Abstract

A constrained optimization process is proposed for camera calibration with an imperfect and not-measured calibration target. The proposed method uses the geometry of the calibration target in an optimization process with constraints based on the pattern design statistically. As a result, the camera can be calibrated in the absolute scale without taking any measurement of the imperfect calibration target. It is verified through simulation and experiment that the reprojection errors by using the proposed method are obviously smaller than those of the traditional calibration approach by trusting an imperfect target. The slightly higher measurement precision is also exemplified through an experimental calibration of a stereo vision system.

© 2013 Optical Society of America

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References

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  1. F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
    [CrossRef]
  2. G. Sansoni, M. Carocci, and R. Rodella, “Calibration and performance evaluation of a 3-D imaging sensor based on the projection of structured light,” IEEE Trans. Instrum. Meas. 49, 628–636 (2000).
    [CrossRef]
  3. J. Y. Bouguet, “Camera Calibration Toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc/ .
  4. R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Autom. 3, 323–344 (1987).
    [CrossRef]
  5. H. Zhang, M. J. Lalor, and D. R. Burton, “Robust, accurate seven-sample phase-shifting algorithm insensitive to nonlinear phase-shift error and second-harmonic distortion: a comparative study,” Opt. Eng. 38, 1524–1533 (1999).
    [CrossRef]
  6. R. Legarda-Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 464–471 (2004).
    [CrossRef]
  7. L. Huang, P. S. K. Chua, and A. Asundi, “Least-squares calibration method for fringe projection profilometry considering camera lens distortion,” Appl. Opt. 49, 1539–1548 (2010).
    [CrossRef]
  8. Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487–493 (2003).
    [CrossRef]
  9. M. C. Knauer, J. Kaminski, and G. Häusler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
    [CrossRef]
  10. M. Petz and R. Tutsch, “Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,” Proc. SPIE 5869, 58691D (2005).
    [CrossRef]
  11. L. Huang, C. Seng Ng, and A. Krishna Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50, 529–533 (2012).
    [CrossRef]
  12. L. Huang, C. S. Ng, and A. K. Asundi, “Dynamic three-dimensional sensing for specular surface with monoscopic fringe reflectometry,” Opt. Express 19, 12809–12814 (2011).
    [CrossRef]
  13. B. Pan, D. Wu, and L. Yu, “Optimization of a three-dimensional digital image correlation system for deformation measurements in extreme environments,” Appl. Opt. 51, 4409–4419 (2012).
    [CrossRef]
  14. D. C. Brown, “Close-range camera calibration,” Photogramm. Eng. 37, 855–866 (1971).
  15. I. Sobel, “Calibrating computer controlled cameras for perceiving 3-D scenes,” Artif. Intell. 5, 185–198 (1974).
    [CrossRef]
  16. J. Lavest, M. Viala, and M. Dhome, “Do we really need an accurate calibration pattern to achieve a reliable camera calibration?” in Proceeding of ECCV’98, 5th European Conference on Computer Vision (Springer, 1998), pp. 158–174.
  17. A. Albarelli, E. Rodolà, and A. Torsello, “Robust camera calibration using inaccurate targets,” in BMVC, F. d. r. Labrosse, R. Zwiggelaar, Y. Liu, and B. Tiddeman, eds. (British Machine Vision Association, 2010), pp. 1–10.
  18. K. H. Strobl and G. Hirzinger, “More accurate pinhole camera calibration with imperfect planar target,” in 2011 IEEE International Conference on Computer Vision Workshops (IEEE, 2011).
  19. K. H. Strobl and G. Hirzinger, “More accurate camera and hand-eye calibrations with unknown grid pattern dimensions,” in IEEE International Conference on Robotics and Automation (IEEE, 2008), pp. 1398–1405.
  20. C. Schmalz, F. Forster, and E. Angelopoulou, “Camera calibration: active versus passive targets,” Opt. Eng. 50, 113601 (2011).
    [CrossRef]
  21. L. Huang, Q. Zhang, and A. Asundi, “Camera calibration with active phase target: improvement on feature detection and optimization,” Opt. Lett. 38, 1446–1448 (2013).
    [CrossRef]
  22. S. I. Granshaw, “Bundle adjustment methods in engineering photogrammetry,” Photogramm. Rec. 10, 181–207 (1980).
    [CrossRef]
  23. B. Triggs, P. McLauchlan, R. Hartley, and A. Fitzgibbon, “Bundle adjustment—a modern synthesis,” in Vision Algorithms: Theory and Practice, B. Triggs, A. Zisserman, and R. Szeliski, eds. (Springer, 2000), pp. 298–372.
  24. A. Albarelli, E. Rodolà, and A. Torsello, “Robust camera calibration using inaccurate targets,” Trans. Pattern Anal. Mach. Intell. 31, 376–383 (2009).

2013 (1)

2012 (2)

L. Huang, C. Seng Ng, and A. Krishna Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50, 529–533 (2012).
[CrossRef]

B. Pan, D. Wu, and L. Yu, “Optimization of a three-dimensional digital image correlation system for deformation measurements in extreme environments,” Appl. Opt. 51, 4409–4419 (2012).
[CrossRef]

2011 (2)

L. Huang, C. S. Ng, and A. K. Asundi, “Dynamic three-dimensional sensing for specular surface with monoscopic fringe reflectometry,” Opt. Express 19, 12809–12814 (2011).
[CrossRef]

C. Schmalz, F. Forster, and E. Angelopoulou, “Camera calibration: active versus passive targets,” Opt. Eng. 50, 113601 (2011).
[CrossRef]

2010 (1)

2009 (1)

A. Albarelli, E. Rodolà, and A. Torsello, “Robust camera calibration using inaccurate targets,” Trans. Pattern Anal. Mach. Intell. 31, 376–383 (2009).

2005 (1)

M. Petz and R. Tutsch, “Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,” Proc. SPIE 5869, 58691D (2005).
[CrossRef]

2004 (2)

M. C. Knauer, J. Kaminski, and G. Häusler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[CrossRef]

R. Legarda-Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 464–471 (2004).
[CrossRef]

2003 (1)

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487–493 (2003).
[CrossRef]

2000 (2)

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

G. Sansoni, M. Carocci, and R. Rodella, “Calibration and performance evaluation of a 3-D imaging sensor based on the projection of structured light,” IEEE Trans. Instrum. Meas. 49, 628–636 (2000).
[CrossRef]

1999 (1)

H. Zhang, M. J. Lalor, and D. R. Burton, “Robust, accurate seven-sample phase-shifting algorithm insensitive to nonlinear phase-shift error and second-harmonic distortion: a comparative study,” Opt. Eng. 38, 1524–1533 (1999).
[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 J. Robot. Autom. 3, 323–344 (1987).
[CrossRef]

1980 (1)

S. I. Granshaw, “Bundle adjustment methods in engineering photogrammetry,” Photogramm. Rec. 10, 181–207 (1980).
[CrossRef]

1974 (1)

I. Sobel, “Calibrating computer controlled cameras for perceiving 3-D scenes,” Artif. Intell. 5, 185–198 (1974).
[CrossRef]

1971 (1)

D. C. Brown, “Close-range camera calibration,” Photogramm. Eng. 37, 855–866 (1971).

Albarelli, A.

A. Albarelli, E. Rodolà, and A. Torsello, “Robust camera calibration using inaccurate targets,” Trans. Pattern Anal. Mach. Intell. 31, 376–383 (2009).

A. Albarelli, E. Rodolà, and A. Torsello, “Robust camera calibration using inaccurate targets,” in BMVC, F. d. r. Labrosse, R. Zwiggelaar, Y. Liu, and B. Tiddeman, eds. (British Machine Vision Association, 2010), pp. 1–10.

Angelopoulou, E.

C. Schmalz, F. Forster, and E. Angelopoulou, “Camera calibration: active versus passive targets,” Opt. Eng. 50, 113601 (2011).
[CrossRef]

Asundi, A.

Asundi, A. K.

Bothe, T.

R. Legarda-Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 464–471 (2004).
[CrossRef]

Brown, D. C.

D. C. Brown, “Close-range camera calibration,” Photogramm. Eng. 37, 855–866 (1971).

Brown, G. M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Burton, D. R.

H. Zhang, M. J. Lalor, and D. R. Burton, “Robust, accurate seven-sample phase-shifting algorithm insensitive to nonlinear phase-shift error and second-harmonic distortion: a comparative study,” Opt. Eng. 38, 1524–1533 (1999).
[CrossRef]

Carocci, M.

G. Sansoni, M. Carocci, and R. Rodella, “Calibration and performance evaluation of a 3-D imaging sensor based on the projection of structured light,” IEEE Trans. Instrum. Meas. 49, 628–636 (2000).
[CrossRef]

Chen, F.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Chiang, F.-P.

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487–493 (2003).
[CrossRef]

Chua, P. S. K.

Dhome, M.

J. Lavest, M. Viala, and M. Dhome, “Do we really need an accurate calibration pattern to achieve a reliable camera calibration?” in Proceeding of ECCV’98, 5th European Conference on Computer Vision (Springer, 1998), pp. 158–174.

Fitzgibbon, A.

B. Triggs, P. McLauchlan, R. Hartley, and A. Fitzgibbon, “Bundle adjustment—a modern synthesis,” in Vision Algorithms: Theory and Practice, B. Triggs, A. Zisserman, and R. Szeliski, eds. (Springer, 2000), pp. 298–372.

Forster, F.

C. Schmalz, F. Forster, and E. Angelopoulou, “Camera calibration: active versus passive targets,” Opt. Eng. 50, 113601 (2011).
[CrossRef]

Fu, Q.

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487–493 (2003).
[CrossRef]

Granshaw, S. I.

S. I. Granshaw, “Bundle adjustment methods in engineering photogrammetry,” Photogramm. Rec. 10, 181–207 (1980).
[CrossRef]

Hartley, R.

B. Triggs, P. McLauchlan, R. Hartley, and A. Fitzgibbon, “Bundle adjustment—a modern synthesis,” in Vision Algorithms: Theory and Practice, B. Triggs, A. Zisserman, and R. Szeliski, eds. (Springer, 2000), pp. 298–372.

Häusler, G.

M. C. Knauer, J. Kaminski, and G. Häusler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[CrossRef]

Hirzinger, G.

K. H. Strobl and G. Hirzinger, “More accurate pinhole camera calibration with imperfect planar target,” in 2011 IEEE International Conference on Computer Vision Workshops (IEEE, 2011).

K. H. Strobl and G. Hirzinger, “More accurate camera and hand-eye calibrations with unknown grid pattern dimensions,” in IEEE International Conference on Robotics and Automation (IEEE, 2008), pp. 1398–1405.

Hu, Q.

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487–493 (2003).
[CrossRef]

Huang, L.

Huang, P. S.

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487–493 (2003).
[CrossRef]

Juptner, W. P.

R. Legarda-Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 464–471 (2004).
[CrossRef]

Kaminski, J.

M. C. Knauer, J. Kaminski, and G. Häusler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[CrossRef]

Knauer, M. C.

M. C. Knauer, J. Kaminski, and G. Häusler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[CrossRef]

Krishna Asundi, A.

L. Huang, C. Seng Ng, and A. Krishna Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50, 529–533 (2012).
[CrossRef]

Lalor, M. J.

H. Zhang, M. J. Lalor, and D. R. Burton, “Robust, accurate seven-sample phase-shifting algorithm insensitive to nonlinear phase-shift error and second-harmonic distortion: a comparative study,” Opt. Eng. 38, 1524–1533 (1999).
[CrossRef]

Lavest, J.

J. Lavest, M. Viala, and M. Dhome, “Do we really need an accurate calibration pattern to achieve a reliable camera calibration?” in Proceeding of ECCV’98, 5th European Conference on Computer Vision (Springer, 1998), pp. 158–174.

Legarda-Saenz, R.

R. Legarda-Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 464–471 (2004).
[CrossRef]

McLauchlan, P.

B. Triggs, P. McLauchlan, R. Hartley, and A. Fitzgibbon, “Bundle adjustment—a modern synthesis,” in Vision Algorithms: Theory and Practice, B. Triggs, A. Zisserman, and R. Szeliski, eds. (Springer, 2000), pp. 298–372.

Ng, C. S.

Pan, B.

Petz, M.

M. Petz and R. Tutsch, “Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,” Proc. SPIE 5869, 58691D (2005).
[CrossRef]

Rodella, R.

G. Sansoni, M. Carocci, and R. Rodella, “Calibration and performance evaluation of a 3-D imaging sensor based on the projection of structured light,” IEEE Trans. Instrum. Meas. 49, 628–636 (2000).
[CrossRef]

Rodolà, E.

A. Albarelli, E. Rodolà, and A. Torsello, “Robust camera calibration using inaccurate targets,” Trans. Pattern Anal. Mach. Intell. 31, 376–383 (2009).

A. Albarelli, E. Rodolà, and A. Torsello, “Robust camera calibration using inaccurate targets,” in BMVC, F. d. r. Labrosse, R. Zwiggelaar, Y. Liu, and B. Tiddeman, eds. (British Machine Vision Association, 2010), pp. 1–10.

Sansoni, G.

G. Sansoni, M. Carocci, and R. Rodella, “Calibration and performance evaluation of a 3-D imaging sensor based on the projection of structured light,” IEEE Trans. Instrum. Meas. 49, 628–636 (2000).
[CrossRef]

Schmalz, C.

C. Schmalz, F. Forster, and E. Angelopoulou, “Camera calibration: active versus passive targets,” Opt. Eng. 50, 113601 (2011).
[CrossRef]

Seng Ng, C.

L. Huang, C. Seng Ng, and A. Krishna Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50, 529–533 (2012).
[CrossRef]

Sobel, I.

I. Sobel, “Calibrating computer controlled cameras for perceiving 3-D scenes,” Artif. Intell. 5, 185–198 (1974).
[CrossRef]

Song, M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Strobl, K. H.

K. H. Strobl and G. Hirzinger, “More accurate pinhole camera calibration with imperfect planar target,” in 2011 IEEE International Conference on Computer Vision Workshops (IEEE, 2011).

K. H. Strobl and G. Hirzinger, “More accurate camera and hand-eye calibrations with unknown grid pattern dimensions,” in IEEE International Conference on Robotics and Automation (IEEE, 2008), pp. 1398–1405.

Torsello, A.

A. Albarelli, E. Rodolà, and A. Torsello, “Robust camera calibration using inaccurate targets,” Trans. Pattern Anal. Mach. Intell. 31, 376–383 (2009).

A. Albarelli, E. Rodolà, and A. Torsello, “Robust camera calibration using inaccurate targets,” in BMVC, F. d. r. Labrosse, R. Zwiggelaar, Y. Liu, and B. Tiddeman, eds. (British Machine Vision Association, 2010), pp. 1–10.

Triggs, B.

B. Triggs, P. McLauchlan, R. Hartley, and A. Fitzgibbon, “Bundle adjustment—a modern synthesis,” in Vision Algorithms: Theory and Practice, B. Triggs, A. Zisserman, and R. Szeliski, eds. (Springer, 2000), pp. 298–372.

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 J. Robot. Autom. 3, 323–344 (1987).
[CrossRef]

Tutsch, R.

M. Petz and R. Tutsch, “Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,” Proc. SPIE 5869, 58691D (2005).
[CrossRef]

Viala, M.

J. Lavest, M. Viala, and M. Dhome, “Do we really need an accurate calibration pattern to achieve a reliable camera calibration?” in Proceeding of ECCV’98, 5th European Conference on Computer Vision (Springer, 1998), pp. 158–174.

Wu, D.

Yu, L.

Zhang, H.

H. Zhang, M. J. Lalor, and D. R. Burton, “Robust, accurate seven-sample phase-shifting algorithm insensitive to nonlinear phase-shift error and second-harmonic distortion: a comparative study,” Opt. Eng. 38, 1524–1533 (1999).
[CrossRef]

Zhang, Q.

Appl. Opt. (2)

Artif. Intell. (1)

I. Sobel, “Calibrating computer controlled cameras for perceiving 3-D scenes,” Artif. Intell. 5, 185–198 (1974).
[CrossRef]

IEEE J. Robot. Autom. (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 J. Robot. Autom. 3, 323–344 (1987).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

G. Sansoni, M. Carocci, and R. Rodella, “Calibration and performance evaluation of a 3-D imaging sensor based on the projection of structured light,” IEEE Trans. Instrum. Meas. 49, 628–636 (2000).
[CrossRef]

Opt. Eng. (5)

H. Zhang, M. J. Lalor, and D. R. Burton, “Robust, accurate seven-sample phase-shifting algorithm insensitive to nonlinear phase-shift error and second-harmonic distortion: a comparative study,” Opt. Eng. 38, 1524–1533 (1999).
[CrossRef]

R. Legarda-Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 464–471 (2004).
[CrossRef]

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487–493 (2003).
[CrossRef]

C. Schmalz, F. Forster, and E. Angelopoulou, “Camera calibration: active versus passive targets,” Opt. Eng. 50, 113601 (2011).
[CrossRef]

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

L. Huang, C. Seng Ng, and A. Krishna Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50, 529–533 (2012).
[CrossRef]

Opt. Lett. (1)

Photogramm. Eng. (1)

D. C. Brown, “Close-range camera calibration,” Photogramm. Eng. 37, 855–866 (1971).

Photogramm. Rec. (1)

S. I. Granshaw, “Bundle adjustment methods in engineering photogrammetry,” Photogramm. Rec. 10, 181–207 (1980).
[CrossRef]

Proc. SPIE (2)

M. C. Knauer, J. Kaminski, and G. Häusler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[CrossRef]

M. Petz and R. Tutsch, “Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,” Proc. SPIE 5869, 58691D (2005).
[CrossRef]

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

A. Albarelli, E. Rodolà, and A. Torsello, “Robust camera calibration using inaccurate targets,” Trans. Pattern Anal. Mach. Intell. 31, 376–383 (2009).

Other (6)

B. Triggs, P. McLauchlan, R. Hartley, and A. Fitzgibbon, “Bundle adjustment—a modern synthesis,” in Vision Algorithms: Theory and Practice, B. Triggs, A. Zisserman, and R. Szeliski, eds. (Springer, 2000), pp. 298–372.

J. Lavest, M. Viala, and M. Dhome, “Do we really need an accurate calibration pattern to achieve a reliable camera calibration?” in Proceeding of ECCV’98, 5th European Conference on Computer Vision (Springer, 1998), pp. 158–174.

A. Albarelli, E. Rodolà, and A. Torsello, “Robust camera calibration using inaccurate targets,” in BMVC, F. d. r. Labrosse, R. Zwiggelaar, Y. Liu, and B. Tiddeman, eds. (British Machine Vision Association, 2010), pp. 1–10.

K. H. Strobl and G. Hirzinger, “More accurate pinhole camera calibration with imperfect planar target,” in 2011 IEEE International Conference on Computer Vision Workshops (IEEE, 2011).

K. H. Strobl and G. Hirzinger, “More accurate camera and hand-eye calibrations with unknown grid pattern dimensions,” in IEEE International Conference on Robotics and Automation (IEEE, 2008), pp. 1398–1405.

J. Y. Bouguet, “Camera Calibration Toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc/ .

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Figures (9)

Fig. 1.
Fig. 1.

Physical (a) and simplified (b) pinhole models are commonly adopted for camera calibration as a basic description of imaging process.

Fig. 2.
Fig. 2.

If error-free feature detection could be achieved, the traditional optimization can be improved by the proposed method with suppressing reprojection errors down to the level of 1010 pixels. The standard deviation of reprojection errors decreases down to a certain level but it could not go further with the traditional method due to the imperfection of target geometry, (a) however, it can be reduced to the order of 1010 pixels with the proposed optimization (b) with showing the distribution of the final reprojection errors by using the traditional method (c) and the proposed method (d).

Fig. 3.
Fig. 3.

Proposed method also successfully improves the traditional optimization with the feature detection errors existing at a practical level (RMSE=0.1pixels) referring to the comparison on performance of the traditional iteration (a) and the proposed one (b) and the distribution of the final reprojection errors of the traditional method (c) and the proposed method (d).

Fig. 4.
Fig. 4.

Estimated target geometry with the proposed method matches with the true target geometry.

Fig. 5.
Fig. 5.

“Poorly” fabricated calibration pattern (b) is used in the experiment for a stereo vision system with 20 views from the left camera (a) and the right one (c).

Fig. 6.
Fig. 6.

Proposed method reduces the reprojection errors in experiment as well with showing the iterations by using traditional method (a) and the proposed method (b) and the error distributions of the traditional method (c) and the proposed method (d).

Fig. 7.
Fig. 7.

VMM is used to test the actual geometry of the calibration target.

Fig. 8.
Fig. 8.

3D shape of the imperfect calibration target is measured by VMM and compared with the conventionally believed plane and estimated geometry (a) with showing the 3D distinction (b).

Fig. 9.
Fig. 9.

Proposed method calibrated stereovision system has higher measuring precision.

Tables (1)

Tables Icon

Table 1. Comparison of Intrinsic Parameters Obtained Using Traditional and Proposed Methods

Equations (13)

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

Xc[xcyczc]=[R,t][xwywzw1][R,t][Xw1].
[xnyn][xc/zcyc/zc],
[xdyd][xnyn]+(k1rn2+k2rn4+k3rn6+)[xnyn]+[2p1xnyn+p2(rn2+2xn2)p1(rn2+2yn2)+2p2xnyn],
[uv1]=[diΔxdicotθΔyu00diΔysinθv0001][xdyd1][ausu00avv0001][xdyd1]A[xdyd1].
[Rn+,tn+,k+,p+,A+]=arg min(Rn,tn,k,p,A)n=1NmnMn(ujn,vjn)f(Rn,tn,k,p,A,Xwmn)2,
[Rn*,tn*,k*,p*,A*,Xwmn*]=arg min(Rn,tn,k,p,A,Xwmn)n=1NmnMn(ujn,vjn)f(Rn+,tn+,k+,p+,A+,Xwmn)2.
mMxwm*=mMxwm,
mMywm*=mMywm,
mMzwm*=mMzwm.
nx*=0,
ny*=0,
mMxwm*ywmxwmywm*0.
mMXwm*Xwm20.

Metrics