Abstract

This paper proposes an adjustment method for binocular vision measurement to calibrate a camera’s internal and external parameters based on a one dimensional (1D) target in the field of view. A 1D target with two feature points lying randomly in the field of view is used to get the images of the feature points. The distance between the two feature points is known. The internal and external parameters can be acquired by solving equations combining the photograph measurement collinear equations and the feature points’ distance equations. To solve these equations, we use linearization of nonlinear equations and the adjustment method. During the process, we deal with the equations as measurement equations and the internal/external parameters and the 3D target points as the unknown parameters to calculate them. According to field experiment results, in about a 600mm×600mm field of view, the relative error of the distance of two points is less than two ten-thousandths, obtained by using the calculated results of the binocular vision system. The calibration process is simple, convenient, and suitable for calibrating a camera on the spot.

© 2012 Optical Society of America

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  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]
  2. O. D. Faugeras, Q. T. Luong, and S. J. Maybank, “Camera self-calibration: theory and experiments,” in Computer Vision—ECCV’92, Vol. 588 of Lecture Notes in Computer Science (Springer, 1992), pp. 321–334.
  3. M. Pollefeys and L. Van Gool, “A stratified approach to metric self-calibration,” in Proceedings of the CVPR (IEEE, 1997), pp. 407–412.
  4. R. I. Hartley, E. Hayman, L. de Agapito, and I. D. Reid, “Camera calibration and search for infinity, ” in Proceedings of the ICCV (IEEE, 1999), pp. 510–517.
  5. L. Zhang, Gang C., Dong. Ye, and R. Che, “Calibrating internal and external parameters of multi-cameras by moving freely rigid ball bar,” Opt. Precis. Eng. 17, 1942–1952 (2009) (in Chinese).
  6. Z. Zhang, “Camera calibration with one-dimensional objects,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 892–899 (2004).
    [CrossRef]
  7. F. C. Wu, Z. Y. Hu, and H. J. Zhu Haijiang, “Camera calibration with moving one-dimensional objects,” Pattern Recogn. 38, 755–765 (2005).
    [CrossRef]
  8. W. Li, J. Jin, X. Li, and B. Li, “Method of rotation angle measurement in machine vision based on calibration pattern with spot array,” Appl. Opt. 49, 1001–1006 (2010).
    [CrossRef]
  9. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
    [CrossRef]
  10. J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion model and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
    [CrossRef]
  11. R. Y. Tsai and R. K. Lenz, “A new technique for fully autonomous and efficient 3D robotics hand/eye calibration,” IEEE Trans. Robotic. Autom. 5, 345–358 (1989).
    [CrossRef]

2010

2009

L. Zhang, Gang C., Dong. Ye, and R. Che, “Calibrating internal and external parameters of multi-cameras by moving freely rigid ball bar,” Opt. Precis. Eng. 17, 1942–1952 (2009) (in Chinese).

2005

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

2004

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

2000

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

1992

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

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]

1989

R. Y. Tsai and R. K. Lenz, “A new technique for fully autonomous and efficient 3D robotics hand/eye calibration,” IEEE Trans. Robotic. Autom. 5, 345–358 (1989).
[CrossRef]

C., Gang

L. Zhang, Gang C., Dong. Ye, and R. Che, “Calibrating internal and external parameters of multi-cameras by moving freely rigid ball bar,” Opt. Precis. Eng. 17, 1942–1952 (2009) (in Chinese).

Che, R.

L. Zhang, Gang C., Dong. Ye, and R. Che, “Calibrating internal and external parameters of multi-cameras by moving freely rigid ball bar,” Opt. Precis. Eng. 17, 1942–1952 (2009) (in Chinese).

Cohen, P.

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

de Agapito, L.

R. I. Hartley, E. Hayman, L. de Agapito, and I. D. Reid, “Camera calibration and search for infinity, ” in Proceedings of the ICCV (IEEE, 1999), pp. 510–517.

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]

O. D. Faugeras, Q. T. Luong, and S. J. Maybank, “Camera self-calibration: theory and experiments,” in Computer Vision—ECCV’92, Vol. 588 of Lecture Notes in Computer Science (Springer, 1992), pp. 321–334.

Hartley, R. I.

R. I. Hartley, E. Hayman, L. de Agapito, and I. D. Reid, “Camera calibration and search for infinity, ” in Proceedings of the ICCV (IEEE, 1999), pp. 510–517.

Hayman, E.

R. I. Hartley, E. Hayman, L. de Agapito, and I. D. Reid, “Camera calibration and search for infinity, ” in Proceedings of the ICCV (IEEE, 1999), pp. 510–517.

Herniou, M.

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

Hu, Z. Y.

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

Jin, J.

Lenz, R. K.

R. Y. Tsai and R. K. Lenz, “A new technique for fully autonomous and efficient 3D robotics hand/eye calibration,” IEEE Trans. Robotic. Autom. 5, 345–358 (1989).
[CrossRef]

Li, B.

Li, W.

Li, X.

Luong, Q. T.

O. D. Faugeras, Q. T. Luong, and S. J. Maybank, “Camera self-calibration: theory and experiments,” in Computer Vision—ECCV’92, Vol. 588 of Lecture Notes in Computer Science (Springer, 1992), pp. 321–334.

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]

O. D. Faugeras, Q. T. Luong, and S. J. Maybank, “Camera self-calibration: theory and experiments,” in Computer Vision—ECCV’92, Vol. 588 of Lecture Notes in Computer Science (Springer, 1992), pp. 321–334.

Pollefeys, M.

M. Pollefeys and L. Van Gool, “A stratified approach to metric self-calibration,” in Proceedings of the CVPR (IEEE, 1997), pp. 407–412.

Reid, I. D.

R. I. Hartley, E. Hayman, L. de Agapito, and I. D. Reid, “Camera calibration and search for infinity, ” in Proceedings of the ICCV (IEEE, 1999), pp. 510–517.

Tsai, R. Y.

R. Y. Tsai and R. K. Lenz, “A new technique for fully autonomous and efficient 3D robotics hand/eye calibration,” IEEE Trans. Robotic. Autom. 5, 345–358 (1989).
[CrossRef]

Van Gool, L.

M. Pollefeys and L. Van Gool, “A stratified approach to metric self-calibration,” in Proceedings of the CVPR (IEEE, 1997), pp. 407–412.

Weng, J.

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

Wu, F. C.

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

Ye, Dong.

L. Zhang, Gang C., Dong. Ye, and R. Che, “Calibrating internal and external parameters of multi-cameras by moving freely rigid ball bar,” Opt. Precis. Eng. 17, 1942–1952 (2009) (in Chinese).

Zhang, L.

L. Zhang, Gang C., Dong. Ye, and R. Che, “Calibrating internal and external parameters of multi-cameras by moving freely rigid ball bar,” Opt. Precis. Eng. 17, 1942–1952 (2009) (in Chinese).

Zhang, Z.

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

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

Zhu Haijiang, H. J.

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

Appl. Opt.

IEEE Trans. Pattern Anal. Mach. Intell.

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

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

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

IEEE Trans. Robotic. Autom.

R. Y. Tsai and R. K. Lenz, “A new technique for fully autonomous and efficient 3D robotics hand/eye calibration,” IEEE Trans. Robotic. Autom. 5, 345–358 (1989).
[CrossRef]

Int. J. Comput. Vis.

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]

Opt. Precis. Eng.

L. Zhang, Gang C., Dong. Ye, and R. Che, “Calibrating internal and external parameters of multi-cameras by moving freely rigid ball bar,” Opt. Precis. Eng. 17, 1942–1952 (2009) (in Chinese).

Pattern Recogn.

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

Other

O. D. Faugeras, Q. T. Luong, and S. J. Maybank, “Camera self-calibration: theory and experiments,” in Computer Vision—ECCV’92, Vol. 588 of Lecture Notes in Computer Science (Springer, 1992), pp. 321–334.

M. Pollefeys and L. Van Gool, “A stratified approach to metric self-calibration,” in Proceedings of the CVPR (IEEE, 1997), pp. 407–412.

R. I. Hartley, E. Hayman, L. de Agapito, and I. D. Reid, “Camera calibration and search for infinity, ” in Proceedings of the ICCV (IEEE, 1999), pp. 510–517.

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Figures (5)

Fig. 1.
Fig. 1.

Binocular vision measurement system of space point P.

Fig. 2.
Fig. 2.

Results of the distance error under different noise.

Fig. 3.
Fig. 3.

Error of part of internal parameters under different noise.

Fig. 4.
Fig. 4.

Error of rotation angle calibration under different noise.

Fig. 5.
Fig. 5.

Error of translation calibration under different noise.

Tables (6)

Tables Icon

Table 1. Internal Parameters of the Camera

Tables Icon

Table 2. Structural Parameters of Binocular Vision System

Tables Icon

Table 3. Internal Parameters of Cameras

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Table 4. Structural Parameters of Cameras

Tables Icon

Table 5. Measurement Data

Tables Icon

Table 6. Pixel Coordinates

Equations (16)

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

slpl=Al[I0]PL=MLPLsrpr=Ar[RT]PL=MRPL.
A=[fx0u00fyv0001]=[f/dX0u00f/dYv0001],[RT]=[a1b1c1Txa2b2c2Tya3b3c3Tz]=[cosβcosγsinαsinβsinγcosαsinγsinβcosγ+sinαcosβsinγTxcosβcosγ+sinαsinβcosγcosαcosγsinβsinγsinαcosβcosγTycosαsinβsinαcosαcosβTz]M=A[RT]=[m11m12m13m14m21m22m23m24m31m32m33m34],
{xlu0l=fxlXZylv0l=fylYZxru0r=fxra1(XXs)+b1(YYs)+c1(ZZs)a3(XXs)+b3(YYs)+c3(ZZs)yrv0r=fyra2(XXs)+b2(YYs)+c2(ZZs)a3(XXs)+b3(YYs)+c3(ZZs).
[ulm31lm11lulm32lm12lulm33lm13lvlm31lm21lvlm32lm22lvlm33lm23lurm31rm11rurm32rm12rurm33rm13rvrm31rm21rvrm32rm22rvrm33rm23r][XYZ]=[m14lulm34lm24lvlm34lm14rurm34rm24rvrm34r].
δx=(xu0)(K1ρ2+K2ρ4),δy=(yv0)(K1ρ2+K2ρ4),x¯=x+δx,y¯=y+δy,
slpl=MLPL=MLMPL=MLPL,srpr=MRPL=MRMPL=MRPL,ML=[fx0u000fyv000010]=[AlR0].
AlR=[fx0u00fyv0001][r11r12r13r21r22r23r31r32r33]=[fx0u00fyv0001]=[fxr11+u0r31fxr12+u0r32fxr13+u0r33fyr21+v0r31fyr22+v0r32fyr23+v0r33r31r32r33].
r31=0,r32=0,r33=1,r23=0,[fxr11fxr12u0fyr21fyr22v0001]=[fx0u00fyv0001].
F(X˜)={F1(X˜)=xl1+δxl1u0lfxlX1Z1=0F2(X˜)=yl1+δyl1v0lfylY1Z1=0F3(X˜)=xr1+δxr1-u0rfxra1(X1Xs)+b1(Y1Ys)+c1(Z1Zs)a3(X1Xs)+b3(Y1Ys)+c3(Z1Zs)=0F4(X˜)=yr1+δyr1-v0rfyra2(X1Xs)+b2(Y1Ys)+c2(Z1Zs)a3(X1Xs)+b3(Y1Ys)+c3(Z1Zs)=0F5(X˜)=xl2+δxl2-u0lfxlX2Z2=0F6(X˜)=yl2+δyl2-v0lfylY2Z2=0F7(X˜)=xr2+δxr2-u0rfxra1(X2Xs)+b1(Y2Ys)+c1(Z2Zs)a3(X2Xs)+b3(Y2Ys)+c3(Z2Zs)=0F8(X˜)=yr2+δyr2-u0rfyra2(X2Xs)+b2(Y2Ys)+c2(Z2Zs)a3(X2Xs)+b3(Y2Ys)+c3(Z2Zs)=0F9(X˜)=(X1X2)2+(Y1Y2)2+(Z1Z2)2L=0,
δxli=(xliu0l)(K1ρli2+K2ρli4),δyli=(yliv0l)(K1ρli2+K2ρli4),δxri=(xriu0r)(K3ρri2+K4ρri4),δyri=(yriv0r)(K3ρri2+K4ρri4),
ρli=(xliu0l)2+(yliv0l)2,ρri=(xriu0r)2+(yriv0r)2(i=1,2).
F(X˜)F(X˜0)+FX˜|X˜0Δ0,
V=F(X˜0)+FX˜|X˜0Δ.
B=[F1u0lF1v0lF1fxlF1fylF1u0rF1v0rF1fxrF1fyrF1K1F1K2F1ZmF2u0lF2v0lF2fxlF2fylF2u0rF2v0rF2fxrF2fyrF2K1F2K2F2ZmFcu0lFc1v0lFcfxlFcfylFcu0rFcv0rFcfxrFcfyrFcK1FcK2FcZm],W=[F1F2Fc]T,
Δ=(BTB)1BTW.
X˜k+1=X˜K+Δ.

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