. IEEE Trans. Pattern Anal. Mach. Intell. 17(11), 1021–1032 (1995)CrossRefGoogle Scholar
  31. 31.
    Vakhitov, A., Funke, J., Moreno-Noguer, F.: Accurate and linear time pose estimation from points and lines. In: Leibe, B., Matas, J., Sebe, N., Welling, M. (eds.) ECCV 2016. LNCS, vol. 9911, pp. 583–599. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-46478-7_36CrossRefGoogle Scholar
  32. 32.
    Wu, W.: Basic principles of mechanical theorem proving in elementary geometries. In: Selected Works Of Wen-Tsun Wu, pp. 195–223. World Scientific (2008)Google Scholar
  33. 33.
    Xu, C., Zhang, L., Cheng, L., Koch, R.: Pose estimation from line correspondences: a complete analysis and a series of solutions. IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1209–1222 (2017)CrossRefGoogle Scholar
  34. 34.
    Yang, S., Scherer, S.: Direct monocular odometry using points and lines. arXiv preprint arXiv:1703.06380 (2017)
  35. 35.
    Zhou, F., Duh, H.B.L., Billinghurst, M.: Trends in augmented reality tracking, interaction and display: a review of ten years of ISMAR. In: Proceedings of the 7th IEEE/ACM International Symposium on Mixed and Augmented Reality, pp. 193–202. IEEE Computer Society (2008)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Robotics InstituteCarnegie Mellon UniversityPittsburghUSA
  2. 2.Institute of Engineering Thermophysics, Chinese Academy of SciencesBeijingChina

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