Estimating Principal Point and Nonlinear Parameters of Camera from a Planar Calibration Image

  • Qiuyu Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7663)


The paper presents a new calibration method of camera’s principal point and nonlinear parameters, by using the characteristic of radial nonlinear distortion and the curvatures of lines formed by control points from a single planar calibration image. The principal point is estimated by using two curved surfaces fitted by curvatures at all control points, and is the zero curvature crossing point of these two curved surfaces. The radial nonlinear parameters are computed by optimizing the curvature cost function, which adopts a backward nonlinear mapping model. The estimated results of simulated camera and real camera show that our method has higher accuracy and less computational complexity. The method can be used for on-line camera calibration where relative low calibration accuracy can be accepted and low algorithm complexity is needed, or as the initial values of complex calibration optimization algorithm.


Camera calibration Principal point Intrinsic parameters Curvature Radial nonlinear distortion 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Zhang, Z.: Camera Calibration with One-Dimensional Objects. IEEE Trans. PAMI 26, 892–899 (2004)CrossRefGoogle Scholar
  2. 2.
    Zhang, Z.: A Flexible New Technique for Camera Calibration. IEEE Trans. PAMI 22, 1330–1334 (2000)CrossRefGoogle Scholar
  3. 3.
    Sturm, F., Maybank, S.J.: On Plane based Camera Calibration: A General Algorithm, Singularities, Applications. Comput. Vision Pattern Recogn., 432–437 (1999)Google Scholar
  4. 4.
    Kaset, S., Kitti, T., Takenobu, M.: A Determination Method of Initial Camera Parameters for Coplanar Calibration. Int. J. Control Autom. Syst. 7(5), 777–787 (2009)CrossRefGoogle Scholar
  5. 5.
    Tian, Y., et al.: A Simple Centroid-based Method to Find the Principal Point of an Image Plane for a Pincushion Distortion. Int. J. Adv. Manu. Techn. 23, 110–115 (2004)CrossRefGoogle Scholar
  6. 6.
    Thormählen, T., Broszio, H., Wassermann, I.: Robust Line-Based Calibration of Lens Distortion from a Single View. In: Proceedings of Mirage 2003, INRIA Rocquencourt, France, pp. 105–112 (2003)Google Scholar
  7. 7.
    Devernay, F., Faugeras, O.: Straight Lines Have to be Straight. Mach. Vision Appl., 14–24 (2001)Google Scholar
  8. 8.
    Fakhrul, Y., et al.: Establishing the Straightness of a Line for Radial Distortion Correction through Conic Fitting. Int. J. Comput. Sci. Network Security 9, 286–293 (2009)Google Scholar
  9. 9.
    Carlos, R., Antonio-Jose, S.: Correcting Non-linear Lens Distortion in Cameras without Using a Model. Opt. Laser Techn. 42, 628–639 (2010)CrossRefGoogle Scholar
  10. 10.
    Perš, J., Kovačič, S.: Nonparametric, Model-based Radial Lens Distortion Correction Using Titled Camera Assumption. In: Proceedings of the Computer Vision Winter Workshop 2002, pp. 286–295 (2002)Google Scholar
  11. 11.
    Ruiz, P.E., Garcia-Mateos, G.: A Note on Principal Point Estimability. In: Proceedings of 16th International Conference on Pattern Recognition 2002, vol. 2, pp. 304–307 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Qiuyu Zhu
    • 1
  1. 1.School of Communication and Information EngineeringShanghai UniversityShanghaiP.R. China

Personalised recommendations