Multimedia Tools and Applications

, Volume 73, Issue 3, pp 1445–1457 | Cite as

Approximate model of fisheye camera based on the optical refraction

  • Haijiang ZhuEmail author
  • Xuan Wang
  • Jinglin Zhou
  • Xuejing Wang


This paper proposes an approximate model of fisheye camera based on the optical refraction. The model of fisheye lens is firstly derived from the optical refraction and the structure of fisheye lenses. Secondly, a suitable linearization of the fisheye model is developed in order to obtain an approximate model, and the approximate model including two parameters is constructed from the linearization of the fisheye model. Finally, the estimation algorithm on the model parameters is presented using the epipolar constraint between two fisheye images. Furthermore, we provide lots of experiments with synthetic data and real fisheye images. To start with, the feasibility of the approximate model is tested through fitting the five common designed model of fisheye lens with synthetic data. Two groups of experiments with real fisheye image are then performed to estimate the model parameters. In practical situation, this method can automatically establish image correspondences using an improved random sample consensus algorithm without calibration objects.


Optical refraction Approximate model Parameter estimation Fisheye lens 



This work was supported by the National Natural Science Foundation of China under grant No.60875023, The Fundamental Research Funds for the Central Universities (No.ZZ1134, No.ZZ1013) and Beijing Training Programme Foundation for the Talents No.2012B009016000004.


  1. 1.
    Basu A, Licardie S (1995) Alternative models for fisheye lenses. Pattern Recogn Lett 16:433–441CrossRefGoogle Scholar
  2. 2.
    Burchardt CB, Voss K (2001) A new algorithm to correct Fisheye and strong wide-angle-lens-distortion from single images, in Proceedings of the IEEE International Conference on Image Processing, pp.225–228Google Scholar
  3. 3.
    Devernay F, Faugeras O (2001) Straight lines have to be straight: automatic calibration and removal of distortion from scenes of structured environments. Mach Vis Appl 13:14–24CrossRefGoogle Scholar
  4. 4.
    Fischler MA, Bolles RC (1981) Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun ACM 24:381–395CrossRefMathSciNetGoogle Scholar
  5. 5.
    Fitzgibbon AW (2001) Simultaneous linear estimation of multiple view geometry and lens distortion. In Proc. Computer Vision and Pattern Recognition, pp:125–132Google Scholar
  6. 6.
    Geyer C, Daniilidis K (2001) Catadioptric projective geometry. Int J Comput Vis 45(3):223–243CrossRefzbMATHGoogle Scholar
  7. 7.
    Hansen P, Corke P, Boles W (2010) Wide-angle visual feature matching for outdoor localization. Int J Robot Res 29(2–3):267–297CrossRefGoogle Scholar
  8. 8.
    Harris C, Stephens MJ (1988) A combined corner and edge detector. In: Proceedings of the 4th alvey vision conference. Springer, Mancherster, pp 147–151Google Scholar
  9. 9.
    Hartley R, Zisserman A (2003) Multiple view geometry in computer vision. University Press, CambridgeGoogle Scholar
  10. 10.
    Ho TH, Davis CC, Milner SD (2005) Using Geometric Constraints for Fisheye Camera Calibration, In Proc. IEEE OMNIVIS WorkshopGoogle Scholar
  11. 11.
    Hughes C, Denny P, Glavin M, Jones E (2010) Equidistant fisheye calibration and rectification by vanishing point extraction. IEEE Trans Pattern Anal Mach Intell 32(12):2289–2296CrossRefGoogle Scholar
  12. 12.
    Hughes C, Denny P, Glavin M, Jones E, Glavin M (2010) Accuracy of fisheye lens models. Appl Optics 49(17):3338–3347CrossRefGoogle Scholar
  13. 13.
    Intersil Announces Fisheye Lens Image Correction Technology:,2011
  14. 14.
    Kannala J, Brandt SS (2006) A generic camera model and calibration method for conventional, wide-eye, and fisheye lenses. IEEE Trans Pattern Anal Mach Intell 28(8):1335–1340CrossRefGoogle Scholar
  15. 15.
    Konstantinos G. Derpanis. Overview of the RANSAC Algorithm, Version 1.2,, May 13, 2010
  16. 16.
    Kruger L, Wohler C (2011) Accurate chequerboard corner localisation for camera calibration. Pattern Recognit Lett 32(10):1428–1435CrossRefGoogle Scholar
  17. 17.
    Lefebvre S, Ambellouis A, Cabestaing F (2011) A 2D approach to correlation-based stereo matching. Image Vision Comput 29(9):580–593CrossRefGoogle Scholar
  18. 18.
    Li S (2008) Binocular spherical stereo. IEEE Trans Intell Transp Syst 9(4):589–600CrossRefGoogle Scholar
  19. 19.
    Li S, Hai Y (2011) Easy calibration of a blind-spot-free fisheye camera system using a scene of a parking space. IEEE Trans Intell Transp Syst 12(1):232–242CrossRefGoogle Scholar
  20. 20.
    Li W, Li YF (2011) Single-camera panoramic stereo imaging system with a fisheye lens and a convex mirror. Opt Express 19(7):5855–5867CrossRefGoogle Scholar
  21. 21.
    Micusik B, Pajdla T (2003) Estimation of omnidirectional camera model from epipolar geometry. In Proceeding of IEEE Computer Vision and Pattern Recognition, pp:485–490Google Scholar
  22. 22.
    Oliensis J (2002) Exact two-image structure from motion. IEEE Trans Pattern Anal Mach Intell 24(12):1618–1633CrossRefGoogle Scholar
  23. 23.
    Ryberg A, Lennartson B, Christiansson AK, Ericsson M, Asplund L (2011) Analysis and evaluation of a general camera model. Comp Vision Image Underst (CVIU) 115(11):1503–1515CrossRefGoogle Scholar
  24. 24.
    Schneider D, Schwalbe E, Mass H-G (2009) Validation of geometric models for fisheye lenses. ISPRS J Photogramm Remote Sens 64:259–266CrossRefGoogle Scholar
  25. 25.
    Wang YC (2007) Fisheye lens optics, Beijing: Science Press, (Chinese)Google Scholar
  26. 26.
    Xu ZH, Zhang F, Sun FM, Hu ZY (2009) Quasi-dense matching by neighborhood transfer for fisheye images. ACTA AUTOMATICA SINICA 35(9):1159–1167, ChineseCrossRefGoogle Scholar
  27. 27.
    Ying X, Hu Z (2004) Can We Consider Central Catadioptric Cameras and Fisheye Cameras within a Unified Imaging Model, ECCV, pp.442–455Google Scholar
  28. 28.
    Zhang Z, Deriche R, Faugeras O (1995) A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry. Artif Intell 78:87–119CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Haijiang Zhu
    • 1
    Email author
  • Xuan Wang
    • 1
  • Jinglin Zhou
    • 1
  • Xuejing Wang
    • 1
  1. 1.College of Information & TechnologyBeijing University of Chemical TechnologyBeijingChina

Personalised recommendations