Lens Distortion Rectification Using Triangulation Based Interpolation

  • Burak BenligirayEmail author
  • Cihan Topal
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9475)


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.


Delaunay Triangulation Distorted Image Bilinear Interpolation Lens Distortion Distortion Parameter 
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.


  1. 1.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, New York (2003)Google Scholar
  2. 2.
    Brown, D.C.: Decentering distortion of lenses. Photometric Eng. 32, 444–462 (1966)Google Scholar
  3. 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. 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. 5.
    Devernay, F., Faugeras, O.: Straight lines have to be straight. Machine Vision and Applications 13, 14–24 (2001)CrossRefGoogle Scholar
  6. 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. 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)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Bukhari, F., Dailey, M.N.: Automatic radial distortion estimation from a single image. J. Math. Imaging Vision 45, 31–45 (2013)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 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. 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)CrossRefGoogle Scholar
  11. 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)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Heikkila, J.: Geometric camera calibration using circular control points. IEEE Trans. Patt. Anal. Machine Intell. 22, 1066–1077 (2000)CrossRefGoogle Scholar
  13. 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. 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)CrossRefGoogle Scholar
  15. 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)CrossRefGoogle Scholar
  16. 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)CrossRefGoogle Scholar
  17. 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. 18.
    Prescott, B., McLean, G.: Line-based correction of radial lens distortion. Graph. Models Image Process. 59, 39–47 (1997)CrossRefGoogle Scholar
  19. 19.
    Strand, R., Hayman, E.: Correcting radial distortion by circle fitting. In: BMVC (2005)Google Scholar
  20. 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. 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)CrossRefMathSciNetGoogle Scholar
  22. 22.
    Lee, D.T., Schachter, B.J.: Two algorithms for constructing a delaunay triangulation. Int. J. Comput. Inf. Sci. 9, 219–242 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Dyn, N., Levin, D., Rippa, S.: Data dependent triangulations for piecewise linear interpolation. IMA J. Numer. Anal. 10, 137–154 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Phong, B.T.: Illumination for computer generated pictures. Commun. ACM 18, 311–317 (1975)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Electrical and Electronics EngineeringAnadolu UniversityEskişehirTurkey

Personalised recommendations