Cluster Computing

, Volume 22, Supplement 1, pp 781–793 | Cite as

Fitting a cluster of line images under central catadioptric camera

  • Huixian Duan
  • Yihong WuEmail author
  • Lei Song
  • Jun Wang
  • Na Liu


Generally, due to the partial occlusion, it is very difficult to correctly estimate the central catadioptric line image from its visible part. Except for the necessary and sufficient conditions that must be satisfied by a set of paracatadioptric line images, we find that if the antipodal points of image points on the visible arc are known, the fitting accuracy can be improved greatly. In this paper, we propose a new method for fitting line images, which can be applied to all central catadioptric projection. Firstly, a new relationship between a pair of antipodal image points and the camera principal point is derived. Next, using this relationship, a new method is proposed to estimate the line images. These estimated line images are used to calibrate camera intrinsic parameters to evaluate the performance of our fitting method. Experimental results on both simulated and real data have demonstrated the effectiveness of our method.


Central catadioptric projection Line image Camera calibration 



This work is sponsored by the National Natural Science Foundation of China (61632003, 61403084, 61402116); by the Project of the Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University(ESSCKF 2015-03); and by the Shanghai Rising-Star Program (17QB1401000); and by the Application Innovation Plan of Ministry of Public Security (2017YYCXSXST030); and by the Special Funds for the Basic R&D Business Expenses of the Central Level Public Welfare Scientific Research Institutions(C17348)“The Construction of Standard Video Dataset and Intelligent Video Evaluation Platform”.


  1. 1.
    Baker, S., Nayer, S.: A theory of single-viewpoint catadioptric image formation. Int. J. Comput. Vis. 35, 175–196 (1999)CrossRefGoogle Scholar
  2. 2.
    Geyer, C., Daniilidis, K.: Catadioptric camera calibration. In: International Conference on Computer Vision, pp. 398–404 (1999)Google Scholar
  3. 3.
    Geyer, C., Daniilidis, K.: Catadioptric projective geometry. Int. J. Comput. Vis. 45, 223–243 (2001)CrossRefzbMATHGoogle Scholar
  4. 4.
    Duan, H.X., Wu, Y.H.: Unified imaging of geometric entities under catadioptric camera and camera calibration. J. Comput. Aided Des. Comput. Graph. 23, 891–898 (2011)Google Scholar
  5. 5.
    Geyer, C., Daniilidis, K.: Paracatadioptric camera calibration. IEEE Trans. Pattern Anal. Mach. Intell. 24, 687–695 (2002)CrossRefGoogle Scholar
  6. 6.
    Barreto, J.P., Araujo, H.: Geometry properties of central catadioptric line images and application in calibration. IEEE Trans. Pattern Anal. Mach. Intell. 27, 1327–1333 (2005)CrossRefGoogle Scholar
  7. 7.
    Deng, X.M., Wu, F.C., Wu, Y.H.: An easy calibration method for central catadioptric cameras. Acta Automation Sin. 33, 801–808 (2007)CrossRefGoogle Scholar
  8. 8.
    Duan, F.Q., Wang, L.: Calibrating central catadioptric cameras based on spatial line projection constraint. In: International Conference on Systems, Man and Cybernetics, pp. 2088–2093 (2010)Google Scholar
  9. 9.
    Duan, H.X., Wu, Y.H.: Paracatadioptric camera calibration using sphere images. In: International Conference on Image Processing, pp. 649–652 (2011)Google Scholar
  10. 10.
    Duan, H.X., Wu, Y.H.: A calibration method for paracatadioptric camera from sphere images. Pattern Recognit. Lett. 33, 677–684 (2012)CrossRefGoogle Scholar
  11. 11.
    Vandeportaele, B., Cattoen, M., Marthon, P., Gurdjo, P.: A New linear calibration method for paracatadioptric cameras. In: International Conference on Pattern Recognition, pp. 647–651 (2006)Google Scholar
  12. 12.
    Wu, F.C., Duan, F.Q., Hu, Z.Y., Wu, Y.H.: A new linear algorithm for calibrating central catadioptric cameras. Pattern Recognit. 41, 3166–3172 (2008)CrossRefGoogle Scholar
  13. 13.
    Ying, X.H., Hu, Z.Y.: Catadioptric camera calibration using geometric invariants. IEEE Trans. Pattern Anal. Mach. Intell. 26, 1260–1271 (2004)CrossRefGoogle Scholar
  14. 14.
    Ying, X.H., Zha, H.B.: Simultaneously calibrating catadioptric camera and detecting line features using hough transform. In: International Conference on Intelligent Robots and Systems, pp. 412–417 (2005)Google Scholar
  15. 15.
    Duan, H.X., Mei, L., Shang, Y.F., Hu, C.P.: Calibrating focal length for paracatadioptric camera from one circle image. In: International Conference on Computer Vision Theory and Application, pp. 56–63 (2014)Google Scholar
  16. 16.
    Barreto, J.P., Araujo, H.: Fitting conics to paracatadioptric projection of lines. Comput. Vis. Image Underst. 101, 151–165 (2006)CrossRefGoogle Scholar
  17. 17.
    Zhang, Z.Y.: Parameter estimation techniques: a tutorial with application to conic fitting. Image Vis. Comput. 15, 59–76 (1997)CrossRefGoogle Scholar
  18. 18.
    Wu, Y.H., Li, Y.F., Hu, Z.Y.: Easy calibration for para-catadioptric-like camera. In: International Conference on Intelligent Robots and Systems, pp. 5719–5724 (2006)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Huixian Duan
    • 1
    • 2
  • Yihong Wu
    • 3
    Email author
  • Lei Song
    • 1
  • Jun Wang
    • 1
  • Na Liu
    • 1
  1. 1.Cyber Physical System R & D Center, The Third Research Institute of Ministry of Public SecurityShanghaiChina
  2. 2.Shanghai International Technology & Trade United Co., LtdShanghaiChina
  3. 3.National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of SciencesBeijingChina

Personalised recommendations