Can We Consider Central Catadioptric Cameras and Fisheye Cameras within a Unified Imaging Model

  • Xianghua Ying
  • Zhanyi Hu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3021)


There are two kinds of omnidirectional cameras often used in computer vision: central catadioptric cameras and fisheye cameras. Previous literatures use different imaging models to describe them separately. A unified imaging model is however presented in this paper. The unified model in this paper can be considered as an extension of the unified imaging model for central catadioptric cameras proposed by Geyer and Daniilidis. We show that our unified model can cover some existing models for fisheye cameras and fit well for many actual fisheye cameras used in previous literatures. Under our unified model, central catadioptric cameras and fisheye cameras can be classified by the model’s characteristic parameter, and a fisheye image can be transformed into a central catadioptric one, vice versa. An important merit of our new unified model is that existing calibration methods for central catadioptric cameras can be directly applied to fisheye cameras. Furthermore, the metric calibration from single fisheye image only using projections of lines becomes possible via our unified model but the existing methods for fisheye cameras in the literatures till now are all non-metric under the same conditions. Experimental results of calibration from some central catadioptric and fisheye images confirm the validity and usefulness of our new unified model.


Conic Section Line Image Quadric Surface Perspective Projection Perspective Image 
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.
    Baker, S., Nayar, S.K.: A Theory of Catadioptric Image Formation. In: Proc. International Conference on Computer Vision, India, pp. 35–42 (1998)Google Scholar
  2. 2.
    Barreto, J.P., Arajo, H.: Geometric Properties of Central Catadioptric Line Images. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2353, pp. 237–251. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Basu, A., Licardie, S.: Alternative models for fish-eye lenses. Pattern Recognition Letters 16(4), 433–441 (1995)CrossRefGoogle Scholar
  4. 4.
    Born, M., Wolf, E.: Principles of Optics. Pergamon Press, Oxford (1965)Google Scholar
  5. 5.
    Bräuer-Burchardt, C., Voss, K.: A new algorithm to correct fish-eye- and strong wide-angle-lens-distortion from single images. In: Proc. ICIP, pp. 225–228 (2001)Google Scholar
  6. 6.
    Brown, D.C.: Close range camera calibration. Photogrammetric Engineering 37(8), 855–866 (1971)Google Scholar
  7. 7.
    Devernay, F., Faugeras, O.: Straight Lines Have to Be Straight: Automatic Calibration and Removal of Distortion from Scenes of Structured Environments. Machine Vision and Applications 1, 14–24 (2001)CrossRefGoogle Scholar
  8. 8.
    Fitzgibbon, A.: Simultaneous linear estimation of multiple view geometry and lens distortion. In: Proceedings of IEEE Conference on CVPR (2001)Google Scholar
  9. 9.
    Fitzgibbon, A., Pilu, M., Fisher, R.: Direct least-square fitting of ellipses. In: ICPR (1996)Google Scholar
  10. 10.
    Fleck, M.M.: Perspective Projection: the Wrong Imaging Model, technical report 95-01, Computer Science, University of Iowa (1995)Google Scholar
  11. 11.
    Geyer, C., Daniilidis, K.: Catadioptric Camera Calibration. In: ICCV, pp. 398–404 (1999)Google Scholar
  12. 12.
    Geyer, C., Daniilidis, K.: A Unifying Theory for Central Panoramic Systems and Practical Implications. In: Vernon, D. (ed.) ECCV 2000. C. Geyer and K. Daniilidis, vol. 1843, pp. 445–462. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  13. 13.
    Geyer, C., Daniilidis, K.: Paracatadioptric Camera Calibration. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(5), 687–695 (2002)CrossRefGoogle Scholar
  14. 14.
    Kang, S.B.: Radial distortion snakes. In: IAPR Workshop on MVA, pp. 603–606 (2000)Google Scholar
  15. 15.
    Micusik, B., Pajdla, T.: Estimation of Omnidirectional Camera Model from Epipolar Geometry. In: CVPR (2003)Google Scholar
  16. 16.
    Miyamoto, K.: Fish eye lens. Journal of Optical Society of America 54, 1060–1061 (1964)CrossRefGoogle Scholar
  17. 17.
    Nayar, S.K.: Omnidirectional Vision. In: Proc. of Eight International Symposium on Robotics Research, Shonan, Japan (October 1997)Google Scholar
  18. 18.
    Nene, S.A., Nayar, S.K.: Stereo with mirrors. In: Proc. International Conference on Computer Vision, India, pp. 1087–1094 (1998)Google Scholar
  19. 19.
    Shah, S., Aggarwal, J.K.: Intrinsic Parameter Calibration Procedure for a (High Distortion) Fish-Eye Lens Camera with Distortion Model and Accuracy Estimation. Pattern Recognition 29(11), 1775–1788 (1996)CrossRefGoogle Scholar
  20. 20.
    Smith, P.W., Johnson, K.B., Abidi, M.A.: Efficient Techniques for Wide-Angle Stereo Vision using Surface Projection Models. In: CVPR (1999)Google Scholar
  21. 21.
    Svoboda, T., Padjla, T., Hlavac, V.: Epipolar geometry for panoramic cameras. In: Burkhardt, H.-J., Neumann, B. (eds.) ECCV 1998. LNCS, vol. 1406, pp. 218–231. Springer, Heidelberg (1998)Google Scholar
  22. 22.
    Swaminathan, R., Nayar, S.K.: Non-Metric Calibration of Wide-Angle Lenses and Polycameras. In: PAMI, pp. 1172–1178 (2000)Google Scholar
  23. 23.
    Urban, M., Svoboda, T., Pajdla, T.: Transformation of Panoramic Images: from hyperbolic mirror with central projection to parabolic mirror with orthogonal projection, Technical report, The Center for Machine Perception, Czech Technical University, Prague (2000)Google Scholar
  24. 24.
    Xiong, Y., Turkowski, K.: Creating Image-Based VR Using a Self-Calibrating Fisheye Lens. In: Proceedings of CVPR, pp. 237–243 (1997)Google Scholar
  25. 25.
    Ying, X., Hu, Z.: Catadioptric Camera Calibration Using Geometric Invariants. In: International Conference on Computer Vision (ICCV 2003), Nice, France (2003)Google Scholar
  26. 26.
    Zhang, Z.: Parameter Estimation Techniques: A Tutorial with Application to Conic Fitting, INRIA Raport de Recherche n 2676 (October 1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Xianghua Ying
    • 1
  • Zhanyi Hu
    • 1
  1. 1.National Laboratory of Pattern Recognition, Institute of AutomationChinese Academy of SciencesP.R. China

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