Skip to main content
SpringerLink
Log in

Quaternion epipolar decomposition for camera pose identification and animation

  • Special Issue
  • Published:
Opto-Electronics Review

Abstract

In the literature of computer vision, computer graphics and robotics, the use of quaternions is exclusively related to 3D rotation representation and interpolation. In this research we found how epipoles in multi-camera systems can be used to represent camera poses in the quaternion domain. The rotational quaternion is decomposed in two epipole rotational quaternions and one z axis rotational quaternion. Quadratic form of the essential matrix is also related to quaternion factors. Thus, five pose parameters are distributed into three independent rotational quaternions resulting in measurement error separation at camera pose identification and greater flexibility at virtual camera animation. The experimental results refer to the design of free viewpoint television.

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. E. Apostolidis, A. Koz, and G. Triantafyllidis, “Watermarking tests for free-view point television,” Proc. IEEE Conf. 3DTV, pp. 1–4, Kos, 2007.

  2. E. Cooke and N. O’Connor, “Multiple image view synthesis for free viewpoint video Applications”, Proc. IEEE Int. Conf. Image Process, pp. 1029–1032, Genoa, 2005.

  3. E. Cooke, P. Kau, and T. Sikora, “Multi-view synthesis: A novel view creation approach for free viewpoint video”, Signal Proces-Image 21, 476–492 (2006).

    Article  Google Scholar 

  4. V. Nozick and H. Saito, “Real-time free viewpoint from multiple moving cameras,” Advanced Concepts for Inelligent Vision Systems, 72–83 (2007).

  5. G. Golub and C. Loan, Matrix Computations, 2nd edition Williamson, Johns Hopkins University Press, Baltimore, 1989.

    MATH  Google Scholar 

  6. J. Kuipers, Quaternions and RotationSsequences, Princeton University Press, Princeton, 2002.

    Google Scholar 

  7. W.R. Hamilton and W.E. Hamilton, Elements of Quaternions, Longmans, Green, & Co., in e-Book Google, 1866.

  8. J. Vince, Quaternions for Computer Graphics, Springer-Verlag London, 2011.

    Book  MATH  Google Scholar 

  9. E. Salamin, Application of quaternions to computation with rotations, Unpublished Internal Report, Standford University, Stanford, 1979.

    Google Scholar 

  10. B.K.P. Horn, “Closed-form solution of absolute orientation using unit quaternions”, Journal of the Optical Society of America A4, 629–642 (1987).

    ADS  Google Scholar 

  11. O. Faugeras and Q. Luang, The Geometry of Multiple Images, The MIT Press, Cambridge, 2001.

    MATH  Google Scholar 

  12. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, Cambridge University Press, 2000.

  13. Q. Luong and O. Faugeras, “On the determination of epipoles using cross-ratios” Comput. Vis. Image Und. 71, 1–18 (1998).

    Article  Google Scholar 

  14. A. Smolic, K. Mueller, P. Merkle, T. Rein, T.M. Kautzner, P. Eisert, and T. Wiegand, “Free viewpoint video extraction, representation, coding, and rendering”, Proc. IEEE Int. Conf. Image Process, 3287–3290, Singapore, 2004.

  15. Y. Ma, S. Soatto, J. Kosecka, and S. Sastry, An Invitation to 3-D Vision, The MIT Press, Cambridge, 2004.

    Book  MATH  Google Scholar 

  16. A. Nowakowski and W. Skarbek, “Homography of central points for optical distortion compensation,” Opto-Electron. Rev. 4, 202–209 (2007).

    Article  ADS  Google Scholar 

  17. W. Skarbek and M. Tomaszewski, “Epipolar angular factorisation of essentail matrix for camera pose calibration,” in 4th Int. Conf. Computer Vision/Computer Graphics Collaboration Techniques, Lect. Notes Comput. Sc. 5496, 401–402 (2009).

    MathSciNet  Google Scholar 

  18. W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C. The Art of Scientific Computing, Cambridge University Press, 2006.

  19. W. Skarbek, M. Tomaszewski, and A. Nowakowski, “Camera calibration by linear decomposition,” Proc. SPIE: 6159, 838–849 (2006).

    Google Scholar 

  20. W. Skarbek and M. Tomaszewski, “On projection matrix identification for camera calibration”, 2nd Int. Conf. on Computer Vision Theory and Applications, Barcelona, 2007.

  21. R. Hartley, “In defense of the eight-point algorithm,” IEEE T. Pattern Anal. Machine Intel. 19, 580–593 (1997).

    Article  Google Scholar 

  22. V. Nozick and H. Saito, “Online multiple view computation for autostereoscopic display”, Pacific Rim Symp. on Image and Video Technology, 399–412, Santiago, 2007.

  23. Y. Ito and H. Saito, “Free-viewpoint image synthesis from multiple-view images taken with uncalibrated moving cameras”, Proc. IEEE Int. Conf. Image Process III, 29–32, Genoa, 2005.

  24. W. Li, J. Zhou, B. Li, and M. Sezan, “Virtual view specification and synthesis in free viewpoint television application,” Proc. IEEE Conf. 3DTV, 464–471, Toronto, 2006.

  25. E. Pervin and J. Webb, Quaternions in Computer Vision and Robotics, Tech. Report, Dept. of Computer Science, Carnegie-Mellon U., CMU-CS-82-150, 1982.

  26. G. Xu and Z. Zhang, Epipolar Geometry in Stereo, Motion, and Object Recognition, Kluwer Academic Publishers, Dordrecht, 1996.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Radioelectronics, Faculty of Electronics and Information Technology, Television Division, Warsaw University of Technology, 15/19 Nowowiejska Str., 00-665, Warsaw, Poland

    W. Skarbek

  2. Polish-Japanese Institute of Information Technology, 86 Koszykowa Str., 02-008, Warsaw, Poland

    M. Tomaszewski

Authors
  1. W. Skarbek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Tomaszewski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to W. Skarbek.

About this article

Cite this article

Skarbek, W., Tomaszewski, M. Quaternion epipolar decomposition for camera pose identification and animation. Opto-Electron. Rev. 21, 63–78 (2013). https://doi.org/10.2478/s11772-013-0075-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11772-013-0075-9

Keywords

Search

Navigation