Abstract

For important camera calibration in the field of computer vision, a new target form, namely, a grid spherical target (GST) that is different from the spherical target, is proposed. The GST has advantages of spherical and checkerboard targets because of the grid on the sphere. And the latitude and longitude circles and the intersection points between latitude and longitude circles on the GST are used to calibrate the camera. Firstly, the Image of Absolute Conic should be obtained using the elliptic curves of latitude and longitude circles on the GST in the images. After obtaining the initial intrinsic and extrinsic parameters of the camera using the Image of Absolute Conic, optimum solutions of the intrinsic and extrinsic parameters are solved through nonlinear optimization by using the latitude circles and the intersection points of the latitude and longitude lines. Finally, the effectiveness of the GST-based method is proven in simulation and physical experiments.

© 2017 Optical Society of America

Full Article  |  PDF Article

Corrections

27 June 2017: Typographical corrections were made to Refs. 2, 3, 10, 12, 14, 18, 19, 21, 23, 29, and 31.


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References

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  1. A. S. Poulin-Girard, S. Thibault, and D. Laurendeau, “Influence of camera calibration conditions on the accuracy of 3D reconstruction,” Opt. Express 24(3), 2678–2686 (2016).
    [Crossref] [PubMed]
  2. B. Sun, J. G. Zhu, L. H. Yang, S. R. Yang, and Z. Y. Niu, “Calibration of line-scan cameras for precision measurement,” Appl. Opt. 55(25), 6836–6843 (2016).
    [Crossref] [PubMed]
  3. W. M. Li, S. Y. Shan, and H. Liu, “High-precision method of binocular camera calibration with a distortion model,” Appl. Opt. 56(8), 2368–2377 (2017).
    [Crossref] [PubMed]
  4. R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV camera and lenses,” IEEE J. Robot. Autom. 3(4), 323–344 (1987).
    [Crossref]
  5. J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Mach. Intell. 22(10), 1066–1077 (2000).
    [Crossref]
  6. J. Y. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion model and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14(10), 965–980 (1992).
    [Crossref]
  7. Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
    [Crossref]
  8. Z. Liu, Q. Wu, X. Chen, and Y. Yin, “High-accuracy calibration of low-cost camera using image disturbance factor,” Opt. Express 24(21), 24321–24336 (2016).
    [Crossref] [PubMed]
  9. J. S. Kim, P. Gurdjos, and I. S. Kweon, “Geometric and algebraic constraints of projected concentric circles and their applications to camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 27(4), 637–642 (2005).
    [Crossref] [PubMed]
  10. Y. H. Wu, X. J. Li, F. C. Wu, and Z. Y. Hu, “Coplanar circles, quasi-affine invariance and calibration,” Image Vis. Comput. 24(4), 319–326 (2006).
    [Crossref]
  11. D. Douxchamps and K. Chihara, “High-accuracy and robust localization of large control markers for geometric camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 376–383 (2009).
    [Crossref] [PubMed]
  12. Z. Y. Zhang, “Camera calibration with one-dimensional objects,” IEEE Trans. Pattern Anal. Mach. Intell. 26(7), 892–899 (2004).
    [Crossref] [PubMed]
  13. F. C. Wu, Z. Y. Hu, and H. J. Zhu, “Camera calibration with moving one-dimensional objects,” Pattern Recognit. 38(5), 755–765 (2005).
    [Crossref]
  14. F. Qi, Q. H. Li, Y. P. Luo, and D. C. Hu, “Camera calibration with one-dimensional objects moving under gravity,” Pattern Recognit. 40(1), 343–345 (2007).
    [Crossref]
  15. M. Agrawal and L. Davis, “Complete camera calibration using spheres: a dual-space approach,” Analysis Int. Math. J. Analysis Appl. 34(3), 257–282 (2003).
  16. H. Teramoto and G. Xu, “Camera calibration by a single image of balls: from conic to the absolute conic,” in Proceedings of the Asian Conference on Computer Vision (ACCV, 2002), pp. 499-506.
  17. H. Zhang, K.-Y. K. Wong, and G. Zhang, “Camera calibration from images of spheres,” IEEE Trans. Pattern Anal. Mach. Intell. 29(3), 499–503 (2007).
    [Crossref] [PubMed]
  18. X. H. Ying and H. B. Zha, “Geometric interpretations of the relation between the image of the absolute conic and sphere images,” IEEE Trans. Pattern Anal. Mach. Intell. 28(12), 2031–2036 (2006).
    [Crossref] [PubMed]
  19. K.-Y. K. Wong, G. Q. Zhang, and Z. H. Chen, “A stratified approach for camera calibration using spheres,” IEEE Trans. Image Process. 20(2), 305–316 (2011).
    [Crossref] [PubMed]
  20. M. H. Ruan and D. Huber, “Calibration of 3D Sensors Using a Spherical Target,” International Conference on 3D Vision (IEEE, 2015), pp. 187–193.
  21. J. H. Sun, H. B. He, and D. B. Zeng, “Global Calibration of Multiple Cameras Based on Sphere Targets,” Sensors (Basel) 16(1), 77 (2016).
    [Crossref] [PubMed]
  22. K. K. Wong, P. R. S. Mendonca, and R. Cipolla, “Camera calibration from surfaces of revolution,” IEEE Trans. Pattern Anal. Mach. Intell. 25(2), 147–161 (2003).
    [Crossref]
  23. Y. H. Wu, H. J. Zhu, Z. Y. Hu, and F. C. Wu, “Camera Calibration from the Quasi-Affine invariance of two parallel circles,” in Proceedings of European Conference on Computer Vision (ECCV, 2004), pp.190–202.
  24. C. Colombo, D. Comanducci, and A. D. Bimbo, “Camera calibration with two arbitrary coaxial circles,” in Proceedings of European Conference on Computer Vision (ECCV, 2006), pp. 265–276.
    [Crossref]
  25. C. Steger, “An Unbiased Detector of Curvilinear Structures,” IEEE Trans. Pattern Anal. Mach. Intell. 20(2), 113–125 (2002).
    [Crossref]
  26. R. Halir and J. Flusser, “Numerically Stable Direct Least Squares Fitting of Ellipses,” (1998).
  27. R. I. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2000).
  28. M. Agrawal and L. S. Davis, “Camera calibration using spheres: a semi-definite programming approach,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE, 2003), pp.782–789.
    [Crossref]
  29. Z. Liu, X. J. Li, and Y. Yin, “On-site calibration of line-structured light vision sensor in complex light environments,” Opt. Express 23(23), 29896–29911 (2015).
    [Crossref] [PubMed]
  30. Z. Liu, X. J. Li, F. J. Li, and G. J. Zhang, “Calibration method for line-structured light vision sensor based on a single ball target,” Opt. Lasers Eng. 69, 20–28 (2015).
    [Crossref]
  31. Z. Liu, F. J. Li, B. K. Huang, and G. J. Zhang, “Real-time and accurate rail wear measurement method and experimental analysis,” J. Opt. Soc. Am. A 31(8), 1721–1729 (2014).
    [Crossref] [PubMed]
  32. J. Y. Bouguet, “The MATLAB open source calibration toolbox,” http://www.vision.caltech.edu/bouguetj/calib _doc/ .
  33. J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–698 (1986).
    [Crossref] [PubMed]

2017 (1)

2016 (4)

2015 (2)

Z. Liu, X. J. Li, and Y. Yin, “On-site calibration of line-structured light vision sensor in complex light environments,” Opt. Express 23(23), 29896–29911 (2015).
[Crossref] [PubMed]

Z. Liu, X. J. Li, F. J. Li, and G. J. Zhang, “Calibration method for line-structured light vision sensor based on a single ball target,” Opt. Lasers Eng. 69, 20–28 (2015).
[Crossref]

2014 (1)

2011 (1)

K.-Y. K. Wong, G. Q. Zhang, and Z. H. Chen, “A stratified approach for camera calibration using spheres,” IEEE Trans. Image Process. 20(2), 305–316 (2011).
[Crossref] [PubMed]

2009 (1)

D. Douxchamps and K. Chihara, “High-accuracy and robust localization of large control markers for geometric camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 376–383 (2009).
[Crossref] [PubMed]

2007 (2)

F. Qi, Q. H. Li, Y. P. Luo, and D. C. Hu, “Camera calibration with one-dimensional objects moving under gravity,” Pattern Recognit. 40(1), 343–345 (2007).
[Crossref]

H. Zhang, K.-Y. K. Wong, and G. Zhang, “Camera calibration from images of spheres,” IEEE Trans. Pattern Anal. Mach. Intell. 29(3), 499–503 (2007).
[Crossref] [PubMed]

2006 (2)

X. H. Ying and H. B. Zha, “Geometric interpretations of the relation between the image of the absolute conic and sphere images,” IEEE Trans. Pattern Anal. Mach. Intell. 28(12), 2031–2036 (2006).
[Crossref] [PubMed]

Y. H. Wu, X. J. Li, F. C. Wu, and Z. Y. Hu, “Coplanar circles, quasi-affine invariance and calibration,” Image Vis. Comput. 24(4), 319–326 (2006).
[Crossref]

2005 (2)

J. S. Kim, P. Gurdjos, and I. S. Kweon, “Geometric and algebraic constraints of projected concentric circles and their applications to camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 27(4), 637–642 (2005).
[Crossref] [PubMed]

F. C. Wu, Z. Y. Hu, and H. J. Zhu, “Camera calibration with moving one-dimensional objects,” Pattern Recognit. 38(5), 755–765 (2005).
[Crossref]

2004 (1)

Z. Y. Zhang, “Camera calibration with one-dimensional objects,” IEEE Trans. Pattern Anal. Mach. Intell. 26(7), 892–899 (2004).
[Crossref] [PubMed]

2003 (2)

M. Agrawal and L. Davis, “Complete camera calibration using spheres: a dual-space approach,” Analysis Int. Math. J. Analysis Appl. 34(3), 257–282 (2003).

K. K. Wong, P. R. S. Mendonca, and R. Cipolla, “Camera calibration from surfaces of revolution,” IEEE Trans. Pattern Anal. Mach. Intell. 25(2), 147–161 (2003).
[Crossref]

2002 (1)

C. Steger, “An Unbiased Detector of Curvilinear Structures,” IEEE Trans. Pattern Anal. Mach. Intell. 20(2), 113–125 (2002).
[Crossref]

2000 (2)

Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Mach. Intell. 22(10), 1066–1077 (2000).
[Crossref]

1992 (1)

J. Y. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion model and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14(10), 965–980 (1992).
[Crossref]

1987 (1)

R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV camera and lenses,” IEEE J. Robot. Autom. 3(4), 323–344 (1987).
[Crossref]

1986 (1)

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–698 (1986).
[Crossref] [PubMed]

Agrawal, M.

M. Agrawal and L. Davis, “Complete camera calibration using spheres: a dual-space approach,” Analysis Int. Math. J. Analysis Appl. 34(3), 257–282 (2003).

M. Agrawal and L. S. Davis, “Camera calibration using spheres: a semi-definite programming approach,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE, 2003), pp.782–789.
[Crossref]

Bimbo, A. D.

C. Colombo, D. Comanducci, and A. D. Bimbo, “Camera calibration with two arbitrary coaxial circles,” in Proceedings of European Conference on Computer Vision (ECCV, 2006), pp. 265–276.
[Crossref]

Canny, J.

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–698 (1986).
[Crossref] [PubMed]

Chen, X.

Chen, Z. H.

K.-Y. K. Wong, G. Q. Zhang, and Z. H. Chen, “A stratified approach for camera calibration using spheres,” IEEE Trans. Image Process. 20(2), 305–316 (2011).
[Crossref] [PubMed]

Chihara, K.

D. Douxchamps and K. Chihara, “High-accuracy and robust localization of large control markers for geometric camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 376–383 (2009).
[Crossref] [PubMed]

Cipolla, R.

K. K. Wong, P. R. S. Mendonca, and R. Cipolla, “Camera calibration from surfaces of revolution,” IEEE Trans. Pattern Anal. Mach. Intell. 25(2), 147–161 (2003).
[Crossref]

Cohen, P.

J. Y. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion model and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14(10), 965–980 (1992).
[Crossref]

Colombo, C.

C. Colombo, D. Comanducci, and A. D. Bimbo, “Camera calibration with two arbitrary coaxial circles,” in Proceedings of European Conference on Computer Vision (ECCV, 2006), pp. 265–276.
[Crossref]

Comanducci, D.

C. Colombo, D. Comanducci, and A. D. Bimbo, “Camera calibration with two arbitrary coaxial circles,” in Proceedings of European Conference on Computer Vision (ECCV, 2006), pp. 265–276.
[Crossref]

Davis, L.

M. Agrawal and L. Davis, “Complete camera calibration using spheres: a dual-space approach,” Analysis Int. Math. J. Analysis Appl. 34(3), 257–282 (2003).

Davis, L. S.

M. Agrawal and L. S. Davis, “Camera calibration using spheres: a semi-definite programming approach,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE, 2003), pp.782–789.
[Crossref]

Douxchamps, D.

D. Douxchamps and K. Chihara, “High-accuracy and robust localization of large control markers for geometric camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 376–383 (2009).
[Crossref] [PubMed]

Flusser, J.

R. Halir and J. Flusser, “Numerically Stable Direct Least Squares Fitting of Ellipses,” (1998).

Gurdjos, P.

J. S. Kim, P. Gurdjos, and I. S. Kweon, “Geometric and algebraic constraints of projected concentric circles and their applications to camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 27(4), 637–642 (2005).
[Crossref] [PubMed]

Halir, R.

R. Halir and J. Flusser, “Numerically Stable Direct Least Squares Fitting of Ellipses,” (1998).

He, H. B.

J. H. Sun, H. B. He, and D. B. Zeng, “Global Calibration of Multiple Cameras Based on Sphere Targets,” Sensors (Basel) 16(1), 77 (2016).
[Crossref] [PubMed]

Heikkila, J.

J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Mach. Intell. 22(10), 1066–1077 (2000).
[Crossref]

Herniou, M.

J. Y. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion model and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14(10), 965–980 (1992).
[Crossref]

Hu, D. C.

F. Qi, Q. H. Li, Y. P. Luo, and D. C. Hu, “Camera calibration with one-dimensional objects moving under gravity,” Pattern Recognit. 40(1), 343–345 (2007).
[Crossref]

Hu, Z. Y.

Y. H. Wu, X. J. Li, F. C. Wu, and Z. Y. Hu, “Coplanar circles, quasi-affine invariance and calibration,” Image Vis. Comput. 24(4), 319–326 (2006).
[Crossref]

F. C. Wu, Z. Y. Hu, and H. J. Zhu, “Camera calibration with moving one-dimensional objects,” Pattern Recognit. 38(5), 755–765 (2005).
[Crossref]

Y. H. Wu, H. J. Zhu, Z. Y. Hu, and F. C. Wu, “Camera Calibration from the Quasi-Affine invariance of two parallel circles,” in Proceedings of European Conference on Computer Vision (ECCV, 2004), pp.190–202.

Huang, B. K.

Huber, D.

M. H. Ruan and D. Huber, “Calibration of 3D Sensors Using a Spherical Target,” International Conference on 3D Vision (IEEE, 2015), pp. 187–193.

Kim, J. S.

J. S. Kim, P. Gurdjos, and I. S. Kweon, “Geometric and algebraic constraints of projected concentric circles and their applications to camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 27(4), 637–642 (2005).
[Crossref] [PubMed]

Kweon, I. S.

J. S. Kim, P. Gurdjos, and I. S. Kweon, “Geometric and algebraic constraints of projected concentric circles and their applications to camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 27(4), 637–642 (2005).
[Crossref] [PubMed]

Laurendeau, D.

Li, F. J.

Z. Liu, X. J. Li, F. J. Li, and G. J. Zhang, “Calibration method for line-structured light vision sensor based on a single ball target,” Opt. Lasers Eng. 69, 20–28 (2015).
[Crossref]

Z. Liu, F. J. Li, B. K. Huang, and G. J. Zhang, “Real-time and accurate rail wear measurement method and experimental analysis,” J. Opt. Soc. Am. A 31(8), 1721–1729 (2014).
[Crossref] [PubMed]

Li, Q. H.

F. Qi, Q. H. Li, Y. P. Luo, and D. C. Hu, “Camera calibration with one-dimensional objects moving under gravity,” Pattern Recognit. 40(1), 343–345 (2007).
[Crossref]

Li, W. M.

Li, X. J.

Z. Liu, X. J. Li, and Y. Yin, “On-site calibration of line-structured light vision sensor in complex light environments,” Opt. Express 23(23), 29896–29911 (2015).
[Crossref] [PubMed]

Z. Liu, X. J. Li, F. J. Li, and G. J. Zhang, “Calibration method for line-structured light vision sensor based on a single ball target,” Opt. Lasers Eng. 69, 20–28 (2015).
[Crossref]

Y. H. Wu, X. J. Li, F. C. Wu, and Z. Y. Hu, “Coplanar circles, quasi-affine invariance and calibration,” Image Vis. Comput. 24(4), 319–326 (2006).
[Crossref]

Liu, H.

Liu, Z.

Luo, Y. P.

F. Qi, Q. H. Li, Y. P. Luo, and D. C. Hu, “Camera calibration with one-dimensional objects moving under gravity,” Pattern Recognit. 40(1), 343–345 (2007).
[Crossref]

Mendonca, P. R. S.

K. K. Wong, P. R. S. Mendonca, and R. Cipolla, “Camera calibration from surfaces of revolution,” IEEE Trans. Pattern Anal. Mach. Intell. 25(2), 147–161 (2003).
[Crossref]

Niu, Z. Y.

Poulin-Girard, A. S.

Qi, F.

F. Qi, Q. H. Li, Y. P. Luo, and D. C. Hu, “Camera calibration with one-dimensional objects moving under gravity,” Pattern Recognit. 40(1), 343–345 (2007).
[Crossref]

Ruan, M. H.

M. H. Ruan and D. Huber, “Calibration of 3D Sensors Using a Spherical Target,” International Conference on 3D Vision (IEEE, 2015), pp. 187–193.

Shan, S. Y.

Steger, C.

C. Steger, “An Unbiased Detector of Curvilinear Structures,” IEEE Trans. Pattern Anal. Mach. Intell. 20(2), 113–125 (2002).
[Crossref]

Sun, B.

Sun, J. H.

J. H. Sun, H. B. He, and D. B. Zeng, “Global Calibration of Multiple Cameras Based on Sphere Targets,” Sensors (Basel) 16(1), 77 (2016).
[Crossref] [PubMed]

Teramoto, H.

H. Teramoto and G. Xu, “Camera calibration by a single image of balls: from conic to the absolute conic,” in Proceedings of the Asian Conference on Computer Vision (ACCV, 2002), pp. 499-506.

Thibault, S.

Tsai, R. Y.

R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV camera and lenses,” IEEE J. Robot. Autom. 3(4), 323–344 (1987).
[Crossref]

Weng, J. Y.

J. Y. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion model and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14(10), 965–980 (1992).
[Crossref]

Wong, K. K.

K. K. Wong, P. R. S. Mendonca, and R. Cipolla, “Camera calibration from surfaces of revolution,” IEEE Trans. Pattern Anal. Mach. Intell. 25(2), 147–161 (2003).
[Crossref]

Wong, K.-Y. K.

K.-Y. K. Wong, G. Q. Zhang, and Z. H. Chen, “A stratified approach for camera calibration using spheres,” IEEE Trans. Image Process. 20(2), 305–316 (2011).
[Crossref] [PubMed]

H. Zhang, K.-Y. K. Wong, and G. Zhang, “Camera calibration from images of spheres,” IEEE Trans. Pattern Anal. Mach. Intell. 29(3), 499–503 (2007).
[Crossref] [PubMed]

Wu, F. C.

Y. H. Wu, X. J. Li, F. C. Wu, and Z. Y. Hu, “Coplanar circles, quasi-affine invariance and calibration,” Image Vis. Comput. 24(4), 319–326 (2006).
[Crossref]

F. C. Wu, Z. Y. Hu, and H. J. Zhu, “Camera calibration with moving one-dimensional objects,” Pattern Recognit. 38(5), 755–765 (2005).
[Crossref]

Y. H. Wu, H. J. Zhu, Z. Y. Hu, and F. C. Wu, “Camera Calibration from the Quasi-Affine invariance of two parallel circles,” in Proceedings of European Conference on Computer Vision (ECCV, 2004), pp.190–202.

Wu, Q.

Wu, Y. H.

Y. H. Wu, X. J. Li, F. C. Wu, and Z. Y. Hu, “Coplanar circles, quasi-affine invariance and calibration,” Image Vis. Comput. 24(4), 319–326 (2006).
[Crossref]

Y. H. Wu, H. J. Zhu, Z. Y. Hu, and F. C. Wu, “Camera Calibration from the Quasi-Affine invariance of two parallel circles,” in Proceedings of European Conference on Computer Vision (ECCV, 2004), pp.190–202.

Xu, G.

H. Teramoto and G. Xu, “Camera calibration by a single image of balls: from conic to the absolute conic,” in Proceedings of the Asian Conference on Computer Vision (ACCV, 2002), pp. 499-506.

Yang, L. H.

Yang, S. R.

Yin, Y.

Ying, X. H.

X. H. Ying and H. B. Zha, “Geometric interpretations of the relation between the image of the absolute conic and sphere images,” IEEE Trans. Pattern Anal. Mach. Intell. 28(12), 2031–2036 (2006).
[Crossref] [PubMed]

Zeng, D. B.

J. H. Sun, H. B. He, and D. B. Zeng, “Global Calibration of Multiple Cameras Based on Sphere Targets,” Sensors (Basel) 16(1), 77 (2016).
[Crossref] [PubMed]

Zha, H. B.

X. H. Ying and H. B. Zha, “Geometric interpretations of the relation between the image of the absolute conic and sphere images,” IEEE Trans. Pattern Anal. Mach. Intell. 28(12), 2031–2036 (2006).
[Crossref] [PubMed]

Zhang, G.

H. Zhang, K.-Y. K. Wong, and G. Zhang, “Camera calibration from images of spheres,” IEEE Trans. Pattern Anal. Mach. Intell. 29(3), 499–503 (2007).
[Crossref] [PubMed]

Zhang, G. J.

Z. Liu, X. J. Li, F. J. Li, and G. J. Zhang, “Calibration method for line-structured light vision sensor based on a single ball target,” Opt. Lasers Eng. 69, 20–28 (2015).
[Crossref]

Z. Liu, F. J. Li, B. K. Huang, and G. J. Zhang, “Real-time and accurate rail wear measurement method and experimental analysis,” J. Opt. Soc. Am. A 31(8), 1721–1729 (2014).
[Crossref] [PubMed]

Zhang, G. Q.

K.-Y. K. Wong, G. Q. Zhang, and Z. H. Chen, “A stratified approach for camera calibration using spheres,” IEEE Trans. Image Process. 20(2), 305–316 (2011).
[Crossref] [PubMed]

Zhang, H.

H. Zhang, K.-Y. K. Wong, and G. Zhang, “Camera calibration from images of spheres,” IEEE Trans. Pattern Anal. Mach. Intell. 29(3), 499–503 (2007).
[Crossref] [PubMed]

Zhang, Z. Y.

Z. Y. Zhang, “Camera calibration with one-dimensional objects,” IEEE Trans. Pattern Anal. Mach. Intell. 26(7), 892–899 (2004).
[Crossref] [PubMed]

Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

Zhu, H. J.

F. C. Wu, Z. Y. Hu, and H. J. Zhu, “Camera calibration with moving one-dimensional objects,” Pattern Recognit. 38(5), 755–765 (2005).
[Crossref]

Y. H. Wu, H. J. Zhu, Z. Y. Hu, and F. C. Wu, “Camera Calibration from the Quasi-Affine invariance of two parallel circles,” in Proceedings of European Conference on Computer Vision (ECCV, 2004), pp.190–202.

Zhu, J. G.

Analysis Int. Math. J. Analysis Appl. (1)

M. Agrawal and L. Davis, “Complete camera calibration using spheres: a dual-space approach,” Analysis Int. Math. J. Analysis Appl. 34(3), 257–282 (2003).

Appl. Opt. (2)

IEEE J. Robot. Autom. (1)

R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV camera and lenses,” IEEE J. Robot. Autom. 3(4), 323–344 (1987).
[Crossref]

IEEE Trans. Image Process. (1)

K.-Y. K. Wong, G. Q. Zhang, and Z. H. Chen, “A stratified approach for camera calibration using spheres,” IEEE Trans. Image Process. 20(2), 305–316 (2011).
[Crossref] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (11)

H. Zhang, K.-Y. K. Wong, and G. Zhang, “Camera calibration from images of spheres,” IEEE Trans. Pattern Anal. Mach. Intell. 29(3), 499–503 (2007).
[Crossref] [PubMed]

X. H. Ying and H. B. Zha, “Geometric interpretations of the relation between the image of the absolute conic and sphere images,” IEEE Trans. Pattern Anal. Mach. Intell. 28(12), 2031–2036 (2006).
[Crossref] [PubMed]

J. S. Kim, P. Gurdjos, and I. S. Kweon, “Geometric and algebraic constraints of projected concentric circles and their applications to camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 27(4), 637–642 (2005).
[Crossref] [PubMed]

J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Mach. Intell. 22(10), 1066–1077 (2000).
[Crossref]

J. Y. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion model and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14(10), 965–980 (1992).
[Crossref]

Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

D. Douxchamps and K. Chihara, “High-accuracy and robust localization of large control markers for geometric camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 376–383 (2009).
[Crossref] [PubMed]

Z. Y. Zhang, “Camera calibration with one-dimensional objects,” IEEE Trans. Pattern Anal. Mach. Intell. 26(7), 892–899 (2004).
[Crossref] [PubMed]

K. K. Wong, P. R. S. Mendonca, and R. Cipolla, “Camera calibration from surfaces of revolution,” IEEE Trans. Pattern Anal. Mach. Intell. 25(2), 147–161 (2003).
[Crossref]

C. Steger, “An Unbiased Detector of Curvilinear Structures,” IEEE Trans. Pattern Anal. Mach. Intell. 20(2), 113–125 (2002).
[Crossref]

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–698 (1986).
[Crossref] [PubMed]

Image Vis. Comput. (1)

Y. H. Wu, X. J. Li, F. C. Wu, and Z. Y. Hu, “Coplanar circles, quasi-affine invariance and calibration,” Image Vis. Comput. 24(4), 319–326 (2006).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Express (3)

Opt. Lasers Eng. (1)

Z. Liu, X. J. Li, F. J. Li, and G. J. Zhang, “Calibration method for line-structured light vision sensor based on a single ball target,” Opt. Lasers Eng. 69, 20–28 (2015).
[Crossref]

Pattern Recognit. (2)

F. C. Wu, Z. Y. Hu, and H. J. Zhu, “Camera calibration with moving one-dimensional objects,” Pattern Recognit. 38(5), 755–765 (2005).
[Crossref]

F. Qi, Q. H. Li, Y. P. Luo, and D. C. Hu, “Camera calibration with one-dimensional objects moving under gravity,” Pattern Recognit. 40(1), 343–345 (2007).
[Crossref]

Sensors (Basel) (1)

J. H. Sun, H. B. He, and D. B. Zeng, “Global Calibration of Multiple Cameras Based on Sphere Targets,” Sensors (Basel) 16(1), 77 (2016).
[Crossref] [PubMed]

Other (8)

Y. H. Wu, H. J. Zhu, Z. Y. Hu, and F. C. Wu, “Camera Calibration from the Quasi-Affine invariance of two parallel circles,” in Proceedings of European Conference on Computer Vision (ECCV, 2004), pp.190–202.

C. Colombo, D. Comanducci, and A. D. Bimbo, “Camera calibration with two arbitrary coaxial circles,” in Proceedings of European Conference on Computer Vision (ECCV, 2006), pp. 265–276.
[Crossref]

R. Halir and J. Flusser, “Numerically Stable Direct Least Squares Fitting of Ellipses,” (1998).

R. I. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2000).

M. Agrawal and L. S. Davis, “Camera calibration using spheres: a semi-definite programming approach,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE, 2003), pp.782–789.
[Crossref]

J. Y. Bouguet, “The MATLAB open source calibration toolbox,” http://www.vision.caltech.edu/bouguetj/calib _doc/ .

H. Teramoto and G. Xu, “Camera calibration by a single image of balls: from conic to the absolute conic,” in Proceedings of the Asian Conference on Computer Vision (ACCV, 2002), pp. 499-506.

M. H. Ruan and D. Huber, “Calibration of 3D Sensors Using a Spherical Target,” International Conference on 3D Vision (IEEE, 2015), pp. 187–193.

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Figures (14)

Fig. 1
Fig. 1 Schematic of the calibration process.
Fig. 2
Fig. 2 (a) Included angle between the normal vectors n1 and n2. (b) Seita angle between the long axis and the y-axis in the image.
Fig. 3
Fig. 3 Extracting and fitting the image of the elliptic curves of the circles of latitude and longitude.
Fig. 4
Fig. 4 (a) Relationship between e l a , l la and ω ; (b) Relationship between l li( i ) , ω and e li ( i ) .
Fig. 5
Fig. 5 The relationship between centers and contours of three spheres in the image.
Fig. 6
Fig. 6 Schematic of solving the translation vector from O t x t y t z t to O c x c y c z c .
Fig. 7
Fig. 7 RMSEs of the intrinsic parameters based on Zhang’s method, GST-based method and SC-based method.
Fig. 8
Fig. 8 Reprojection errors of the target points. (a) Reprojection errors in the u direction; (b) Reprojection errors in the v direction.
Fig. 9
Fig. 9 Physical map of calibration setup. (a) Zhang’s method; (b) GST-based method; (c) SC-based method.
Fig. 10
Fig. 10 Two sets of experiments about curve fitting in dark, bright and non-uniform lighting situation. (a) Set 1; (b) Set 2.
Fig. 11
Fig. 11 Images used for calibration. (a) Checkerboard target images; (b) GST images; (c) Sphere images.
Fig. 12
Fig. 12 Reprojection errors of the target feature points. (a) Reprojection errors distribution based on Zhang’s method; (b) Reprojection errors diatribution based on GST method; (c) The statistics form of the reprojection errors based on Zhang’s method; (d) The statistics form of the reprojection errors based on GST method.
Fig. 13
Fig. 13 Repeatability results analysis based on the three methods. (a) Repeatability of fx based on the three methods; (b) Repeatability of fy based on the three methods; (c) Repeatability of u0 based on the three methods; (d) Repeatability of fx based on Zhang’s method and GST; (e) Repeatability of fy based on Zhang’s method and GST; (f) Repeatability of u0 based on Zhang’s method and GST; (g) Repeatability of v0 based on the three methods; (h) Repeatability of r based on the three methods; (i) Repeatability of v0 based on Zhang’s method and GST; (j) Repeatability of r based on Zhang’s method and GST.
Fig. 14
Fig. 14 Reprojection errors of the target feature points.

Tables (1)

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Table 1 Comparison of the Intrinsic Parameters

Equations (21)

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ρ p = ρ K [ R t ] q = [ a x γ u 0 0 a y v 0 0 0 1 ] [ R t ] q
ω = K -T K 1
L = E O = [ 1 0 0 1 a b a b a 2 + b 2 r 2 ] [ a b 1 ] = [ 0 0 r 2 ] = λ [ 0 0 1 ] = λ L
e = H T E H 1 E = H T e H
o c = H O
l = H T L = λ H T L
λ l = e o c
l la = λ e la ( j ) o la ( j )
l la = λ e ˜ la ( j ) o
l li ( i ) = λ e li ( i ) o li ( i )
l li ( i ) = λ e li ( i ) o
{ C 2 C 1 l 12 = β 2 β 1 l 12 C 3 C 1 l 13 = β 3 β 1 l 13 C 2 C 3 l 23 = β 2 β 3 l 23
{ l la = λ 1 ω v 1 l li( i ) = λ 2 ω v 2
{ v 1 = μ 1 K R d 1 v 2 = μ 2 K R d 2 { K 1 v 1 = μ 1 R d 1 K 1 v 2 = μ 2 R d 2
{ r 3 = ± ( K 1 v 1 ) / K 1 v 1 r 2 = ± ( K 1 v 2 ) / K 1 v 2
r 1 = r 2 × r 3
C la ( j ) = λ H T e la ( j ) H
C la ( j ) = λ H T e la ( j ) H C la ( j ) = λ ( K [ r 1 , r 2 , t ˜ ]) T e la ( j ) K [ r 1 , r 2 , t ˜ ] C la ( j ) = λ [ r 1 , r 2 , t ˜ ] T ( K T e la ( j ) K )[ r 1 , r 2 , t ˜ ]
- d j 2 = t ˜ T ( K T e la ( j ) K ) t ˜ / ( r 1 T ( K T e la ( j ) K ) r 1 )
f ( a ) = min ( l = 1 L ( j = 1 N e la( j l ) H la( j l ) C la( j l ) ) )
f ( b ) = min ( j = 1 m i = 1 n d ( p ^ i j , p i j ) )

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