Abstract

High-precision calibration of binocular vision systems plays an important role in accurate dimensional measurements. In this paper, an improved camera calibration method is proposed. First, an accurate intrinsic parameters calibration method based on active vision with perpendicularity compensation is developed. Compared to the previous work, this method eliminates the effect of non-perpendicularity of the camera motion on calibration accuracy. The principal point, scale factors, and distortion factors are calculated independently in this method, thereby allowing the strong coupling of these parameters to be eliminated. Second, an accurate global optimization method with only 5 images is presented. The results of calibration experiments show that the accuracy of the calibration method can reach 99.91%.

© 2015 Optical Society of America

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References

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  1. C. Ricolfe-Viala and A.-J. Sanchez-Salmeron, “Camera calibration under optimal conditions,” Opt. Express 19(11), 10769–10775 (2011).
    [Crossref] [PubMed]
  2. R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3d machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE Trans. Robot. Autom. 3(4), 323–344 (1987).
    [Crossref]
  3. Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE T. Pattern Anal. 22(11), 1330–1334 (2000).
    [Crossref]
  4. Z. Zhang, “Flexible camera calibration by viewing a plane from unknown orientations,” in Proceedings of the Seventh IEEE International Conference on Computer Vision (IEEE, 1999), pp. 666–673.
    [Crossref]
  5. E. Kruppa, Zur Ermittlung eines Objektes aus zwei Perspektiven mit innerer Orientierung (Hölder, 1913).
  6. R. I. Hartley, “Euclidean reconstruction from uncalibrated views,” in Applications of Invariance in Computer Vision (Springer, 1994), pp. 235–256.
  7. S. J. Maybank and O. D. Faugeras, “A theory of self-calibration of a moving camera,” Int. J. Comput. Vis. 8(2), 123–151 (1992).
    [Crossref]
  8. Q. T. Luong and O. Faugeras, “Self-calibration of a camera using multiple images,” in Proceedings of the 11th IAPR International Conference on Pattern Recognition, Vol. I, Conference A: Computer Vision and Applications (IEEE, 1992), pp. 9–12.
    [Crossref]
  9. O. D. Faugeras, Q. T. Luong, and S. J. Maybank, “Camera self-calibration: Theory and experiments,” in Computer Vision ECCV'92 (Springer, 1992), pp. 321–334.
  10. O. D. Faugeras, “What can be seen in three dimensions with an uncalibrated stereo rig?” in Computer Vision ECCV'92 (Springer, 1992), pp. 563–578.
  11. Q. T. Luong and O. D. Faugeras, “The fundamental matrix: Theory, algorithms, and stability analysis,” Int. J. Comput. Vis. 17(1), 43–75 (1996).
    [Crossref]
  12. T. Svoboda, D. Martinec, and T. Pajdla, “A convenient multicamera self-calibration for virtual environments,” Presence-Teleop, Virt. 14(4), 407–422 (2005).
  13. M. Hödlmoser and M. Kampel, “Multiple camera self-calibration and 3D reconstruction using pedestrians,” in Advances in Visual Computing (Springer, 2010), pp. 1–10.
  14. F. Yılmaztürk, “Full-automatic self-calibration of color digital cameras using color targets,” Opt. Express 19(19), 18164–18174 (2011).
    [Crossref] [PubMed]
  15. R. I. Hartley, “Self-calibration of stationary cameras,” Int. J. Comput. Vis. 22(1), 5–23 (1997).
    [Crossref]
  16. F. Du and M. Brady, “Self-calibration of the intrinsic parameters of cameras for active vision systems,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1993), pp. 477–482.
    [Crossref]
  17. S. D. Ma, “A self-calibration technique for active vision systems,” IEEE Trans. Robot. Autom. 12(1), 114–120 (1996).
    [Crossref]
  18. A. Gruen, “Calibration and orientation of cameras in computer vision,” Meas. Sci. Technol. 13(2), 231 (2002).
    [Crossref]
  19. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University Press, 2003).

2011 (2)

2005 (1)

T. Svoboda, D. Martinec, and T. Pajdla, “A convenient multicamera self-calibration for virtual environments,” Presence-Teleop, Virt. 14(4), 407–422 (2005).

2002 (1)

A. Gruen, “Calibration and orientation of cameras in computer vision,” Meas. Sci. Technol. 13(2), 231 (2002).
[Crossref]

2000 (1)

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

1997 (1)

R. I. Hartley, “Self-calibration of stationary cameras,” Int. J. Comput. Vis. 22(1), 5–23 (1997).
[Crossref]

1996 (2)

S. D. Ma, “A self-calibration technique for active vision systems,” IEEE Trans. Robot. Autom. 12(1), 114–120 (1996).
[Crossref]

Q. T. Luong and O. D. Faugeras, “The fundamental matrix: Theory, algorithms, and stability analysis,” Int. J. Comput. Vis. 17(1), 43–75 (1996).
[Crossref]

1992 (1)

S. J. Maybank and O. D. Faugeras, “A theory of self-calibration of a moving camera,” Int. J. Comput. Vis. 8(2), 123–151 (1992).
[Crossref]

1987 (1)

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

Brady, M.

F. Du and M. Brady, “Self-calibration of the intrinsic parameters of cameras for active vision systems,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1993), pp. 477–482.
[Crossref]

Du, F.

F. Du and M. Brady, “Self-calibration of the intrinsic parameters of cameras for active vision systems,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1993), pp. 477–482.
[Crossref]

Faugeras, O. D.

Q. T. Luong and O. D. Faugeras, “The fundamental matrix: Theory, algorithms, and stability analysis,” Int. J. Comput. Vis. 17(1), 43–75 (1996).
[Crossref]

S. J. Maybank and O. D. Faugeras, “A theory of self-calibration of a moving camera,” Int. J. Comput. Vis. 8(2), 123–151 (1992).
[Crossref]

Gruen, A.

A. Gruen, “Calibration and orientation of cameras in computer vision,” Meas. Sci. Technol. 13(2), 231 (2002).
[Crossref]

Hartley, R. I.

R. I. Hartley, “Self-calibration of stationary cameras,” Int. J. Comput. Vis. 22(1), 5–23 (1997).
[Crossref]

Luong, Q. T.

Q. T. Luong and O. D. Faugeras, “The fundamental matrix: Theory, algorithms, and stability analysis,” Int. J. Comput. Vis. 17(1), 43–75 (1996).
[Crossref]

Ma, S. D.

S. D. Ma, “A self-calibration technique for active vision systems,” IEEE Trans. Robot. Autom. 12(1), 114–120 (1996).
[Crossref]

Martinec, D.

T. Svoboda, D. Martinec, and T. Pajdla, “A convenient multicamera self-calibration for virtual environments,” Presence-Teleop, Virt. 14(4), 407–422 (2005).

Maybank, S. J.

S. J. Maybank and O. D. Faugeras, “A theory of self-calibration of a moving camera,” Int. J. Comput. Vis. 8(2), 123–151 (1992).
[Crossref]

Pajdla, T.

T. Svoboda, D. Martinec, and T. Pajdla, “A convenient multicamera self-calibration for virtual environments,” Presence-Teleop, Virt. 14(4), 407–422 (2005).

Ricolfe-Viala, C.

Sanchez-Salmeron, A.-J.

Svoboda, T.

T. Svoboda, D. Martinec, and T. Pajdla, “A convenient multicamera self-calibration for virtual environments,” Presence-Teleop, Virt. 14(4), 407–422 (2005).

Tsai, R. Y.

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

Yilmaztürk, F.

Zhang, Z.

Z. Zhang, “Flexible camera calibration by viewing a plane from unknown orientations,” in Proceedings of the Seventh IEEE International Conference on Computer Vision (IEEE, 1999), pp. 666–673.
[Crossref]

Zhang, Z. Y.

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

IEEE T. Pattern Anal. (1)

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

IEEE Trans. Robot. Autom. (2)

S. D. Ma, “A self-calibration technique for active vision systems,” IEEE Trans. Robot. Autom. 12(1), 114–120 (1996).
[Crossref]

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

Int. J. Comput. Vis. (3)

Q. T. Luong and O. D. Faugeras, “The fundamental matrix: Theory, algorithms, and stability analysis,” Int. J. Comput. Vis. 17(1), 43–75 (1996).
[Crossref]

R. I. Hartley, “Self-calibration of stationary cameras,” Int. J. Comput. Vis. 22(1), 5–23 (1997).
[Crossref]

S. J. Maybank and O. D. Faugeras, “A theory of self-calibration of a moving camera,” Int. J. Comput. Vis. 8(2), 123–151 (1992).
[Crossref]

Meas. Sci. Technol. (1)

A. Gruen, “Calibration and orientation of cameras in computer vision,” Meas. Sci. Technol. 13(2), 231 (2002).
[Crossref]

Opt. Express (2)

Presence-Teleop, Virt. (1)

T. Svoboda, D. Martinec, and T. Pajdla, “A convenient multicamera self-calibration for virtual environments,” Presence-Teleop, Virt. 14(4), 407–422 (2005).

Other (9)

M. Hödlmoser and M. Kampel, “Multiple camera self-calibration and 3D reconstruction using pedestrians,” in Advances in Visual Computing (Springer, 2010), pp. 1–10.

F. Du and M. Brady, “Self-calibration of the intrinsic parameters of cameras for active vision systems,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1993), pp. 477–482.
[Crossref]

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

Q. T. Luong and O. Faugeras, “Self-calibration of a camera using multiple images,” in Proceedings of the 11th IAPR International Conference on Pattern Recognition, Vol. I, Conference A: Computer Vision and Applications (IEEE, 1992), pp. 9–12.
[Crossref]

O. D. Faugeras, Q. T. Luong, and S. J. Maybank, “Camera self-calibration: Theory and experiments,” in Computer Vision ECCV'92 (Springer, 1992), pp. 321–334.

O. D. Faugeras, “What can be seen in three dimensions with an uncalibrated stereo rig?” in Computer Vision ECCV'92 (Springer, 1992), pp. 563–578.

Z. Zhang, “Flexible camera calibration by viewing a plane from unknown orientations,” in Proceedings of the Seventh IEEE International Conference on Computer Vision (IEEE, 1999), pp. 666–673.
[Crossref]

E. Kruppa, Zur Ermittlung eines Objektes aus zwei Perspektiven mit innerer Orientierung (Hölder, 1913).

R. I. Hartley, “Euclidean reconstruction from uncalibrated views,” in Applications of Invariance in Computer Vision (Springer, 1994), pp. 235–256.

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Figures (17)

Fig. 1
Fig. 1 Camera model. (OCXCYCZC and OWXWYWZW indicate the camera coordinate system and the world coordinate system, respectively).
Fig. 2
Fig. 2 Principle diagram of the active vision calibration method based on perpendicular linear motions.
Fig. 3
Fig. 3 Simulation of the effect of the perpendicularity of the linear guides on the calibration results. (Ii represents the image plane of the camera).
Fig. 4
Fig. 4 The estimation errors of (a) focal length fx, (b) focal length fy, (c) principle point u0, and (d) principle point v0.
Fig. 5
Fig. 5 The reconstruction errors under different perpendicularities.
Fig. 6
Fig. 6 Experimental system and the reconstruction target.
Fig. 7
Fig. 7 The reconstruction error under different perpendicularities in the experiment.
Fig. 8
Fig. 8 Euler transformation relationship between different coordinate systems.
Fig. 9
Fig. 9 The experimental system used for calibration.
Fig. 10
Fig. 10 Perpendicularity measurement experiment. The straightness measurement system of (a) the X axis and (b) the Y axis.
Fig. 11
Fig. 11 Calibration experiments of intrinsic parameters.
Fig. 12
Fig. 12 Camera motions in intrinsic parameters calibration process.
Fig. 13
Fig. 13 Calibration experiments of the global optimization.
Fig. 14
Fig. 14 Images of the global optimization experiment. (a)–(e) show five arbitrary positions of the calibration target during the global optimization.
Fig. 15
Fig. 15 Accuracy verification experiment of the calibration method.
Fig. 16
Fig. 16 The accuracy of the proposed calibration method.
Fig. 17
Fig. 17 The accuracy of different calibration methods.

Tables (6)

Tables Icon

Table 1 The motions and postures of the intrinsic parameters calibration

Tables Icon

Table 2 Calibration results of principal point and scale factors with perpendicularity compensation.

Tables Icon

Table 3 Calibration results of principal point and scale factors without perpendicularity compensation.

Tables Icon

Table 4 Calibration results of the global optimization.

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Table 5 The reconstruction relative error of different groups of reconstruction distances.

Tables Icon

Table 6 Calibration result of the global optimization without perpendicular compensation.

Equations (19)

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

[ u v 1 ]= [ f x 0 0 0 f y 0 u 0 v 0 1 0 0 0 ] K [ R t 0 T 1 ] [R | t] [ X W Y W Z W 1 ]=K[R|t][ X W Y W Z W 1 ]=M[ X W Y W Z W 1 ],
K=[ f x 0 u 0 0 f y v 0 0 0 1 ].
( m j1 - u 0 )( m j2 - u 0 )/ f x 2 +( n j1 - v 0 )( n j2 - v 0 )/ f y 2 +1=0,j=1,2,3,4,
u 0 ( y 1 y 2 )+ v 0 ( x 2 x 1 )= x 2 y 1 x 1 y 2 ,
M P p T =N M=[ y 1 y 2 x 1 x 2 y 2 y 3 x 2 x 3 ], P p =[ u 0 v 0 ] N=[ x 2 y 1 x 1 y 2 x 3 y 2 x 2 y 3 ]
( A j 2 C j 2 sin 2 θ) x 2 +( B j 2 D j 2 sin 2 θ) y 2 +(2 A j B j C j D j - A j 2 D j 2 cos 2 θ- B j 2 C j 2 cos 2 θ)xy+, (2 A j C j - A j 2 cos 2 θ- C j 2 cos 2 θ)x+(2 B j D j - B j 2 cos 2 θ- D j 2 cos 2 θ)y+ sin 2 θ=0
P i = R 0 P i + t 0 .
f( R 0 , t 0 )= i=1 n R 0 P i + t 0 - P i .
{ P ¯ = 1 n i=1 n P i P ¯ = 1 n i=1 n P i .
{ P ˜ i = P i P ¯ , P ˜ i = P i P ¯
P ˜ i = R 0 P ˜ i .
f( R 0 )= i=1 n R 0 P ˜ i - P ˜ i .
t 0 = P ¯ i R 0 P ¯ i .
R= R R R 1 ,
t= t R R t l .
{ u ˜ i = ( f x r 11 + u 0 r 31 ) X iW +( f x r 12 + u 0 r 32 ) Y iW +( f x r 13 + u 0 r 33 ) Z iW + f x t 1 + u 0 t 3 r 31 X iW + r 32 Y iW + r 33 Z iW + t 3 v ˜ i = ( f y r 21 + v 0 r 31 ) X iW +( f y r 22 + v 0 r 32 ) Y iW +( f y r 23 + v 0 r 33 ) Z iW + f y t 2 + v 0 t 3 r 31 X iW + r 32 Y iW + r 33 Z iW + t 3
[ u ^ i v ^ i ]=(1+ k 1 r 2 + k 2 r 4 )[ u ˜ i v ˜ i ],
f(k, K L , K R ,R,t)= i=1 m ( ( u i - u ^ i ) 2 + ( v i - v ^ i ) 2 ) ,
F(k, K L , K R ,R,t)= min k, K L , K R ,R,t j=1 n f(k, K L , K R ,R,t) .

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