New Efficient Solution to the Absolute Pose Problem for Camera with Unknown Focal Length and Radial Distortion

  • Martin Bujnak
  • Zuzana Kukelova
  • Tomas Pajdla
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6492)


In this paper we present a new efficient solution to the absolute pose problem for a camera with unknown focal length and radial distortion from four 2D-to-3D point correspondences. We propose to solve the problem separately for non-planar and for planar scenes. By decomposing the problem into these two situations we obtain simpler and more efficient solver than the previously known general solver. We demonstrate in synthetic and real experiments significant speedup as our new solvers are about 40× (non-planar) and 160× (planar) faster than the general solver. Moreover, we show that our two solvers can be joined into a new general solver, which gives comparable or better results than the existing general solver for of most planar as well as non-planar scenes.


Focal Length Image Point Projection Matrix Point Correspondence Specialized Solver 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    2D3. Boujou,
  2. 2.
    Abdel-Aziz, Y., Karara, H.: Direct linear transformation from comparator to object space coordinates in close-range photogrammetry. In: ASP Symp. Close-Range Photogrammetry, pp. 1–18 (1971)Google Scholar
  3. 3.
    Abidi, M.A., Chandra, T.: A new efficient and direct solution for pose estimation using quadrangular targets: Algorithm and evaluation. IEEE PAMI 17, 534–538 (1985)CrossRefGoogle Scholar
  4. 4.
    Ameller, M.A., Quan, M., Triggs, L.: Camera pose revisited – new linear algorithms. In: ECCV (2000)Google Scholar
  5. 5.
    Bujnak, M., Kukelova, Z., Pajdla, T.: A general solution to the P4P problem for camera with unknown focal length. In: CVPR (2008)Google Scholar
  6. 6.
    Byröd, M., Josephson, K., Åström, K.: Fast and Stable Polynomial Equation Solving and Its Application to Computer Vision. Int. J. Computer Vision 84, 237–255 (2009)CrossRefGoogle Scholar
  7. 7.
    Chum, O., Matas, J., Kittler, J.: Locally optimized RANSAC. In: DAGM, pp. 236–243 (2003)Google Scholar
  8. 8.
    Cox, D., Little, J., O’Shea, D.: Using Algebraic Geometry, 2nd edn., vol. 185. Springer, Berlin (2005)zbMATHGoogle Scholar
  9. 9.
    Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Comm. ACM 24, 381–395 (1981)CrossRefGoogle Scholar
  10. 10.
    Fitzgibbon, A.: Simultaneous linear estimation of multiple view geometry and lens distortion. In: CVPR, pp. 125–132 (2001)Google Scholar
  11. 11.
    Grunert, J.A.: Das pothenot’sche problem, in erweiterter gestalt; nebst bemerkungen über seine anwendung in der geodäsie. Archiv der Mathematik und Physik 1, 238–248 (1841)Google Scholar
  12. 12.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  13. 13.
    Moreno-Noguer, F., Lepetit, V., Fua, P.: Accurate non-iterative o(n) solution to the pnp problems. In: ICCV (2007)Google Scholar
  14. 14.
    Josephson, K., Byröd, M., Aström, K.: Pose Estimation with Radial Distortion and Unknown Focal Length. In: CVPR (2009)Google Scholar
  15. 15.
    Kukelova, Z., Bujnak, M., Pajdla, T.: Automatic Generator of Minimal Problem Solvers. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part III. LNCS, vol. 5304, pp. 302–315. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Leibe, B., Cornelis, N., Cornelis, K., Gool, L.J.V.: Dynamic 3d scene analysis from a moving vehicle. In: CVPR (2007)Google Scholar
  17. 17.
    Leibe, B., Schindler, K., Gool, L.J.V.: Coupled detection and trajectory estimation for multi-object. In: ICCV (2007)Google Scholar
  18. 18.
    Quan, L., Lan, Z.-D.: Linear n-point camera pose determination. IEEE PAMI 21, 774–780 (1999)CrossRefGoogle Scholar
  19. 19.
    Reid, G., Tang, J., Zhi, L.: A complete symbolic-numeric linear method for camera pose determination. In: ISSAC, pp. 215–223 (2003)Google Scholar
  20. 20.
    Slama, C.C. (ed.): Manual of Photogrammetry. American Society of Photogrammetry and Remote Sensing, Falls Church, Virginia (1980)Google Scholar
  21. 21.
    Snavely, N., Seitz, S.M., Szeliski, R.: Photo tourism: Exploring photo collections in 3D. ACM Trans. Graphics Proc. 25 (2006)Google Scholar
  22. 22.
    Stewénius, H., Engels, C., Nistér, D.: Recent developments on direct relative orientation. ISPRS J. Photogrammetry Remote Sensing 60, 284–294 (2006)CrossRefGoogle Scholar
  23. 23.
    Triggs, B.: Camera pose and calibration from 4 or 5 known 3d points. In: ICCV, pp. 278–284 (1999)Google Scholar
  24. 24.
    Wu, Y., Hu, Z.: PNP problem revisited. J. Math. Imaging Vision 24, 131–141 (2006)CrossRefGoogle Scholar
  25. 25.
    Zhi, L., Tang, J.: A complete linear 4-point algorithm for camera pose determination. In: AMSS, Academia Sinica (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Martin Bujnak
  • Zuzana Kukelova
    • 1
  • Tomas Pajdla
    • 1
  1. 1.Center for Machine PerceptionCzech Technical UniversityPragueCzech Republic

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