The Visual Computer

, Volume 32, Issue 5, pp 663–674 | Cite as

Camera re-calibration after zooming based on sets of conics

  • Iuri Frosio
  • Cristina Turrini
  • Alberto AlzatiEmail author
Original Article


We describe a method to compute the internal parameters (focal and principal point) of a camera with known position and orientation, based on the observation of two or more conics on a known plane. The conics can even be degenerate (e.g., pairs of lines). The proposed method can be used to re-estimate the internal parameters of a fully calibrated camera after zooming to a new, unknown, focal length. It also allows estimating the internal parameters when a second, fully calibrated camera observes the same conics. The parameters estimated through the proposed method are coherent with the output of more traditional procedures that require a higher number of calibration images. A deep analysis of the geometrical configurations that influence the proposed method is also reported.


Camera calibration Conics Degenerate conics Ellipses Zoom lens Line detection 


  1. 1.
    Lu, X., Wang, Y., Xu, H., Zhou, X., Zhao, K.: A new method for camera stratified self-calibration under circular motion. Visual Comput. 29(11), 1107–1119 (2012)CrossRefGoogle Scholar
  2. 2.
    Zhang, Z.: Camera calibration. In: Medioni, G., Kang, S.B. (eds.) Emergin Topics in Computer Vision, vol. 2, pp. 4–43. Prentice Hall Professional Technical Reference, Upper Saddle River (2004)Google Scholar
  3. 3.
    Zhang, Z.: Flexible Camera Calibration by Viewing a Plane from Unknown Orientations. In: Proceedings of ICCV99 (1999)Google Scholar
  4. 4.
    Bouguet, J.-Y.: Camera Calibration Toolbox for Matlab,
  5. 5.
    Abad, F., Camahort, E., Viv, Roberto: Camera Calibration Using Two Concentric Circles. In: International Conference on Image Analysis and Recognition, pp. 688–696 (2004)Google Scholar
  6. 6.
    Ying, X., Zha, A.H.: Camera calibration using principal-axes aligned conics, In: Proceedings of the 8th Asian Conference on Computer Vision, vol. part I, pp. 138–148 (2007)Google Scholar
  7. 7.
    Yang, C., Sun, F., Hu, Z.: Planar conic based camera calibration. In: Proceedings of the 15th International Conference on Pattern Recognition, vol. 1, pp. 555–558 (2000)Google Scholar
  8. 8.
    Agapito, L., Hayman, E., Reid, I.: Self-calibration of rotating and zooming camera. IJCV 45(2), 107–127 (2001)CrossRefzbMATHGoogle Scholar
  9. 9.
    Frosio, I., Alzati, A., Bertolini, M., Turrini, C., Borghese, N.A.: Linear pose estimate from corresponding conics. Pattern Recog. 45, 4169–4181 (2012)CrossRefGoogle Scholar
  10. 10.
    Kahl, F., Heyden, A.: Using conic correspondences in two images to estimate the epipolar geometry. In: Proceedings of the International Conference on Computer Vision, 761–766 (1998)Google Scholar
  11. 11.
    Borghese, N.A., Colombo, F.M., Alzati, A.: Computing camera focal length by zooming a single point. Pattern Recognit. 39, 1522–1529 (2006)CrossRefGoogle Scholar
  12. 12.
    Li, C., Lu, P., Ma, L.: A camera on-line recalibration framework using SIFT. Visual Comput. 26(3), 227–240 (2010)CrossRefGoogle Scholar
  13. 13.
    Faugeras, O.: Three-Dimensional Computer Vision: A Geometric Viewpoint. MIT Press, Cambridge (1993)Google Scholar
  14. 14.
    Nikon website,
  15. 15.
    Canon website,
  16. 16.
    Fraser, C.S., Ajlouni, A.S.S.: Zoom-dependent camera calibration in digital close-range photogrammetry. Photogramm. Eng. Remote Sens. 72(9), 1017–1026 (2006)CrossRefGoogle Scholar
  17. 17.
    Sun, X., Sun, J., Zhang, J., Li, M.: Simple zoom-lens digital camera calibration method based on exif, in Three-Dimensional Image Capture and Applications VI 79 (2004)Google Scholar
  18. 18.
    Fitzgibbon, A.W., Fisher, R.B.: A buyer’s guide to conic fitting. Proceedings of British Machine Vision Conference Birmingham (1995)Google Scholar
  19. 19.
    Madsen, K., Nielsen, H.B., Tingleff, O.: Methods for Non-Linear Least Squares Problems, 2nd edn. Informatics and Mathematical Modelling, Technical University of Denmark, Kongens Lyngby (2004)Google Scholar
  20. 20.
    Triggs, B., McLauchlan, P.F., Hartley, R.I., Fitzgibbon, A.W.: Bundle adjustment—a modern synthesis. In: Proceedings of the International Workshop on Visual Algorithm: Theory and Practice, ICCV (1999)Google Scholar
  21. 21.
    Ahmed, M.T., Farag, A.A.: Zoom-lens camera calibration from noisy data with outliers, Proceedings of the British Machine Vision Conference 2000, BMVC 2000, Bristol, UK, 11–14 Sept 2000Google Scholar
  22. 22.
    Wan, D., Zhou, J.: Stereo vision using two PTZ cameras. Comput. Vision Image Underst. 112, 184–194 (2008)CrossRefGoogle Scholar
  23. 23.
    Calore, E., Pedersini, F., Frosio, I.: Accelerometer based horizon and keystone perspective correction. In: Instrumentation and Measurement Technology Conference (I2MTC), 2012 IEEE International, 205–209 (2012)Google Scholar
  24. 24.
    Yu, C., Sharma, G.: Plane-based calibration of cameras with zoom variation. In: Proceedings of SPIE Visual Communication and Image Processing ’06Google Scholar
  25. 25.
    Valera, M., Velastin, S.A.: Intelligent distributed surveillance systems: a review. In: Proceedings of Visual Image Signal Processing, 152(2), (2005)Google Scholar
  26. 26.
    Buch, N., Velastin, S.A., Orwell, J.: A review of computer vision techniques for the analysis of urban traffic. IEEE Trans. Int. Transp. Sys. 12(3), 920–939 (2011)CrossRefGoogle Scholar
  27. 27.
    Calore, E., Frosio, I.: Accelerometer-based correction of skewed horizon and keystone distortion in digital photography. Image Vision Comput. 32(9), 606–615 (2014)CrossRefGoogle Scholar
  28. 28.
    Troccoli, A., Pajak, D., Pulli, K.: FCam for Multiple Cameras. SPIE Electronic Imaging: Multimedia on Mobile Images 2012, (January 2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.NVIDIASanta ClaraUSA
  2. 2.Mathematics DepartmentUniversity of MilanMilanItaly

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