Abstract

Based on analyzing the measurement model of binocular vision sensor, we proposed a new flexible calibration method for binocular vision sensor using a planar target with several parallel lines. It only requires the sensor to observe the planar target at a few (at least two) different orientations. Relying on vanishing feature constraints and spacing constraints of parallel lines, linear method and nonlinear optimization are combined to estimate the structure parameters of binocular vision sensor. Linear method achieves the separation of the rotation matrix and translation vector which reduces the complexity of computation; Nonlinear algorithm ensures the calibration results for the global optimization. Towards the factors that affect the accuracy of the calibration, theoretical analysis and computer simulation are carried out respectively consequence in qualitative analysis and quantitative result. Real data shows that the accuracy of the proposed calibration method is about 0.040mm with the working distance of 800mm and the view field of 300 × 300mm. The comparison with Bougust toolbox and the method based on known length indicates that the proposed calibration method is precise and is efficient and convenient as its simple calculation and easy operation, especially for onsite calibration and self-calibration.

© 2015 Optical Society of America

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References

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  1. G. Zhang, Visual Measurement, 1nd ed. (Beijing Sciences, 2008).
  2. S. Ma and Z. Zhang, Computer Vision: Theory and Algorithms, 1st ed. (Beijing Sciences, 1998).
  3. F. Zhou, J. Zhu, and X. Yang, “A field calibration technique for binocular vision sensor,” Yiqi Yibiao Xuebao 21(2), 142–145 (2000).
  4. G. Zhang and F. Zhou, “The calibration method of stereo visual sensor structural parameters based on standard length,” in Proceedings of CSAA on Aviation Industry Measurement and Control Technology, ed. (Academic, 2001), pp. 259–263.
  5. J. Sun, Z. Wu, Q. Liu, and G. Zhang, “Field calibration of stereo vision sensor with large FOV,” Opt. Precision Eng. 17(3), 633–640 (2009).
  6. F. Zhou, G. Zhang, and Z. Wei, “Calibrating binocular vision sensor with one-dimensional target of unknown motion,” Chin. J. Mech. Ens-EN 42(6), 92–96 (2006).
  7. R. Hartley, “Estimation of relative camera positions for uncalibrated cameras” In Proceedings of. European Conference on Computer Vision, ed. (Academic, 1992) pp. 579–587.
    [Crossref]
  8. M. Li, A. Zhang, and S. Hu, “On 3D measuring system of sheet metal surface based on computer vision,” Chin. Mech. Eng. 13(14), 1177–1180 (2002).
  9. Y. Ma and W. Liu, “A linear self-calibration algorithm based on binocular active vision,” Robot 26(6), 486–490 (2004).
  10. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University, 2003).
  11. J. Bouguet, “Camera calibration toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc/ .
  12. Z. Wei, C. Li, and B. Ding, “Line structured light vision sensor calibration using parallel straight lines features,” Optik (Stuttg.) 125(17), 4990–4997 (2014).
    [Crossref]
  13. Z. Wei, M. Shao, G. Zhang, and Y. Wang, “Parallel-based calibration method for line-structured light vision sensor,” Opt. Eng. 53(3), 033101 (2014).
    [Crossref]
  14. Z. Wei, M. Xie, and G. Zhang, “Calibration method for line structured light vision sensor based on vanish points and lines,” inProcceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp.794–797.
    [Crossref]
  15. Moré J J, “The Levenberg-Marquardt algorithm: implementation and theory,” in Numerical Analysis (Springer Berlin Heidelberg, 1978), pp. 105–116.
  16. M. Lourakis, “Levmar: Levenberg-marquardt nonlinear least squares algorithms in C/C++,” (Ics.forth, 2004), http://www. ics. forth. gr/~lourakis/levmar .
  17. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
    [Crossref]
  18. C. Steger, “Unbiased extraction of curvilinear structures from 2D and 3D image,” Ph.D. Dissertation, Technische Universitaet Muenchen (1998).
  19. P. D. Kovesi, “MATLAB and Octave functions for computer vision and image processing,” http://www. csse. uwa. edu . au/~pk/Research/MatlabFns/# match.
  20. Rodrigues O, “Des lois géométriques qui régissent les déplacements d'un système solide dans l'espace: et de la variation des cordonnées provenant de ces déplacements considérés indépendamment des causes qui peuvent les produire,” (Publisher not identified, 1840).
  21. Y. Fei, Error Theory and Data Processing, 1st ed. (China Machine, 2010).

2014 (2)

Z. Wei, C. Li, and B. Ding, “Line structured light vision sensor calibration using parallel straight lines features,” Optik (Stuttg.) 125(17), 4990–4997 (2014).
[Crossref]

Z. Wei, M. Shao, G. Zhang, and Y. Wang, “Parallel-based calibration method for line-structured light vision sensor,” Opt. Eng. 53(3), 033101 (2014).
[Crossref]

2009 (1)

J. Sun, Z. Wu, Q. Liu, and G. Zhang, “Field calibration of stereo vision sensor with large FOV,” Opt. Precision Eng. 17(3), 633–640 (2009).

2006 (1)

F. Zhou, G. Zhang, and Z. Wei, “Calibrating binocular vision sensor with one-dimensional target of unknown motion,” Chin. J. Mech. Ens-EN 42(6), 92–96 (2006).

2004 (1)

Y. Ma and W. Liu, “A linear self-calibration algorithm based on binocular active vision,” Robot 26(6), 486–490 (2004).

2002 (1)

M. Li, A. Zhang, and S. Hu, “On 3D measuring system of sheet metal surface based on computer vision,” Chin. Mech. Eng. 13(14), 1177–1180 (2002).

2000 (2)

F. Zhou, J. Zhu, and X. Yang, “A field calibration technique for binocular vision sensor,” Yiqi Yibiao Xuebao 21(2), 142–145 (2000).

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

Ding, B.

Z. Wei, C. Li, and B. Ding, “Line structured light vision sensor calibration using parallel straight lines features,” Optik (Stuttg.) 125(17), 4990–4997 (2014).
[Crossref]

Hu, S.

M. Li, A. Zhang, and S. Hu, “On 3D measuring system of sheet metal surface based on computer vision,” Chin. Mech. Eng. 13(14), 1177–1180 (2002).

Li, C.

Z. Wei, C. Li, and B. Ding, “Line structured light vision sensor calibration using parallel straight lines features,” Optik (Stuttg.) 125(17), 4990–4997 (2014).
[Crossref]

Li, M.

M. Li, A. Zhang, and S. Hu, “On 3D measuring system of sheet metal surface based on computer vision,” Chin. Mech. Eng. 13(14), 1177–1180 (2002).

Liu, Q.

J. Sun, Z. Wu, Q. Liu, and G. Zhang, “Field calibration of stereo vision sensor with large FOV,” Opt. Precision Eng. 17(3), 633–640 (2009).

Liu, W.

Y. Ma and W. Liu, “A linear self-calibration algorithm based on binocular active vision,” Robot 26(6), 486–490 (2004).

Ma, Y.

Y. Ma and W. Liu, “A linear self-calibration algorithm based on binocular active vision,” Robot 26(6), 486–490 (2004).

Shao, M.

Z. Wei, M. Shao, G. Zhang, and Y. Wang, “Parallel-based calibration method for line-structured light vision sensor,” Opt. Eng. 53(3), 033101 (2014).
[Crossref]

Sun, J.

J. Sun, Z. Wu, Q. Liu, and G. Zhang, “Field calibration of stereo vision sensor with large FOV,” Opt. Precision Eng. 17(3), 633–640 (2009).

Wang, Y.

Z. Wei, M. Shao, G. Zhang, and Y. Wang, “Parallel-based calibration method for line-structured light vision sensor,” Opt. Eng. 53(3), 033101 (2014).
[Crossref]

Wei, Z.

Z. Wei, M. Shao, G. Zhang, and Y. Wang, “Parallel-based calibration method for line-structured light vision sensor,” Opt. Eng. 53(3), 033101 (2014).
[Crossref]

Z. Wei, C. Li, and B. Ding, “Line structured light vision sensor calibration using parallel straight lines features,” Optik (Stuttg.) 125(17), 4990–4997 (2014).
[Crossref]

F. Zhou, G. Zhang, and Z. Wei, “Calibrating binocular vision sensor with one-dimensional target of unknown motion,” Chin. J. Mech. Ens-EN 42(6), 92–96 (2006).

Z. Wei, M. Xie, and G. Zhang, “Calibration method for line structured light vision sensor based on vanish points and lines,” inProcceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp.794–797.
[Crossref]

Wu, Z.

J. Sun, Z. Wu, Q. Liu, and G. Zhang, “Field calibration of stereo vision sensor with large FOV,” Opt. Precision Eng. 17(3), 633–640 (2009).

Xie, M.

Z. Wei, M. Xie, and G. Zhang, “Calibration method for line structured light vision sensor based on vanish points and lines,” inProcceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp.794–797.
[Crossref]

Yang, X.

F. Zhou, J. Zhu, and X. Yang, “A field calibration technique for binocular vision sensor,” Yiqi Yibiao Xuebao 21(2), 142–145 (2000).

Zhang, A.

M. Li, A. Zhang, and S. Hu, “On 3D measuring system of sheet metal surface based on computer vision,” Chin. Mech. Eng. 13(14), 1177–1180 (2002).

Zhang, G.

Z. Wei, M. Shao, G. Zhang, and Y. Wang, “Parallel-based calibration method for line-structured light vision sensor,” Opt. Eng. 53(3), 033101 (2014).
[Crossref]

J. Sun, Z. Wu, Q. Liu, and G. Zhang, “Field calibration of stereo vision sensor with large FOV,” Opt. Precision Eng. 17(3), 633–640 (2009).

F. Zhou, G. Zhang, and Z. Wei, “Calibrating binocular vision sensor with one-dimensional target of unknown motion,” Chin. J. Mech. Ens-EN 42(6), 92–96 (2006).

Z. Wei, M. Xie, and G. Zhang, “Calibration method for line structured light vision sensor based on vanish points and lines,” inProcceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp.794–797.
[Crossref]

Zhang, Z.

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

Zhou, F.

F. Zhou, G. Zhang, and Z. Wei, “Calibrating binocular vision sensor with one-dimensional target of unknown motion,” Chin. J. Mech. Ens-EN 42(6), 92–96 (2006).

F. Zhou, J. Zhu, and X. Yang, “A field calibration technique for binocular vision sensor,” Yiqi Yibiao Xuebao 21(2), 142–145 (2000).

Zhu, J.

F. Zhou, J. Zhu, and X. Yang, “A field calibration technique for binocular vision sensor,” Yiqi Yibiao Xuebao 21(2), 142–145 (2000).

Chin. J. Mech. Ens-EN (1)

F. Zhou, G. Zhang, and Z. Wei, “Calibrating binocular vision sensor with one-dimensional target of unknown motion,” Chin. J. Mech. Ens-EN 42(6), 92–96 (2006).

Chin. Mech. Eng. (1)

M. Li, A. Zhang, and S. Hu, “On 3D measuring system of sheet metal surface based on computer vision,” Chin. Mech. Eng. 13(14), 1177–1180 (2002).

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

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

Opt. Eng. (1)

Z. Wei, M. Shao, G. Zhang, and Y. Wang, “Parallel-based calibration method for line-structured light vision sensor,” Opt. Eng. 53(3), 033101 (2014).
[Crossref]

Opt. Precision Eng. (1)

J. Sun, Z. Wu, Q. Liu, and G. Zhang, “Field calibration of stereo vision sensor with large FOV,” Opt. Precision Eng. 17(3), 633–640 (2009).

Optik (Stuttg.) (1)

Z. Wei, C. Li, and B. Ding, “Line structured light vision sensor calibration using parallel straight lines features,” Optik (Stuttg.) 125(17), 4990–4997 (2014).
[Crossref]

Robot (1)

Y. Ma and W. Liu, “A linear self-calibration algorithm based on binocular active vision,” Robot 26(6), 486–490 (2004).

Yiqi Yibiao Xuebao (1)

F. Zhou, J. Zhu, and X. Yang, “A field calibration technique for binocular vision sensor,” Yiqi Yibiao Xuebao 21(2), 142–145 (2000).

Other (13)

G. Zhang and F. Zhou, “The calibration method of stereo visual sensor structural parameters based on standard length,” in Proceedings of CSAA on Aviation Industry Measurement and Control Technology, ed. (Academic, 2001), pp. 259–263.

G. Zhang, Visual Measurement, 1nd ed. (Beijing Sciences, 2008).

S. Ma and Z. Zhang, Computer Vision: Theory and Algorithms, 1st ed. (Beijing Sciences, 1998).

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University, 2003).

J. Bouguet, “Camera calibration toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc/ .

R. Hartley, “Estimation of relative camera positions for uncalibrated cameras” In Proceedings of. European Conference on Computer Vision, ed. (Academic, 1992) pp. 579–587.
[Crossref]

Z. Wei, M. Xie, and G. Zhang, “Calibration method for line structured light vision sensor based on vanish points and lines,” inProcceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp.794–797.
[Crossref]

Moré J J, “The Levenberg-Marquardt algorithm: implementation and theory,” in Numerical Analysis (Springer Berlin Heidelberg, 1978), pp. 105–116.

M. Lourakis, “Levmar: Levenberg-marquardt nonlinear least squares algorithms in C/C++,” (Ics.forth, 2004), http://www. ics. forth. gr/~lourakis/levmar .

C. Steger, “Unbiased extraction of curvilinear structures from 2D and 3D image,” Ph.D. Dissertation, Technische Universitaet Muenchen (1998).

P. D. Kovesi, “MATLAB and Octave functions for computer vision and image processing,” http://www. csse. uwa. edu . au/~pk/Research/MatlabFns/# match.

Rodrigues O, “Des lois géométriques qui régissent les déplacements d'un système solide dans l'espace: et de la variation des cordonnées provenant de ces déplacements considérés indépendamment des causes qui peuvent les produire,” (Publisher not identified, 1840).

Y. Fei, Error Theory and Data Processing, 1st ed. (China Machine, 2010).

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Figures (18)

Fig. 1
Fig. 1 Measurement model of BVS.
Fig. 2
Fig. 2 Calibration model of BVS.
Fig. 3
Fig. 3 Vanishing line formation.
Fig. 4
Fig. 4 Back-projection of lines.
Fig. 5
Fig. 5 The diagram of target images.
Fig. 6
Fig. 6 The target plane П t vs. planes S 1 , S 2 , S 3 , S 4 .
Fig. 7
Fig. 7 The position of the planar target.
Fig. 8
Fig. 8 Relative standard deviation vs. the noise level when N=3 and D = 15mm, 20mm, 25mm, 30mm.
Fig. 9
Fig. 9 Relative standard deviation vs. the noise level when N=5 and D = 15mm, 20mm, 25mm, 30mm.
Fig. 10
Fig. 10 Relative standard deviation vs. the noise level when N=7 and D = 15mm, 20mm, 25mm, 30mm.
Fig. 11
Fig. 11 Relative standard deviation vs. the space of parallel lines when σ=0.2 and N = 3, 5, 7.
Fig. 12
Fig. 12 Relative standard deviation vs. the angle of the target plane w.r.t. the image plane.
Fig. 13
Fig. 13 The physical system.
Fig. 14
Fig. 14 A sample of image pairs used for calibration: (a) left image; (b) right image.
Fig. 15
Fig. 15 (a) Target images; (b) Extracted lines.
Fig. 16
Fig. 16 Known length for calibrating structure parameters.
Fig. 17
Fig. 17 The reconstruction of all feature points of testing data using our proposed calibration method.
Fig. 18
Fig. 18 Determining a plane’s vanishing line from imaged equally spaced parallel lines.

Tables (4)

Tables Icon

Table 1 Intrinsic parameters of cameras

Tables Icon

Table 2 Calibration results of cameras’ intrinsic parameters

Tables Icon

Table 3 Comparative result of the structure parameters

Tables Icon

Table 4 Measurement results of chessboard corners

Equations (31)

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

s l m l = A l [ I 0 ]M= P l M,
s r m r = A r [ R T ]M= P r M.
[ u l p 31 l p 11 l v l p 31 l p 21 l u r p 31 r p 11 r v r p 31 r p 21 r u l p 32 l p 12 l v l p 32 l p 22 l u r p 32 r p 12 r v r p 32 r p 22 r u l p 33 l p 13 l v l p 33 l p 23 l u r p 33 r p 13 r v r p 33 r p 23 r ][ X Y Z ]=[ p 14 l u l p 34 l p 24 l v l p 34 l p 14 r u r p 34 r p 24 r v r p 34 r ].
n= A T l,
π l = P l T l l , π r = P r T l r ,
L * = π l π r T π r π l T ,
n l = A l T l l / A l T l l , n r = A r T l r / A r T l r .
n r =R n l .
π li = P l T l i , π ri = P r T r i .
L i * = π li π ri T π ri π li T =[ ( A l T l i r i T A r R R T A r T r i l i T A l ) 3×3 ( A l T l i r i T A r T) 3×1 ( T T A r T r i l i T A l ) 1×3 0 ].
L i * v=0.
{ L i П t =0 L i S i =0
{ n i × B i T d i a i =0 n t × B i Tk a i =0
minF(R,T)= ρ 1 i=1 n j=1 m1 | D d j ( x j+1 i , x j i ) |+ ρ 2 i=1 n | n r i R n l i | ,
( b 0 b n )α( a 0 a n )β= a n b 0 a 0 b n .
α a 0 = b n β b 0 b n , α b 0 = a n α b 0 b n , α a n = b 0 β b 0 b n , α b n = a 0 α b 0 b n ,
β a 0 = b n β a 0 a n , β b 0 = a n α a 0 a n , β a n = b 0 β a 0 a n , β b n = a 0 α a 0 a n .
Δα= β b n b 0 b n Δ a 0 + a n α b 0 b n Δ b 0 + b 0 β b 0 b n Δ a n + α a 0 b 0 b n Δ b n ,
Δβ= b n β a 0 a n Δ a 0 + α a n a 0 a n Δ b 0 + β b 0 a 0 a n Δ a n + a 0 α a 0 a n Δ b n .
s[ u p v p 1 ]=A[ R w c T w c ][ x w y w z w 1 ],
sp=H M ˜ ,
H=A[ r w c1 r w c2 T w c ]=[ f x 0 u 0 0 f y v 0 0 0 1 ][ cosθ 0 0 0 1 0 sinθ 0 t z ],
H T =[ 1 f x cosθ 0 sinθ t z f x cosθ 0 1 f y 0 u 0 f x cosθ v 0 f y u 0 sinθ t z f x cosθ + 1 t z ].
l= H T l ' .
l 0 = H T l 0 ' = b f y [ a f y b f x cosθ 1 a u 0 f y b f x cosθ + v 0 ],
l n = H T l n ' = b f y [ a f y b f x cosθ + nD f y sinθ b t z f x cosθ 1 nD b t z ( u 0 f y sinθ f x cosθ + f y )+ a u 0 f y b f x cosθ + v 0 ].
b 0 b n = nD b t z ( u 0 f y f x tanθ+ f y ),( 0 ° <θ< 90 ° ),
a 0 a n = nD f y b t z f x tanθ,( 0 ° <θ< 90 ° ).
l n = l 0 +nl ρ n ( a n 1 b n )= ρ 0 ( a 0 1 b 0 )+n( α 1 β ),
[ n 0 a 0 a n 0 n b 0 b n ][ α β ρ 0 ]=n[ a n b n ].
[ 1 0 a 0 a 1 0 1 b 0 b 1 2 0 a 0 a 2 0 2 b 0 b 2 n 0 a 0 a n 0 n b 0 b n ][ α β ρ 0 ]=[ a 1 b 1 2 a 2 2 b 2 n a n n b n ].

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