Skip to main content
SpringerLink
Log in

A New Solution to the Relative Orientation Problem Using Only 3 Points and the Vertical Direction

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

This paper presents a new method to solve the relative pose between two images, using three pairs of homologous points and the knowledge of the vertical direction. The vertical direction can be determined in two ways: The first requires direct physical measurements such as the ones provided by an IMU (inertial measurement unit). The other uses the automatic extraction of the vanishing point corresponding to the vertical direction in an image. This knowledge of the vertical direction solves two unknowns among the three parameters of the relative rotation, so that only three homologous couples of points are requested to position a couple of images. Rewriting the coplanarity equations thus leads to a much simpler solution. The remaining unknowns resolution is performed by “hiding a variable” approach. The elements necessary to build a specific algebraic solver are given in this paper, allowing for a real-time implementation. The results on real and synthetic data show the efficiency of this method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Antone, M., Teller, S.: Automatic Recovery of Relative Camera Rotations for Urban Scenes, vol. 02, pp. 282–289. IEEE Computer Society, Los Alamitos (2000)

    Google Scholar 

  2. Barnard, S.T.: Interpreting perspective images. Artif. Intell. 21, 435–462 (1983)

    Article  Google Scholar 

  3. Batra, D., Nabbe, B., Hebert, M.: An Alternative Formulation for Five Point Relative Pose Problem, pp. 21–21 (2007)

  4. Cox, D., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms, 3rd edn. Undergraduate Texts in Mathematics. Springer, New York (2007)

    Book  MATH  Google Scholar 

  5. Elkadi, M., Mourrain, B.: Symbolic-numeric methods for solving polynomial equations and applications. In: Dickenstein, A., Emiris, I.Z. (eds.) Solving Polynomial Equations: Foundations, Algorithms, and Applications, pp. 124–168 (2005)

    Google Scholar 

  6. 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)

    Article  MathSciNet  Google Scholar 

  7. Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004)

    MATH  Google Scholar 

  8. http://www.xsens.com/

  9. Kalantari, M., Jung, F., Paparoditis, N., Guédon, J.P.: Robust and automatic vanishing points detection with their uncertainties from a single uncalibrated image, by planes extraction on the unit sphere. In: IAPRS, Beijing, China, vol. 37 (Part 3A), pp. 203–208 (2008)

    Google Scholar 

  10. Kukelova, Z., Bujnak, M., Pajdla, T.: Polynomial eigenvalue solutions to the 5-pt and 6-pt relative pose problems (2008)

  11. Li, H.D., Hartley, R.I.: Five-Point Motion Estimation Made Easy, pp. I: 630–633 (2006)

  12. Lobo, J., Dias, J.: Vision and inertial sensor cooperation using gravity as a vertical reference. IEEE Trans. Pattern Anal. Mach. Intell. 25(12), 1597–1608 (2003)

    Article  Google Scholar 

  13. Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60(2), 91–110 (2004)

    Article  Google Scholar 

  14. Lutton, E., Maitre, H., Lopez-Krahe, J.: Contribution to the determination of vanishing points using Hough transform. IEEE Trans. Pattern Anal. Mach. Intell. 16(4), 430–438 (1994)

    Article  Google Scholar 

  15. Nistér, D.: An efficient solution to the five-point relative pose problem. IEEE Trans. Pattern Anal. Mach. Intell. 26(6), 756–777 (2004)

    Article  Google Scholar 

  16. Philip, J.: A non-iterative algorithm for determining all essential matrices corresponding to five point pairs. Photogramm. Rec. 15(88), 589–599 (1996)

    Article  Google Scholar 

  17. Schaffalitzky, F., Zisserman, A.: Planar grouping for automatic detection of vanishing lines and points. Image Vis. Comput. 18, 647–658 (2000)

    Article  Google Scholar 

  18. Segvic, M., Schweighofer, G., Pinz, A.: Performance evaluation of the five-point relative pose with emphasis on planar scenes. In: Performance Evaluation for Computer Vision, Workshop of the Austrian Association for Pattern Recognition, Austria, pp. 33–40 (2007)

    Google Scholar 

  19. Shufelt, J.A.: Performance evaluation and analysis of vanishing point detection techniques. IEEE Trans. PAMI 21(3), 282–288 (1999)

    Google Scholar 

  20. Stewénius, H.: Matlab code for solving the fivepoint problem. http://vis.uky.edu/~stewe/FIVEPOINT/

  21. Stewénius, H., Engels, C., Nistér, D.: Recent developments on direct relative orientation. ISPRS J. Photogramm. Remote Sens. 60(4), 284–294 (2006)

    Article  Google Scholar 

  22. Strecha, C., von Hansen, W., Van Gool, L.J., Fua, P., Thoennessen, U.: On Benchmarking Camera Calibration and Multi-view Stereo for High Resolution Imagery, pp. 1–8 (2008)

  23. Triggs, B.: Routines for relative pose of two calibrated cameras from 5 points. Technical report, INRIA (2000)

  24. van den Heuvel, F.A.: Vanishing point detection for architectural photogrammetry. Int. Arch. Photogramm. Remote Sens. 32(5), 652–659 (1998)

    Google Scholar 

  25. Vieville, T., Clergue, E., Facao, P.E.D.: Computation of ego motion using the vertical cue. Mach. Vis. Appl. 8(1), 41–52 (1995)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ecole Nationale des Sciences Géographiques, IGN France, Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN), UMR CNRS 6597, Polytech’Nantes, Nantes, France

    Mahzad Kalantari

  2. Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Amir Hashemi

  3. Commissariat général au développement durable, Direction de la recherche et de l’innovation, Ministère de l’écologie, de l’énergie, du développement durable et de la mer, en charge des technologies vertes et des négociations sur le climat, La Défense, France

    Franck Jung

  4. Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN), UMR CNRS 6597, Polytech’Nantes, Nantes, France

    Jean-Pierre Guedon

Authors
  1. Mahzad Kalantari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amir Hashemi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Franck Jung
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jean-Pierre Guedon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mahzad Kalantari.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kalantari, M., Hashemi, A., Jung, F. et al. A New Solution to the Relative Orientation Problem Using Only 3 Points and the Vertical Direction. J Math Imaging Vis 39, 259–268 (2011). https://doi.org/10.1007/s10851-010-0234-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10851-010-0234-2

Keywords

Search

Navigation