Abstract

Different methods based on photogrammetry or self-calibration exist to calibrate intrinsic and extrinsic camera parameters and also for data pre- and post-processing. From a practical viewpoint, it is quite difficult to decide which calibration method gives accurate results and even whether any data processing is necessary. This paper proposes a set of optimal conditions to resolve the calibration process accurately. The calibration method uses several images of a 2D pattern. Optimal conditions define the number of points and the number of images to resolve the calibration accurately, as well as positions and orientations from where images should be taken.

© 2011 OSA

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. D. Huynh, R. Hartley, and A. Heyden, “Outlier correction in image sequences for the affine camera,” in Proceedings of 9th IEEE International Conference on Computer Vision 1, (2003) 585–591.
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    [CrossRef]
  11. R. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-self TV camera lenses,” IEEE J. Robot. Autom. RA-3, 323–344 (1997).
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    [CrossRef]
  13. W. Sun and J. Cooperstock, “An empirical evaluation of factors influencing camera calibration accuracy using three publicly available techniques,” Mach. Vis. Appl. 17(1), 51–67 (2006).
    [CrossRef]

2008 (1)

2007 (1)

2006 (2)

W. Sun and J. Cooperstock, “An empirical evaluation of factors influencing camera calibration accuracy using three publicly available techniques,” Mach. Vis. Appl. 17(1), 51–67 (2006).
[CrossRef]

K. S. Choi, E. Y. Lam, and K. K. Y. Wong, “Automatic source camera identification using the intrinsic lens radial distortion,” Opt. Express 14(24), 11551–11565 (2006).
[CrossRef] [PubMed]

2002 (1)

J. Salvi, X. Armangué, and J. Batlle, “A Comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recognit. 35(7), 1617–1635 (2002).
[CrossRef]

2001 (1)

S. Kopparapu and P. Corke, “The effect of noise on camera calibration parameters,” Graph. Models 63(5), 277–303 (2001).
[CrossRef]

2000 (1)

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

1997 (2)

R. Hartley, “In defence of the eight point algorithm,” IEEE Trans. Pattern Anal. Mach. Intell. 19(6), 580–593 (1997).
[CrossRef]

R. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-self TV camera lenses,” IEEE J. Robot. Autom. RA-3, 323–344 (1997).

1992 (1)

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

Armangué, X.

J. Salvi, X. Armangué, and J. Batlle, “A Comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recognit. 35(7), 1617–1635 (2002).
[CrossRef]

Batlle, J.

J. Salvi, X. Armangué, and J. Batlle, “A Comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recognit. 35(7), 1617–1635 (2002).
[CrossRef]

Bauer, M.

Choi, K. S.

Cohen, P.

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

Cooperstock, J.

W. Sun and J. Cooperstock, “An empirical evaluation of factors influencing camera calibration accuracy using three publicly available techniques,” Mach. Vis. Appl. 17(1), 51–67 (2006).
[CrossRef]

Corke, P.

S. Kopparapu and P. Corke, “The effect of noise on camera calibration parameters,” Graph. Models 63(5), 277–303 (2001).
[CrossRef]

Grießbach, D.

Hartley, R.

R. Hartley, “In defence of the eight point algorithm,” IEEE Trans. Pattern Anal. Mach. Intell. 19(6), 580–593 (1997).
[CrossRef]

Hermerschmidt, A.

Herniou, M.

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

Kopparapu, S.

S. Kopparapu and P. Corke, “The effect of noise on camera calibration parameters,” Graph. Models 63(5), 277–303 (2001).
[CrossRef]

Krüger, S.

Lam, E. Y.

Lin, P. D.

Salvi, J.

J. Salvi, X. Armangué, and J. Batlle, “A Comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recognit. 35(7), 1617–1635 (2002).
[CrossRef]

Scheele, M.

Schischmanow, A.

Sun, W.

W. Sun and J. Cooperstock, “An empirical evaluation of factors influencing camera calibration accuracy using three publicly available techniques,” Mach. Vis. Appl. 17(1), 51–67 (2006).
[CrossRef]

Sung, C. K.

Tsai, R.

R. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-self TV camera lenses,” IEEE J. Robot. Autom. RA-3, 323–344 (1997).

Weng, J.

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

Wong, K. K. Y.

Zhang, Z.

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

Graph. Models (1)

S. Kopparapu and P. Corke, “The effect of noise on camera calibration parameters,” Graph. Models 63(5), 277–303 (2001).
[CrossRef]

IEEE J. Robot. Autom. (1)

R. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-self TV camera lenses,” IEEE J. Robot. Autom. RA-3, 323–344 (1997).

IEEE Trans. Pattern Anal. Mach. Intell. (3)

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

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

R. Hartley, “In defence of the eight point algorithm,” IEEE Trans. Pattern Anal. Mach. Intell. 19(6), 580–593 (1997).
[CrossRef]

Mach. Vis. Appl. (1)

W. Sun and J. Cooperstock, “An empirical evaluation of factors influencing camera calibration accuracy using three publicly available techniques,” Mach. Vis. Appl. 17(1), 51–67 (2006).
[CrossRef]

Opt. Express (3)

Pattern Recognit. (1)

J. Salvi, X. Armangué, and J. Batlle, “A Comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recognit. 35(7), 1617–1635 (2002).
[CrossRef]

Other (3)

J. Lavest, M. Viala, and M. Dhome, “Do we really need accurate calibration pattern to achieve a reliable camera calibration,” in Proceedings of European Conference on Computer Vision 1, (1998) 158–174.

D. Huynh, R. Hartley, and A. Heyden, “Outlier correction in image sequences for the affine camera,” in Proceedings of 9th IEEE International Conference on Computer Vision 1, (2003) 585–591.

G. Stewart, “Perturbation theory for the singular value,” University of Maryland, (Tech. Report TR90 −124, 1990).

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Figures (3)

Fig. 1
Fig. 1

(left) Scene and camera coordinate systems. Orientation is computed starting with camera location. Optical axis goes through origin of coordinates in the scene (middle) First rotation angle (right) second rotation angle. Xc remains parallel to the X-Y plane of the scene.

Fig. 2
Fig. 2

Optimal positions for taking images of the planar template. Camera is moved along X or Y scene coordinates axis system and its altitude in the Z axis is defined with the expression (17).

Fig. 3
Fig. 3

Comparison of intrinsic camera parameters calibration errors under optimal and non- optimal calibration process conditions changing the number of points.

Equations (13)

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[ v 11 T v 22 T v 12 T ] b = 0
v i j T = [ h i 1 h j 1 h i 1 h j 2 + h i 2 h j 1 h i 2 h j 2 h i 3 h j 1 + h i 1 h j 3 h i 3 h j 2 + h i 2 h j 3 h i 3 h j 3 ]
cos β = t y m 1 sin β = t x m 1 cos α = | t z | m 2 sin α = m 1 m 2 m 1 = t x 2 + t y 2 m 2 = t x 2 + t y 2 + t z 2
( v l 11 T v l 22 T ) · v l 12 = 0
( v l 11 T v l 22 T ) · ( v l 11 v l 22 ) v l 12 T · v l 12 = 0
( v 1 11 T v 1 22 T ) · v 1 12 = 0
( v 1 11 T v 1 22 T ) · ( v 1 11 v 1 22 ) ( v 1 12 T · v 1 12 ) = 0
( v 2 11 T v 2 22 T ) · v 2 12 = 0
( v 2 11 T v 2 22 T ) · ( v 2 11 v 2 22 ) ( v 2 12 T · v 2 12 ) = 0
( v 1 11 T v 1 22 T ) · v 2 12 = 0
( v 1 11 T v 1 22 T ) · ( v 2 11 v 2 22 ) = 0
v 1 12 T · ( v 2 11 T v 2 22 T ) = 0
t 1 z = ± 2 · t 1 x 2 ( 1 2 · t 1 x 2 2 · t 1 x 4 + ( 3 4 · t 1 x 2 + 12 · t 1 x 4 ) ) 1 + 3 · t 1 x 2 + t 1 x 4 t 1 z = ± 2 · t 1 y 2 ( 1 2 · t 1 y 2 2 · t 1 y 4 + ( 3 4 · t 1 y 2 + 12 · t 1 y 4 ) ) 1 + 3 · t 1 y 2 + t 1 y 4

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