Skip to main content
SpringerLink
Log in
Book cover

Asian Conference on Computer Vision

ACCV 2014: Computer Vision – ACCV 2014 pp 307–321Cite as

Stable Radial Distortion Calibration by Polynomial Matrix Inequalities Programming

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9003))

Abstract

Polynomial and rational functions are the number one choice when it comes to modeling of radial distortion of lenses. However, several extrapolation and numerical issues may arise while using these functions that have not been covered by the literature much so far. In this paper, we identify these problems and show how to deal with them by enforcing nonnegativity of certain polynomials. Further, we show how to model these nonnegativities using polynomial matrix inequalities (PMI) and how to estimate the radial distortion parameters subject to PMI constraints using semidefinite programming (SDP). Finally, we suggest several approaches on how to incorporate the proposed method into the overall camera calibration procedure.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Ladybug 3 camera. http://www.ptgrey.com/products/ladybug3

  2. Open source computer vision library. www.opencv.org

  3. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge, March 2004

    Google Scholar 

  4. Brown, D.C.: Decentering distortion of lenses. Photometric Eng. 3, 444–462 (1966)

    Google Scholar 

  5. Brown, D.C.: Close-range camera calibration. Photogrammetric Eng. 37, 855–866 (1971)

    Google Scholar 

  6. Choi, M.-D., Lam, T.Y., Reznick. B.: Sums of squares of real polynomials. In: Proceedings of Symposia in Pure mathematics, vol. 58, pp. 103–126. American Mathematical Society (1995)

    Google Scholar 

  7. Golub, G.H., Van Loan, C.F.: Matrix computations (2012)

    Google Scholar 

  8. Hartley, R., Kang, S.B.: Parameter-free radial distortion correction with center of distortion estimation. IEEE Trans. Pattern Anal. Mach. Intell. 29(8), 1309–1321 (2007)

    Article  Google Scholar 

  9. Hartley, R., Zisserman, A.: Multiple view geometry in computer vision, 2nd edn. Cambridge University, Cambridge (2003)

    MATH  Google Scholar 

  10. Henrion, D., Lasserre, J.-B.: Convergent relaxations of polynomial matrix inequalities and static output feedback. IEEE Trans. Autom. Control 51(02), 192–202 (2006)

    Article  MathSciNet  Google Scholar 

  11. Löfberg, J.: YALMIP: A toolbox for modeling and optimization in MATLAB. In: Proceedings of the CACSD Conference, Taipei, Taiwan (2004)

    Google Scholar 

  12. Ma, L., Chen, Y., Moore, K.: Rational radial distortion models of camera lenses with analytical solution for distortion correction. Int. J. Inf. Acquis. 1(02), 135–147 (2004)

    Article  Google Scholar 

  13. Nesterov, Y.: Squared functional systems and optimization problems. In: Frenk, H., Roos, K., Terlaky, T., Zhang, S. (eds.) High Performance Optimization, vol. 33, pp. 405–440. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  14. Slama, C.C., Theurer, C., Henriksen, S.W., et al.: Manual of Photogrammetry, 4th edn. American Society of photogrammetry, New York (1980)

    Google Scholar 

  15. Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11–12, 625–653 (1999)

    Article  MathSciNet  Google Scholar 

  16. Sturm, P., Ramalingam, S., Tardif, J.-P., Gasparini, S., Barreto, J.: Camera models and fundamental concepts used in geometric computer vision. Found. Trends Comput. Graph. Vis. 6(1–2), 1–183 (2011)

    Google Scholar 

  17. Szeliski, R.: Computer vision: algorithms and applications. Texts in Computer Science, vol. XX, p. 812. Springer, Heidelberg (2011)

    Book  Google Scholar 

  18. Tardif, J.-P., Sturm, P., Trudeau, M., Roy, S.: Calibration of cameras with radially symmetric distortion. IEEE Trans. Pattern Anal. Mach. Intell. 31(9), 1552–1566 (2009)

    Article  Google Scholar 

  19. Triggs, B., McLauchlan, P.F., Hartley, R.I., Fitzgibbon, A.W.: Bundle adjustment - a modern synthesis. In: ICCV ’99: Proceedings of the International Workshop on Vision Algorithms, pp. 298–372 (2000)

    Google Scholar 

  20. Tsai, R.Y.: An efficient and accurate camera calibration technique for 3D machine vision. In: Conference on Computer Vision and Pattern Recognition (1986)

    Google Scholar 

  21. Zhang, Z.: A Flexible new technique for camera calibration. IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000)

    Article  Google Scholar 

Download references

Acknowledgments

The authors were supported by the EC under project FP7-SPACE-2012-312377 PRoViDE.

Author information

Authors and Affiliations

  1. Faculty of Electrical Engineering, Czech Technical University in Prague, 166 27 Praha 6, Technická 2, Czech Republic

    Jan Heller, Didier Henrion & Tomáš Pajdla

  2. CNRS-LAAS, 7 Avenue du Colonel Roche, 31077, Toulouse, France

    Didier Henrion

  3. Université de Toulouse, 31077, Toulouse, France

    Didier Henrion

Authors
  1. Jan Heller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Didier Henrion
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tomáš Pajdla
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jan Heller .

Editor information

Editors and Affiliations

  1. Technische Universität München, Garching, Bayern, Germany

    Daniel Cremers

  2. University of Adelaide, Adelaide, South Australia, Australia

    Ian Reid

  3. Keio University, Yokohama, Kanagawa, Japan

    Hideo Saito

  4. University of California at Merced, Merced, California, USA

    Ming-Hsuan Yang

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Heller, J., Henrion, D., Pajdla, T. (2015). Stable Radial Distortion Calibration by Polynomial Matrix Inequalities Programming. In: Cremers, D., Reid, I., Saito, H., Yang, MH. (eds) Computer Vision – ACCV 2014. ACCV 2014. Lecture Notes in Computer Science(), vol 9003. Springer, Cham. https://doi.org/10.1007/978-3-319-16865-4_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-16865-4_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16864-7

  • Online ISBN: 978-3-319-16865-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation