Abstract

Camera calibration is a critical step in many vision applications. It is a delicate and complex process that is highly sensitive to environmental conditions. This paper presents a novel virtual calibration technique that can be used to study the impact of various factors on the calibration parameters. To highlight the possibilities of the method, the calibration parameters’ behavior has been studied regarding the effects of tolerancing and temperature for a specific lens. This technique could also be used in many other promising areas to make calibration in the laboratory or in the field easier.

© 2014 Optical Society of America

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References

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  1. E. Adelson and J. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
    [CrossRef]
  2. Z. Kiraly, G. Springer, and J. Van Dam, “Stereoscopic vision system,” Opt. Eng. 45, 043006 (2006).
    [CrossRef]
  3. A. Ude, C. Gaskett, and G. Cheng, “Foveated vision systems with two cameras per eye,” in Proceedings of IEEE International Conference on Robotics and Automation (Institute of Electrical and Electronics Engineers, 2006), pp. 3457–3462.
  4. T. Nishimoto and J. Yamaguchi, “Three dimensional measurement using fisheye stereo vision,” in Proceedings of 46th SICE Annual Conference (Institute of Electrical and Electronics Engineers, 2007), pp. 2008–2012.
  5. Y. Caulier, “Inspection of complex surfaces by means of structured light patterns,” Opt. Express 18, 6642–6660 (2010).
    [CrossRef]
  6. D. Fiedler and H. Müller, “Impact of thermal and environmental conditions on the kinect sensor,” in Proceedings of International Workshop of Advances in Depth Image Analysis and Applications, Lecture Notes on Computer Vision (SpringerLink, 2012), Vol. 7854, pp. 21–31.
  7. M. J. Smith and E. Cope, “The effects of temperature variation on single-lens-reflex digital camera calibration parameters,” in International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, Commission V Symposium (International Society for Photogrammetry and Remote Sensing, 2010), Vol. XXXVIII, Part 5, pp. 554–559.
  8. M. Laikin, Lens Design, 4th ed. (CRC Press, 2006).
  9. Zebase 6 Optical Design Database (ZEMAX Development Corporation, 2007).
  10. D. Scaramuzza, “OCamCalib: omnidirectional camera calibration toolbox for MATLAB,” https://sites.google.com/site/scarabotix/ocamcalib-toolbox .
  11. D. Scaramuzza, A. Martinelli, and R. Siegwart, “A flexible technique for accurate omnidirectional camera calibration and structure from motion,” in Proceedings of IEEE International Conference of Vision Systems (Institute of Electrical and Electronics Engineers, 2006), pp. 45–52.
  12. D. Scaramuzza, A. Martinelli, and R. Siegwart, “A toolbox for easy calibrating omnidirectional cameras,” in Proceedings to IEEE International Conference on Intelligent Robots and Systems (Institute of Electrical and Electronics Engineers, 2006), pp. 5695–5701.
  13. J. Parent and S. Thibault, “Tolerancing panoramic lenses,” Proc. SPIE 7433, 74330D (2009).
    [CrossRef]
  14. D. Scaramuzza, Omnidirectional Vision: From Calibration to Robot Motion Estimation, (ETH Zurich, 2008).
  15. J.-Y. Bouguet, “Camera calibration toolbox for MATLAB,” http://www.vision.caltech.edu/bouguetj/calib_doc/index.html .
  16. Z. Zhang, “Flexible calibration by viewing a plane from unknown orientations,” in Proceedings of 7th IEEE International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, 1999), pp. 666–673.
  17. “Thermal analysis,” in ZEMAX User’s Manual, (ZEMAX Development Corporation, 2013), pp. 667–672.
  18. Optimax Systems, Inc., “Manufacturing tolerance chart,” http://www.optimaxsi.com/innovation/optical-manufacturing-tolerance-chart/ .

2010

2009

J. Parent and S. Thibault, “Tolerancing panoramic lenses,” Proc. SPIE 7433, 74330D (2009).
[CrossRef]

2006

Z. Kiraly, G. Springer, and J. Van Dam, “Stereoscopic vision system,” Opt. Eng. 45, 043006 (2006).
[CrossRef]

1992

E. Adelson and J. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
[CrossRef]

Adelson, E.

E. Adelson and J. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
[CrossRef]

Caulier, Y.

Cheng, G.

A. Ude, C. Gaskett, and G. Cheng, “Foveated vision systems with two cameras per eye,” in Proceedings of IEEE International Conference on Robotics and Automation (Institute of Electrical and Electronics Engineers, 2006), pp. 3457–3462.

Cope, E.

M. J. Smith and E. Cope, “The effects of temperature variation on single-lens-reflex digital camera calibration parameters,” in International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, Commission V Symposium (International Society for Photogrammetry and Remote Sensing, 2010), Vol. XXXVIII, Part 5, pp. 554–559.

Fiedler, D.

D. Fiedler and H. Müller, “Impact of thermal and environmental conditions on the kinect sensor,” in Proceedings of International Workshop of Advances in Depth Image Analysis and Applications, Lecture Notes on Computer Vision (SpringerLink, 2012), Vol. 7854, pp. 21–31.

Gaskett, C.

A. Ude, C. Gaskett, and G. Cheng, “Foveated vision systems with two cameras per eye,” in Proceedings of IEEE International Conference on Robotics and Automation (Institute of Electrical and Electronics Engineers, 2006), pp. 3457–3462.

Kiraly, Z.

Z. Kiraly, G. Springer, and J. Van Dam, “Stereoscopic vision system,” Opt. Eng. 45, 043006 (2006).
[CrossRef]

Laikin, M.

M. Laikin, Lens Design, 4th ed. (CRC Press, 2006).

Martinelli, A.

D. Scaramuzza, A. Martinelli, and R. Siegwart, “A flexible technique for accurate omnidirectional camera calibration and structure from motion,” in Proceedings of IEEE International Conference of Vision Systems (Institute of Electrical and Electronics Engineers, 2006), pp. 45–52.

D. Scaramuzza, A. Martinelli, and R. Siegwart, “A toolbox for easy calibrating omnidirectional cameras,” in Proceedings to IEEE International Conference on Intelligent Robots and Systems (Institute of Electrical and Electronics Engineers, 2006), pp. 5695–5701.

Müller, H.

D. Fiedler and H. Müller, “Impact of thermal and environmental conditions on the kinect sensor,” in Proceedings of International Workshop of Advances in Depth Image Analysis and Applications, Lecture Notes on Computer Vision (SpringerLink, 2012), Vol. 7854, pp. 21–31.

Nishimoto, T.

T. Nishimoto and J. Yamaguchi, “Three dimensional measurement using fisheye stereo vision,” in Proceedings of 46th SICE Annual Conference (Institute of Electrical and Electronics Engineers, 2007), pp. 2008–2012.

Parent, J.

J. Parent and S. Thibault, “Tolerancing panoramic lenses,” Proc. SPIE 7433, 74330D (2009).
[CrossRef]

Scaramuzza, D.

D. Scaramuzza, Omnidirectional Vision: From Calibration to Robot Motion Estimation, (ETH Zurich, 2008).

D. Scaramuzza, A. Martinelli, and R. Siegwart, “A toolbox for easy calibrating omnidirectional cameras,” in Proceedings to IEEE International Conference on Intelligent Robots and Systems (Institute of Electrical and Electronics Engineers, 2006), pp. 5695–5701.

D. Scaramuzza, A. Martinelli, and R. Siegwart, “A flexible technique for accurate omnidirectional camera calibration and structure from motion,” in Proceedings of IEEE International Conference of Vision Systems (Institute of Electrical and Electronics Engineers, 2006), pp. 45–52.

Siegwart, R.

D. Scaramuzza, A. Martinelli, and R. Siegwart, “A flexible technique for accurate omnidirectional camera calibration and structure from motion,” in Proceedings of IEEE International Conference of Vision Systems (Institute of Electrical and Electronics Engineers, 2006), pp. 45–52.

D. Scaramuzza, A. Martinelli, and R. Siegwart, “A toolbox for easy calibrating omnidirectional cameras,” in Proceedings to IEEE International Conference on Intelligent Robots and Systems (Institute of Electrical and Electronics Engineers, 2006), pp. 5695–5701.

Smith, M. J.

M. J. Smith and E. Cope, “The effects of temperature variation on single-lens-reflex digital camera calibration parameters,” in International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, Commission V Symposium (International Society for Photogrammetry and Remote Sensing, 2010), Vol. XXXVIII, Part 5, pp. 554–559.

Springer, G.

Z. Kiraly, G. Springer, and J. Van Dam, “Stereoscopic vision system,” Opt. Eng. 45, 043006 (2006).
[CrossRef]

Thibault, S.

J. Parent and S. Thibault, “Tolerancing panoramic lenses,” Proc. SPIE 7433, 74330D (2009).
[CrossRef]

Ude, A.

A. Ude, C. Gaskett, and G. Cheng, “Foveated vision systems with two cameras per eye,” in Proceedings of IEEE International Conference on Robotics and Automation (Institute of Electrical and Electronics Engineers, 2006), pp. 3457–3462.

Van Dam, J.

Z. Kiraly, G. Springer, and J. Van Dam, “Stereoscopic vision system,” Opt. Eng. 45, 043006 (2006).
[CrossRef]

Wang, J.

E. Adelson and J. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
[CrossRef]

Yamaguchi, J.

T. Nishimoto and J. Yamaguchi, “Three dimensional measurement using fisheye stereo vision,” in Proceedings of 46th SICE Annual Conference (Institute of Electrical and Electronics Engineers, 2007), pp. 2008–2012.

Zhang, Z.

Z. Zhang, “Flexible calibration by viewing a plane from unknown orientations,” in Proceedings of 7th IEEE International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, 1999), pp. 666–673.

IEEE Trans. Pattern Anal. Mach. Intell.

E. Adelson and J. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
[CrossRef]

Opt. Eng.

Z. Kiraly, G. Springer, and J. Van Dam, “Stereoscopic vision system,” Opt. Eng. 45, 043006 (2006).
[CrossRef]

Opt. Express

Proc. SPIE

J. Parent and S. Thibault, “Tolerancing panoramic lenses,” Proc. SPIE 7433, 74330D (2009).
[CrossRef]

Other

D. Scaramuzza, Omnidirectional Vision: From Calibration to Robot Motion Estimation, (ETH Zurich, 2008).

J.-Y. Bouguet, “Camera calibration toolbox for MATLAB,” http://www.vision.caltech.edu/bouguetj/calib_doc/index.html .

Z. Zhang, “Flexible calibration by viewing a plane from unknown orientations,” in Proceedings of 7th IEEE International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, 1999), pp. 666–673.

“Thermal analysis,” in ZEMAX User’s Manual, (ZEMAX Development Corporation, 2013), pp. 667–672.

Optimax Systems, Inc., “Manufacturing tolerance chart,” http://www.optimaxsi.com/innovation/optical-manufacturing-tolerance-chart/ .

A. Ude, C. Gaskett, and G. Cheng, “Foveated vision systems with two cameras per eye,” in Proceedings of IEEE International Conference on Robotics and Automation (Institute of Electrical and Electronics Engineers, 2006), pp. 3457–3462.

T. Nishimoto and J. Yamaguchi, “Three dimensional measurement using fisheye stereo vision,” in Proceedings of 46th SICE Annual Conference (Institute of Electrical and Electronics Engineers, 2007), pp. 2008–2012.

D. Fiedler and H. Müller, “Impact of thermal and environmental conditions on the kinect sensor,” in Proceedings of International Workshop of Advances in Depth Image Analysis and Applications, Lecture Notes on Computer Vision (SpringerLink, 2012), Vol. 7854, pp. 21–31.

M. J. Smith and E. Cope, “The effects of temperature variation on single-lens-reflex digital camera calibration parameters,” in International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, Commission V Symposium (International Society for Photogrammetry and Remote Sensing, 2010), Vol. XXXVIII, Part 5, pp. 554–559.

M. Laikin, Lens Design, 4th ed. (CRC Press, 2006).

Zebase 6 Optical Design Database (ZEMAX Development Corporation, 2007).

D. Scaramuzza, “OCamCalib: omnidirectional camera calibration toolbox for MATLAB,” https://sites.google.com/site/scarabotix/ocamcalib-toolbox .

D. Scaramuzza, A. Martinelli, and R. Siegwart, “A flexible technique for accurate omnidirectional camera calibration and structure from motion,” in Proceedings of IEEE International Conference of Vision Systems (Institute of Electrical and Electronics Engineers, 2006), pp. 45–52.

D. Scaramuzza, A. Martinelli, and R. Siegwart, “A toolbox for easy calibrating omnidirectional cameras,” in Proceedings to IEEE International Conference on Intelligent Robots and Systems (Institute of Electrical and Electronics Engineers, 2006), pp. 5695–5701.

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Figures (5)

Fig. 1.
Fig. 1.

Zemax design layout for a 170 deg FOV and F/1.8 camera lens (F_006). The effective focal length is 5.2 mm. The position of the aperture stop (AS) is indicated above.

Fig. 2.
Fig. 2.

Simulated calibration targets in object space representing nine checkerboards with 11×11 control points. The black dot marks the camera position.

Fig. 3.
Fig. 3.

Image points corresponding to the simulated calibration targets. The black dot represents the position of the optical axis (also the center of the image and the principal point).

Fig. 4.
Fig. 4.

Influence of temperature on the projective function. (a) Variation of projective function coefficients a0 and a2 depending on the temperature. (b) Difference between nominal and gradient (10°C at front lens to 30°C at last lens) projective functions.

Fig. 5.
Fig. 5.

Calibration results for a toleranced design as a function of the temperature between 10°C and 30°C. The calibration parameters are (a) the projective function coefficients a0 and a2; (b) the principal point coordinates xc and yc; (c) parameter c of the affine transformation; (d) parameters d and e of the affine transformation.

Tables (2)

Tables Icon

Table 1. Calibration Parameters for Decentering and Tilt of Two Different Optical Elements

Tables Icon

Table 2. Range of Calibration Parameters for Perturbed Designs

Equations (3)

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

[xyz]=[uvf(u,v)].
f(ρ)=a0+a2ρ2.
[uv]=[cde1][uv]+[xcyc].

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