Abstract

This paper presents a method for camera calibration based on the orthogonal vanishing point calibration using concentric circles grating and wedge grating. This method, which we believe is new, uses the high-precision characteristics of phase extraction to obtain the feature points, thus decreasing the calibration errors caused by the traditional marker extraction errors of gray pattern. According to the simulation experiment analysis results, the concentric circles grating was designed with seven periods and the wedge grating was designed with four periods. In the real measuring experiment, the grating target and the similar gray concentric circles target were used to calibrate the camera, respectively. Through comparing the reprojective errors of the two methods, the method proposed is proven to improve the calibration accuracy and robustness for the vanishing point calibration algorithm.

© 2012 Optical Society of America

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References

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  1. Z. Hu and Z. Tan, “Calibration of stereo cameras from two perpendicular planes,” Appl. Opt. 44, 5086–5090(2005).
    [CrossRef]
  2. M. K. Hor, C. Y. Tang, Y. L. Wu, K. H. Chan, and J. F. Tsai, “Robust refinement methods for camera calibration and 3D reconstruction from multiple images,” Pattern Recogn. Lett. 32, 1210–1221 (2011).
    [CrossRef]
  3. F. Zhu, H. Shi, P. Bai, and X. He, “Three-dimensional shape measurement and calibration for fringe projection by considering unequal height of the projector and the camera,” Appl. Opt. 50, 1575–1583 (2011).
    [CrossRef]
  4. R. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Autom. 3, 323–344 (1987).
    [CrossRef]
  5. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
    [CrossRef]
  6. J. Li and D. Zhang, “Camera calibration with a near-parallel imaging system based on geometric moments,” Opt. Eng. 50, 023601 (2011).
    [CrossRef]
  7. Y. Liu and X. Su, “Camera calibration with planar crossed fringe patterns,” Optik 123, 171–175 (2012).
    [CrossRef]
  8. L. Grammatikopoulos, G. Karras, and E. Petsa, “An automatic approach for camera calibration from vanishing points,” ISPRS J. Photogramm. Remote Sens. 62, 64–76 (2007).
    [CrossRef]
  9. G. Seetharaman, H. Bao, and G. Shivaram, “Calibration of camera parameters using vanishing points,” J. Franklin Inst. 331, 555–585 (1994).
    [CrossRef]
  10. J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1066–1077 (2000).
    [CrossRef]
  11. B. Li, K. Peng, X. Ying, and H. Zha, “Simultaneous vanishing point detection and camera calibration from single images,” in Advances in Visual Computing, G. Bebis, R. Boyle, B. Parvin, D. Koracin, R. Chung, R. Hammound, M. Hussain, T. Kar-Han, R. Crawfis, D. Thalmann, D. Kao, and L. Avila, eds. (Springer, 2010), pp. 151–160.
  12. R. Hartley, “Estimation of relative camera positions for uncalibrated cameras,” Computer Vision—ECCV’92, G. Sandini, ed. (Springer, 1992), pp. 579–587.
  13. S. J. Maybank and O. D. Faugeras, “A theory of self-calibration of a moving camera,” Int. J. Comput. Vis. 8, 123–151(1992).
    [CrossRef]
  14. X. Meng and Z. Hu, “A new easy camera calibration technique based on circular points,” Pattern Recogn. 36, 1155–1164 (2003).
    [CrossRef]
  15. J.-S. Kim, H.-W. Kim, and I.-S. Kweon, “A camera calibration method using concentric circles for vision applications,” in Proceedings of the 5th Asian Conference on Computer Vision, ACCV 2002 (Asian Federation of Computer Vision Societies, 2002).
  16. P. S. Huang and S. Zhang, “Fast three-step phase-shifting algorithm,” Appl. Opt. 45, 5086–5091 (2006).
    [CrossRef]
  17. X. Su, G. Zhang, and L. Guo, “Phase-only composite filter,” Opt. Eng. 26, 520–523 (1987).
  18. W. Li and X. Su, “Real-time calibration algorithm for phase shifting in phase-measuring profilometry,” Opt. Eng. 40, 761–766 (2001).
    [CrossRef]
  19. W. Li and Y. F. Li, “Single-camera panoramic stereo imaging system with a fisheye lens and a convex mirror,” Opt. Express 19, 5855–5867 (2011).
    [CrossRef]
  20. H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D. Malacara, ed. (Wiley, 2007), pp. 547–655.

2012 (1)

Y. Liu and X. Su, “Camera calibration with planar crossed fringe patterns,” Optik 123, 171–175 (2012).
[CrossRef]

2011 (4)

M. K. Hor, C. Y. Tang, Y. L. Wu, K. H. Chan, and J. F. Tsai, “Robust refinement methods for camera calibration and 3D reconstruction from multiple images,” Pattern Recogn. Lett. 32, 1210–1221 (2011).
[CrossRef]

F. Zhu, H. Shi, P. Bai, and X. He, “Three-dimensional shape measurement and calibration for fringe projection by considering unequal height of the projector and the camera,” Appl. Opt. 50, 1575–1583 (2011).
[CrossRef]

J. Li and D. Zhang, “Camera calibration with a near-parallel imaging system based on geometric moments,” Opt. Eng. 50, 023601 (2011).
[CrossRef]

W. Li and Y. F. Li, “Single-camera panoramic stereo imaging system with a fisheye lens and a convex mirror,” Opt. Express 19, 5855–5867 (2011).
[CrossRef]

2007 (1)

L. Grammatikopoulos, G. Karras, and E. Petsa, “An automatic approach for camera calibration from vanishing points,” ISPRS J. Photogramm. Remote Sens. 62, 64–76 (2007).
[CrossRef]

2006 (1)

2005 (1)

2003 (1)

X. Meng and Z. Hu, “A new easy camera calibration technique based on circular points,” Pattern Recogn. 36, 1155–1164 (2003).
[CrossRef]

2001 (1)

W. Li and X. Su, “Real-time calibration algorithm for phase shifting in phase-measuring profilometry,” Opt. Eng. 40, 761–766 (2001).
[CrossRef]

2000 (2)

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

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

1994 (1)

G. Seetharaman, H. Bao, and G. Shivaram, “Calibration of camera parameters using vanishing points,” J. Franklin Inst. 331, 555–585 (1994).
[CrossRef]

1992 (1)

S. J. Maybank and O. D. Faugeras, “A theory of self-calibration of a moving camera,” Int. J. Comput. Vis. 8, 123–151(1992).
[CrossRef]

1987 (2)

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

X. Su, G. Zhang, and L. Guo, “Phase-only composite filter,” Opt. Eng. 26, 520–523 (1987).

Bai, P.

Bao, H.

G. Seetharaman, H. Bao, and G. Shivaram, “Calibration of camera parameters using vanishing points,” J. Franklin Inst. 331, 555–585 (1994).
[CrossRef]

Bruning, J. H.

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D. Malacara, ed. (Wiley, 2007), pp. 547–655.

Chan, K. H.

M. K. Hor, C. Y. Tang, Y. L. Wu, K. H. Chan, and J. F. Tsai, “Robust refinement methods for camera calibration and 3D reconstruction from multiple images,” Pattern Recogn. Lett. 32, 1210–1221 (2011).
[CrossRef]

Faugeras, O. D.

S. J. Maybank and O. D. Faugeras, “A theory of self-calibration of a moving camera,” Int. J. Comput. Vis. 8, 123–151(1992).
[CrossRef]

Grammatikopoulos, L.

L. Grammatikopoulos, G. Karras, and E. Petsa, “An automatic approach for camera calibration from vanishing points,” ISPRS J. Photogramm. Remote Sens. 62, 64–76 (2007).
[CrossRef]

Guo, L.

X. Su, G. Zhang, and L. Guo, “Phase-only composite filter,” Opt. Eng. 26, 520–523 (1987).

Hartley, R.

R. Hartley, “Estimation of relative camera positions for uncalibrated cameras,” Computer Vision—ECCV’92, G. Sandini, ed. (Springer, 1992), pp. 579–587.

He, X.

Heikkila, J.

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

Hor, M. K.

M. K. Hor, C. Y. Tang, Y. L. Wu, K. H. Chan, and J. F. Tsai, “Robust refinement methods for camera calibration and 3D reconstruction from multiple images,” Pattern Recogn. Lett. 32, 1210–1221 (2011).
[CrossRef]

Hu, Z.

Z. Hu and Z. Tan, “Calibration of stereo cameras from two perpendicular planes,” Appl. Opt. 44, 5086–5090(2005).
[CrossRef]

X. Meng and Z. Hu, “A new easy camera calibration technique based on circular points,” Pattern Recogn. 36, 1155–1164 (2003).
[CrossRef]

Huang, P. S.

Karras, G.

L. Grammatikopoulos, G. Karras, and E. Petsa, “An automatic approach for camera calibration from vanishing points,” ISPRS J. Photogramm. Remote Sens. 62, 64–76 (2007).
[CrossRef]

Kim, H.-W.

J.-S. Kim, H.-W. Kim, and I.-S. Kweon, “A camera calibration method using concentric circles for vision applications,” in Proceedings of the 5th Asian Conference on Computer Vision, ACCV 2002 (Asian Federation of Computer Vision Societies, 2002).

Kim, J.-S.

J.-S. Kim, H.-W. Kim, and I.-S. Kweon, “A camera calibration method using concentric circles for vision applications,” in Proceedings of the 5th Asian Conference on Computer Vision, ACCV 2002 (Asian Federation of Computer Vision Societies, 2002).

Kweon, I.-S.

J.-S. Kim, H.-W. Kim, and I.-S. Kweon, “A camera calibration method using concentric circles for vision applications,” in Proceedings of the 5th Asian Conference on Computer Vision, ACCV 2002 (Asian Federation of Computer Vision Societies, 2002).

Li, B.

B. Li, K. Peng, X. Ying, and H. Zha, “Simultaneous vanishing point detection and camera calibration from single images,” in Advances in Visual Computing, G. Bebis, R. Boyle, B. Parvin, D. Koracin, R. Chung, R. Hammound, M. Hussain, T. Kar-Han, R. Crawfis, D. Thalmann, D. Kao, and L. Avila, eds. (Springer, 2010), pp. 151–160.

Li, J.

J. Li and D. Zhang, “Camera calibration with a near-parallel imaging system based on geometric moments,” Opt. Eng. 50, 023601 (2011).
[CrossRef]

Li, W.

W. Li and Y. F. Li, “Single-camera panoramic stereo imaging system with a fisheye lens and a convex mirror,” Opt. Express 19, 5855–5867 (2011).
[CrossRef]

W. Li and X. Su, “Real-time calibration algorithm for phase shifting in phase-measuring profilometry,” Opt. Eng. 40, 761–766 (2001).
[CrossRef]

Li, Y. F.

Liu, Y.

Y. Liu and X. Su, “Camera calibration with planar crossed fringe patterns,” Optik 123, 171–175 (2012).
[CrossRef]

Maybank, S. J.

S. J. Maybank and O. D. Faugeras, “A theory of self-calibration of a moving camera,” Int. J. Comput. Vis. 8, 123–151(1992).
[CrossRef]

Meng, X.

X. Meng and Z. Hu, “A new easy camera calibration technique based on circular points,” Pattern Recogn. 36, 1155–1164 (2003).
[CrossRef]

Peng, K.

B. Li, K. Peng, X. Ying, and H. Zha, “Simultaneous vanishing point detection and camera calibration from single images,” in Advances in Visual Computing, G. Bebis, R. Boyle, B. Parvin, D. Koracin, R. Chung, R. Hammound, M. Hussain, T. Kar-Han, R. Crawfis, D. Thalmann, D. Kao, and L. Avila, eds. (Springer, 2010), pp. 151–160.

Petsa, E.

L. Grammatikopoulos, G. Karras, and E. Petsa, “An automatic approach for camera calibration from vanishing points,” ISPRS J. Photogramm. Remote Sens. 62, 64–76 (2007).
[CrossRef]

Schreiber, H.

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D. Malacara, ed. (Wiley, 2007), pp. 547–655.

Seetharaman, G.

G. Seetharaman, H. Bao, and G. Shivaram, “Calibration of camera parameters using vanishing points,” J. Franklin Inst. 331, 555–585 (1994).
[CrossRef]

Shi, H.

Shivaram, G.

G. Seetharaman, H. Bao, and G. Shivaram, “Calibration of camera parameters using vanishing points,” J. Franklin Inst. 331, 555–585 (1994).
[CrossRef]

Su, X.

Y. Liu and X. Su, “Camera calibration with planar crossed fringe patterns,” Optik 123, 171–175 (2012).
[CrossRef]

W. Li and X. Su, “Real-time calibration algorithm for phase shifting in phase-measuring profilometry,” Opt. Eng. 40, 761–766 (2001).
[CrossRef]

X. Su, G. Zhang, and L. Guo, “Phase-only composite filter,” Opt. Eng. 26, 520–523 (1987).

Tan, Z.

Tang, C. Y.

M. K. Hor, C. Y. Tang, Y. L. Wu, K. H. Chan, and J. F. Tsai, “Robust refinement methods for camera calibration and 3D reconstruction from multiple images,” Pattern Recogn. Lett. 32, 1210–1221 (2011).
[CrossRef]

Tsai, J. F.

M. K. Hor, C. Y. Tang, Y. L. Wu, K. H. Chan, and J. F. Tsai, “Robust refinement methods for camera calibration and 3D reconstruction from multiple images,” Pattern Recogn. Lett. 32, 1210–1221 (2011).
[CrossRef]

Tsai, R.

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

Wu, Y. L.

M. K. Hor, C. Y. Tang, Y. L. Wu, K. H. Chan, and J. F. Tsai, “Robust refinement methods for camera calibration and 3D reconstruction from multiple images,” Pattern Recogn. Lett. 32, 1210–1221 (2011).
[CrossRef]

Ying, X.

B. Li, K. Peng, X. Ying, and H. Zha, “Simultaneous vanishing point detection and camera calibration from single images,” in Advances in Visual Computing, G. Bebis, R. Boyle, B. Parvin, D. Koracin, R. Chung, R. Hammound, M. Hussain, T. Kar-Han, R. Crawfis, D. Thalmann, D. Kao, and L. Avila, eds. (Springer, 2010), pp. 151–160.

Zha, H.

B. Li, K. Peng, X. Ying, and H. Zha, “Simultaneous vanishing point detection and camera calibration from single images,” in Advances in Visual Computing, G. Bebis, R. Boyle, B. Parvin, D. Koracin, R. Chung, R. Hammound, M. Hussain, T. Kar-Han, R. Crawfis, D. Thalmann, D. Kao, and L. Avila, eds. (Springer, 2010), pp. 151–160.

Zhang, D.

J. Li and D. Zhang, “Camera calibration with a near-parallel imaging system based on geometric moments,” Opt. Eng. 50, 023601 (2011).
[CrossRef]

Zhang, G.

X. Su, G. Zhang, and L. Guo, “Phase-only composite filter,” Opt. Eng. 26, 520–523 (1987).

Zhang, S.

Zhang, Z.

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

Zhu, F.

Appl. Opt. (3)

IEEE J. Robot. Autom. (1)

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

IEEE Trans. Pattern Anal. Mach. Intell. (1)

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

IEEE Trans. Pattern Anal. Machine Intell. (1)

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

Int. J. Comput. Vis. (1)

S. J. Maybank and O. D. Faugeras, “A theory of self-calibration of a moving camera,” Int. J. Comput. Vis. 8, 123–151(1992).
[CrossRef]

ISPRS J. Photogramm. Remote Sens. (1)

L. Grammatikopoulos, G. Karras, and E. Petsa, “An automatic approach for camera calibration from vanishing points,” ISPRS J. Photogramm. Remote Sens. 62, 64–76 (2007).
[CrossRef]

J. Franklin Inst. (1)

G. Seetharaman, H. Bao, and G. Shivaram, “Calibration of camera parameters using vanishing points,” J. Franklin Inst. 331, 555–585 (1994).
[CrossRef]

Opt. Eng. (3)

J. Li and D. Zhang, “Camera calibration with a near-parallel imaging system based on geometric moments,” Opt. Eng. 50, 023601 (2011).
[CrossRef]

X. Su, G. Zhang, and L. Guo, “Phase-only composite filter,” Opt. Eng. 26, 520–523 (1987).

W. Li and X. Su, “Real-time calibration algorithm for phase shifting in phase-measuring profilometry,” Opt. Eng. 40, 761–766 (2001).
[CrossRef]

Opt. Express (1)

Optik (1)

Y. Liu and X. Su, “Camera calibration with planar crossed fringe patterns,” Optik 123, 171–175 (2012).
[CrossRef]

Pattern Recogn. (1)

X. Meng and Z. Hu, “A new easy camera calibration technique based on circular points,” Pattern Recogn. 36, 1155–1164 (2003).
[CrossRef]

Pattern Recogn. Lett. (1)

M. K. Hor, C. Y. Tang, Y. L. Wu, K. H. Chan, and J. F. Tsai, “Robust refinement methods for camera calibration and 3D reconstruction from multiple images,” Pattern Recogn. Lett. 32, 1210–1221 (2011).
[CrossRef]

Other (4)

J.-S. Kim, H.-W. Kim, and I.-S. Kweon, “A camera calibration method using concentric circles for vision applications,” in Proceedings of the 5th Asian Conference on Computer Vision, ACCV 2002 (Asian Federation of Computer Vision Societies, 2002).

B. Li, K. Peng, X. Ying, and H. Zha, “Simultaneous vanishing point detection and camera calibration from single images,” in Advances in Visual Computing, G. Bebis, R. Boyle, B. Parvin, D. Koracin, R. Chung, R. Hammound, M. Hussain, T. Kar-Han, R. Crawfis, D. Thalmann, D. Kao, and L. Avila, eds. (Springer, 2010), pp. 151–160.

R. Hartley, “Estimation of relative camera positions for uncalibrated cameras,” Computer Vision—ECCV’92, G. Sandini, ed. (Springer, 1992), pp. 579–587.

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D. Malacara, ed. (Wiley, 2007), pp. 547–655.

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Figures (7)

Fig. 1.
Fig. 1.

Grating target: (a) concentric circles grating, (b) wedge grating, (c) wrapped image with zero-phase curves (the dots are zero-phase points).

Fig. 2.
Fig. 2.

Schematic diagram of vanishing point solution: (a) scene model, (b) perspective image of model.

Fig. 3.
Fig. 3.

Error curve of calibration parameters obtained when the number of rings changed.

Fig. 4.
Fig. 4.

Error curve of calibration parameters obtained when the number of camera operations changed.

Fig. 5.
Fig. 5.

Error curve of calibration parameters obtained when the image noise changed.

Fig. 6.
Fig. 6.

Hardware configuration of the calibration experiment.

Fig. 7.
Fig. 7.

Real images of the calibration pattern (the dots are marks): (a) proposed phase pattern, (b) gray pattern.

Tables (2)

Tables Icon

Table 1. Intrinsic Parameters of the Camera

Tables Icon

Table 2. Calibration Results with Different Calibration Methods

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

λm˜=K[RT]M˜,
K=[fusu00fvv0001],
{In(r)=a+bcos(2πrT+2πnN)In(θ)=a+bcos(2πθT+2πnN),
Φ(u,v)=arctan[g4(u,v)g2(u,v)g1(u,v)g3(u,v)],
Φ(u,v)=arctan[g4(u,v)g2(u,v)g1(u,v)g3(u,v)].
{(A,B;O,P1)=1(C,D;O,P2)=1.
{(Am,Bm;Om,P1)=1(Cm,Dm;Om,P2)=1.
{uP1=uO(uA+uB)2uAuB2uOuAuBvP1=vO(vA+vB)2vAvB2vOvAvBuP2=uO(uC+uD)2uCuD2uOuCuDvP2=vO(vC+vD)2vCvD2vOvCvD.
cos90°=dABTdCDdABTdCD·dABTdCD=P1TωP2P1TωP1·P2TωP2=0.
P1TωP2=P1TKTK1P2=0,
uP1uP2ω1+(vP1uP2+uP1vP2)ω2+vP1vP2ω3+(uP1+uP2)ω4+(vP1+vP3)ω5+ω6=0.

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