Skip to main content

Camera re-calibration after zooming based on sets of conics

The Visual Computer volume 32, pages 663–674 (2016)Cite this article

Abstract

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.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3

References

  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)

    Article  Google Scholar 

  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. Zhang, Z.: Flexible Camera Calibration by Viewing a Plane from Unknown Orientations. In: Proceedings of ICCV99 (1999)

  4. Bouguet, J.-Y.: Camera Calibration Toolbox for Matlab, http://www.vision.caltech.edu/bouguetj

  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)

  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)

  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)

  8. Agapito, L., Hayman, E., Reid, I.: Self-calibration of rotating and zooming camera. IJCV 45(2), 107–127 (2001)

    Article  MATH  Google Scholar 

  9. Frosio, I., Alzati, A., Bertolini, M., Turrini, C., Borghese, N.A.: Linear pose estimate from corresponding conics. Pattern Recog. 45, 4169–4181 (2012)

    Article  Google Scholar 

  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)

  11. Borghese, N.A., Colombo, F.M., Alzati, A.: Computing camera focal length by zooming a single point. Pattern Recognit. 39, 1522–1529 (2006)

    Article  Google Scholar 

  12. Li, C., Lu, P., Ma, L.: A camera on-line recalibration framework using SIFT. Visual Comput. 26(3), 227–240 (2010)

    Article  Google Scholar 

  13. Faugeras, O.: Three-Dimensional Computer Vision: A Geometric Viewpoint. MIT Press, Cambridge (1993)

    Google Scholar 

  14. Nikon website, http://www.nikon.com/

  15. Canon website, http://www.canon.com/

  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)

    Article  Google Scholar 

  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)

  18. Fitzgibbon, A.W., Fisher, R.B.: A buyer’s guide to conic fitting. Proceedings of British Machine Vision Conference Birmingham (1995)

  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. 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)

  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 2000

  22. Wan, D., Zhou, J.: Stereo vision using two PTZ cameras. Comput. Vision Image Underst. 112, 184–194 (2008)

    Article  Google Scholar 

  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)

  24. Yu, C., Sharma, G.: Plane-based calibration of cameras with zoom variation. In: Proceedings of SPIE Visual Communication and Image Processing ’06

  25. Valera, M., Velastin, S.A.: Intelligent distributed surveillance systems: a review. In: Proceedings of Visual Image Signal Processing, 152(2), (2005)

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  28. Troccoli, A., Pajak, D., Pulli, K.: FCam for Multiple Cameras. SPIE Electronic Imaging: Multimedia on Mobile Images 2012, (January 2012)

Download references

Author information

Authors and Affiliations

  1. NVIDIA, Santa Clara, CA, USA

    Iuri Frosio

  2. Mathematics Department, University of Milan, Milan, Italy

    Cristina Turrini & Alberto Alzati

Authors
  1. Iuri Frosio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cristina Turrini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alberto Alzati
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alberto Alzati.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Frosio, I., Turrini, C. & Alzati, A. Camera re-calibration after zooming based on sets of conics. Vis Comput 32, 663–674 (2016). https://doi.org/10.1007/s00371-015-1089-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-015-1089-8

Keywords

  • Camera calibration
  • Conics
  • Degenerate conics
  • Ellipses
  • Zoom lens
  • Line detection