Skip to main content
SpringerLink
Log in

Lens Distortion Rectification Using Triangulation Based Interpolation

  • Conference paper
  • First Online:
Advances in Visual Computing (ISVC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9475))

Included in the following conference series:

Abstract

Nonlinear lens distortion rectification is a common first step in image processing applications where the assumption of a linear camera model is essential. For rectifying the lens distortion, forward distortion model needs to be known. However, many self-calibration methods estimate the inverse distortion model. In the literature, the inverse of the estimated model is approximated for image rectification, which introduces additional error to the system. We propose a novel distortion rectification method that uses the inverse distortion model directly. The method starts by mapping the distorted pixels to the rectified image using the inverse distortion model. The resulting set of points with subpixel locations are triangulated. The pixel values of the rectified image are linearly interpolated based on this triangulation. The method is applicable to all camera calibration methods that estimate the inverse distortion model and performs well across a large range of parameters.

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

Access this chapter

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

Institutional subscriptions

References

  1. Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, New York (2003)

    Google Scholar 

  2. Brown, D.C.: Decentering distortion of lenses. Photometric Eng. 32, 444–462 (1966)

    Google Scholar 

  3. Fitzgibbon, A.W.: Simultaneous linear estimation of multiple view geometry and lens distortion. In: Computer Vision and Pattern Recognition, IEEE (2001)

    Google Scholar 

  4. Mallon, J., Whelan, P.F.: Precise radial un-distortion of images. In: Proceedings of the 17th International Conference on Pattern Recognition ICPR 2004, vol. 1, pp. 18–21. IEEE (2004)

    Google Scholar 

  5. Devernay, F., Faugeras, O.: Straight lines have to be straight. Machine Vision and Applications 13, 14–24 (2001)

    Article  Google Scholar 

  6. Brauer-Burchardt, C., Voss, K.: A new algorithm to correct fish-eye-and strong wide-angle-lens-distortion from single images. In: International Conference on Image Processing, vol. 1, pp. 225–228. IEEE (2001)

    Google Scholar 

  7. Wang, A., Qiu, T., Shao, L.: A simple method of radial distortion correction with centre of distortion estimation. J. Math. Imaging Vision 35, 165–172 (2009)

    Article  MathSciNet  Google Scholar 

  8. Bukhari, F., Dailey, M.N.: Automatic radial distortion estimation from a single image. J. Math. Imaging Vision 45, 31–45 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  9. Cucchiara, R., Grana, C., Prati, A., Vezzani, R.: A hough transform-based method for radial lens distortion correction. In: 2003 Proceedings of 12th International Conference on Image Analysis and Processing, pp. 182–187. IEEE (2003)

    Google Scholar 

  10. Gonzalez-Aguilera, D., Gomez-Lahoz, J., Rodríguez-Gonzálvez, P.: An automatic approach for radial lens distortion correction from a single image. IEEE Sens. J 11, 956–965 (2011)

    Article  Google Scholar 

  11. Alvarez, L., Gómez, L., Sendra, J.R.: An algebraic approach to lens distortion by line rectification. J. Math. Imaging Vision 35, 36–50 (2009)

    Article  MathSciNet  Google Scholar 

  12. Heikkila, J.: Geometric camera calibration using circular control points. IEEE Trans. Patt. Anal. Machine Intell. 22, 1066–1077 (2000)

    Article  Google Scholar 

  13. Heikkila, J., Silvén, O.: A four-step camera calibration procedure with implicit image correction. In: Proceedings of 1997 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 1106–1112. IEEE (1997)

    Google Scholar 

  14. Wei, G.Q., De Ma, S.: Implicit and explicit camera calibration: theory and experiments. IEEE Trans. Patt. Anal. Mach. Intell. 16, 469–480 (1994)

    Article  Google Scholar 

  15. Grammatikopoulos, L., Karras, G., Petsa, E.: An automatic approach for camera calibration from vanishing points. ISPRS J. Photogrammetry Remote Sens. 62, 64–76 (2007)

    Article  Google Scholar 

  16. Ahmed, M., Farag, A.: Nonmetric calibration of camera lens distortion: differential methods and robust estimation. IEEE Transactions on Image Processing 14, 1215–1230 (2005)

    Article  Google Scholar 

  17. Thormählen, T., Broszio, H., Wassermann, I.: Robust line-based calibration of lens distortion from a single view. In: Proceedings of MIRAGE, pp. 105–112 (2003)

    Google Scholar 

  18. Prescott, B., McLean, G.: Line-based correction of radial lens distortion. Graph. Models Image Process. 59, 39–47 (1997)

    Article  Google Scholar 

  19. Strand, R., Hayman, E.: Correcting radial distortion by circle fitting. In: BMVC (2005)

    Google Scholar 

  20. Brauer-Burchardt, C., Voss, K.: Automatic correction of weak radial lens distortion in single views of urban scenes using vanishing points. In: International Conference on Image Processing, vol. 3, pp.865–868. IEEE (2002)

    Google Scholar 

  21. Lertrattanapanich, S., Bose, N.K.: High resolution image formation from low resolution frames using Delaunay triangulation. IEEE Transactions on Image Processing 11, 1427–1441 (2002)

    Article  MathSciNet  Google Scholar 

  22. Lee, D.T., Schachter, B.J.: Two algorithms for constructing a delaunay triangulation. Int. J. Comput. Inf. Sci. 9, 219–242 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  23. Dyn, N., Levin, D., Rippa, S.: Data dependent triangulations for piecewise linear interpolation. IMA J. Numer. Anal. 10, 137–154 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  24. Phong, B.T.: Illumination for computer generated pictures. Commun. ACM 18, 311–317 (1975)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Anadolu University, Eskişehir, Turkey

    Burak Benligiray & Cihan Topal

Authors
  1. Burak Benligiray
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cihan Topal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Burak Benligiray .

Editor information

Editors and Affiliations

  1. University of Nevada, Reno, Nevada, USA

    George Bebis

  2. NASA Ames Research Center, Moffett Field, California, USA

    Richard Boyle

  3. Lawrence Berkeley National Laboratory, Berkeley, California, USA

    Bahram Parvin

  4. Desert Research Institute, Reno, Nevada, USA

    Darko Koracin

  5. University of Houston, Houston, Texas, USA

    Ioannis Pavlidis

  6. IBM T.J. Watson Research Center, Yorktown Heights, New York, USA

    Rogerio Feris

  7. Purdue University, West Lafayette, Indiana, USA

    Tim McGraw

  8. Side Effects Software, Santa Monica, California, USA

    Mark Elendt

  9. The DiVE, Durham, North Carolina, USA

    Regis Kopper

  10. Texas A&M University, College Station, Texas, USA

    Eric Ragan

  11. Kent State University, Kent, Ohio, USA

    Zhao Ye

  12. Lawrence Berkeley National Laboratory, Berkeley, California, USA

    Gunther Weber

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Benligiray, B., Topal, C. (2015). Lens Distortion Rectification Using Triangulation Based Interpolation. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2015. Lecture Notes in Computer Science(), vol 9475. Springer, Cham. https://doi.org/10.1007/978-3-319-27863-6_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-27863-6_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27862-9

  • Online ISBN: 978-3-319-27863-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation