Skip to main content
Log in

A calibration method for paracatadioptric cameras based on circular sections

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

Camera calibration is a crucial step in 3D reconstruction. To improve the reconstruction accuracy, we propose a calibration method for the paracatadioptric camera based on the projective properties of spheres. The starting point of the method is to consider the three great circles that are parallel to the projection of the sphere onto the unit viewing sphere in the imaging model of the paracatadioptric camera. The absolute conic is determined from the orthogonal vanishing points obtained from the intersections of the projections of the three great circles on the image plane. Then, the intrinsic parameters are obtained from the algebraic constraints on the image of the absolute conic. Compared with results obtained by Zhao’s, Yu’s and Li′s methods, 3D reconstruction using our method appears more accurate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Agrawal M, Davis LS (2003) Camera calibration using spheres: asemi-definite programming approach, in Proceedings of the IEEE International Conference on Computer Vision (2003), pp. 782–789

  2. Agrawal M, Davis LS (2007) Complete camera calibration using spheres: a dual-space approach. Anal. Int Math J Anal Appl 34(3):257–282

    Google Scholar 

  3. Baker S, Nayar SK (1999) A theory of single-viewpoint catadioptricimage formation. Int J Comput Vis 35(2):175–196

    Article  Google Scholar 

  4. Barreto JP, Araujo H (2003) Paracatadioptric camera calibration using lines, in Proceedings of the IEEE International Conference on Computer Vision, pp. 1–7

  5. Duan H, Wu Y (2011) Paracatadioptric camera calibration using sphere images, in Processing IEEE International Conference on Image, pp. 641–643

  6. Duan H, Wu Y (2012) A calibration method for paracatadioptric camera from sphere images. Pattern Recogn Lett 33(6):677–684

    Article  Google Scholar 

  7. Duan F, Wu F, Zhou M, Deng X, Tian Y (2012) Calibrating effective focal length for central catadioptric cameras using one space line. Pattern Recogn Lett 33(5):646–653

    Article  Google Scholar 

  8. Duan HX, Wu YH, Song L, Wang J, Liu N (2014) Properties of central catadioptric circle images and camera calibration,in Springer International Conference on Rough Sets and Knowledge Technology, pp. 229–240

  9. Duan HX, Wu YH, Song L, Wang J (2019) Fitting a cluster of line images under central catadioptric camera. Cluster Computer 22:781–793

    Article  Google Scholar 

  10. Geyer C, Daniilidis K (2000) Equivalence of catadioptric projectionsand mappings of the sphere, in Proceedings of the IEEE Work.shop on Omnidirectional Vision (2000), pp. 91–96

  11. Geyer C, Daniilidis K (2001) Catadioptric projective geometry. Int J Comput Vis 45(3):223–243

    Article  Google Scholar 

  12. Geyer C, Daniilidis K (2002) Paracatadioptric camera calibration. IEEE Trans Pattern Anal Mach Intell 24(5):687–695

    Article  Google Scholar 

  13. Jia J, Jiang G, Cheng-Ke WU (2010) Geometric interpretations and applications of the extrinsic parameters derived from the cameracalibration based on spheres. IEEE Trans Pattern Anal Mach Intell 23(2):160–164

    Google Scholar 

  14. Li YZ, Zhao Y (2017) Calibration of paracatadioptric camera by projection imaging of single sphere. Appl Opt 10:2230–2240

    Article  Google Scholar 

  15. Li YZ, Zhao Y, Zheng BH (2018) Calibrating a paracatadioptric camera by the property of the polar of a point at infinity with respect to a circle. Applied Optics 57(15):4345–4352

    Article  Google Scholar 

  16. lllingworth J, Kittler J (1988) A survey of the Hough transform. Comput. Vis. Graph. Image Process 43:765–768

    Google Scholar 

  17. Marr D (1982) Vision. W. H, Freeman and Company (San Fransisco

    Google Scholar 

  18. Micusik B, Pajdla T (2004) Para-catadioptric camera auto-calibration from epipolar geometry, in Proceedings of the Asian Conference on Computer Vision (AFCV), pp. 748–753

  19. Teramoto H, Xu G (2002) Camera calibration by a single image of balls: from conics to the absolute conic, in Proceedings of the5th Asian Conference on Computer Vision (2002), pp. 499–506

  20. Wang YL, Zhao Y (2015) Intricsic parameter determination of a paracatadioptric camera by the intersection of two sphere projections. Optical Society of America A 32(1):2201–2209

    Google Scholar 

  21. Wang YL, Zhao Y (2019) Paracatadioptric camera calibration based on the projecting relationship of the relative position between two spheres. Springer Multimedia Tools and Applications 78:12223–12249

    Article  Google Scholar 

  22. Wang SW, Zhao Y, You J (2020) Calibration of paracatadioptric cameras based on sphere images and pole-polar relationship. OSA Continuum 3(4):993–1012

    Article  Google Scholar 

  23. Wu YH, Hu ZY (2005) Geometric invariants and applications under catadioptric camera model, in Proceedings of the IEEE International Conference on Computer Vision pp.1547–1554.

  24. Xu G, Hao Z, Li X, Su J, Liu H, Zhang X (2016) Calibration method of the laser plane equation for vision measurement adoptingobjective function of uniform horizontal height of feature points. Opt Rev 23(1):33–39

    Article  Google Scholar 

  25. Yang S, Liu M, Song J, Yin S, Guo Y, Ren Y, Zhu J (2017) Projector calibration method based on stereo vision system. Opt Rev 24(5):727–733

    Article  Google Scholar 

  26. Ying X, Hu Z (2004) Spherical objects based motion estimation forcatadioptric cameras, in Proceedings of the IEEE InternationalConference on Pattern Recognition (2004), pp. 231–234

  27. Ying X, Hu Z (2004) Catadioptric camera calibration using geometric invariants. IEEE Trans Pattern Anal Mach Intell 26(10):1260–1271

    Article  Google Scholar 

  28. Ying X, Zha H (2008) Identical projective geometric properties of central catadioptric line images and sphere images with applications to calibration. Int J Comput Vis 78(1):89–105

    Article  Google Scholar 

  29. Zhang X, Ji X (2012) An improved Harris corner detection algorithm for noised images, in International Conference on Materials Science and Information Technology, pp. 6151–6156

  30. Zhang H, Zhang G, Wong KY (2005) Camera calibration with spheres: linear approaches, in Proceedings of the IEEE International Conference on Image Processing, pp. 1150–1153

  31. Zhang H, Wong KY, Zhang G (2007) Camera calibration from images of spheres. IEEE Trans Pattern Anal Mach Intell 29(3):1499–1502

    Article  Google Scholar 

  32. Zhang L, Du X, Hu JL (2010) Using concurrent lines in central catadioptric camera calibration. Zhejiang University Science C 12(3):239–249

    Article  Google Scholar 

  33. Zhao Y, Gu WJ (2016) Method to solve intrinsic geometric parameters of a paracatadioptric camera using 3D lines. Optick 127(5):2325–2330

    MathSciNet  Google Scholar 

  34. Zhao Y, Yu XJ (2019) Paracatadioptric camera calibration using sphere iamges and common self-polar triangles. Opt Rev 26(11):1–12

    Article  Google Scholar 

Download references

Funding

National Natural Science Foundation of China (62063034).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Junhua Zhang.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, R., Zhang, J. A calibration method for paracatadioptric cameras based on circular sections. Multimed Tools Appl (2022). https://doi.org/10.1007/s11042-022-12918-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11042-022-12918-9

Keywords

Navigation