Abstract

In this paper, a new and convenient calibration algorithm is proposed for unsynchronized camera networks with a large capture volume. The proposed method provides a simple and accurate means of calibration using a small 3D reference object. Moreover, since the inaccuracy of the object is also compensated simultaneously, the manufacturing cost can be decreased. The extrinsic and intrinsic parameters are recovered simultaneously by capturing an object placed arbitrarily in different locations in the capture volume. The proposed method first resolves the problem linearly by factorizing projection matrices into the camera and the object pose parameters. Due to the multi-view constraints imposed on factorization, consistency of the rigid transformations among cameras and objects can be imposed. These consistent estimation results can be further refined using a non-linear optimization process. The proposed algorithm is evaluated via simulated and real experiments in order to verify that it is more efficient than previous methods.

© 2012 OSA

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  1. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd. ed. (Cambridge University Press, 2003).
  2. Z. Zhang, “A flexible new technique for camera calibration,” Tech. Rep. MSR-TR-98-71, Microsoft Corporation (1998).
  3. T. Ueshiba and F. Tomita, “Plane-based calibration algorithm for multi-camera systems via factorization of homography matrices,” in “Proc. IEEE International Conference on Computer Vision,” (Nice, France, 2003), pp. 966–973.
  4. T. Svoboda, D. Martinec, and T. Pajdla, “A convenient multi-camera selfcalibration for virtual environments,” Presence: Teleop. Virt. Environ.14, 407–422 (2005).
    [CrossRef]
  5. G. Kurillo, Z. Li, and R. Bajcsy, “Wide-area external multi-camera calibration using vision graphs and virtual calibration object,” in “Proc. ACM/IEEE International Conference on Distributed Smart Cameras,” (2008), pp. 1–9.
  6. H. Medeiros, H. Iwaki, and J. Park, “Online distributed calibration of a large network of wireless cameras using dynamic clustering,” in “Proc. ACM/IEEE International Conference on Distributed Smart Cameras,” (2008), pp. 1–10.
  7. X. Chen, J. Davis, and P. Slusallek, “Wide area camera calibration using virtual calibration objects,” in “Proc. IEEE International Conference on Computer Vision and Pattern Recognition,” Hilton Head, SC, USA (2000), pp. 520–527.
  8. S. N. Sinha and M. Pollefeys, “Camera network calibration and synchronization from silhouettes in archived video,” Int. J. Comput. Vision87, 266–283 (2010).
    [CrossRef]
  9. E. Boyer, “On using silhouettes for camera calibration,” in “Proc. Asian Conference on Computer Vision,” Hyderabad, India (2006), pp. 1–10.
  10. J. Kassebaum, N. Bulusu, and W.-C. Feng, “3-d target-based distributed smart camera network localization,” IEEE Trans. Image Process.19, 2530–2539 (2010).
    [CrossRef] [PubMed]
  11. C. Tomasi and T. Kanade, “Shape and motion from image streams under orthography: a factorization method,” Int. J. Comput. Vision9, 137–154 (1992).
    [CrossRef]
  12. P. Sturm and B. Triggs, “A factorization based algorithm for multi-image projective structure and motion,” in “Proc. European Conference on Computer Vision,” Cambridge, UK (1996), pp. 709–720.
  13. D. Jacobs, “Linear fitting with missing data: Applications to structure from motion and to characterizing intensity images,” in “Proc. IEEE International Conference on Computer Vision and Pattern Recognition,” San Juan, Puerto Rico (1997), pp. 206–212.
  14. D. Martinec and T. Pajdla, “Structure from many perspective images with occlusions,” in “Proc. European Conference on Computer Vision,” Copenhagen, Denmark, (2002), pp. 355–369.
  15. P. Sturm, “Algorithms for plane-based pose estimation,” in “Proc. IEEE International Conference on Computer Vision and Pattern Recognition,” Hilton Head Island, SC, USA, (2000), pp. 706–711.
  16. M. Wilczkowiak, P. Sturm, and E. Boyer, “Using geometric constraints through parallelepipeds for calibration and 3D modelling,” IEEE Trans. Pattern Anal. Mach. Intell.27, 194–207 (2005).
    [CrossRef] [PubMed]
  17. O. Faugeras, Three-Dimensional Computer Vision (The MIT Press, 1993).
  18. K. S. Arun, T. S. Huang, and S. D. Blosten, “Least-squares fitting of two 3-D point sets,” IEEE Trans. Pattern Anal. Mach. Intell.PAMI-9, 698–700 (1987).
    [CrossRef]
  19. A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Trans. Pattern Anal. Mach. Intell.21, 476–480 (1999).
    [CrossRef]
  20. R. Hartley, “In defence of the 8-point algorithm,” in “Proc. International Conference on Computer Vision,” Sendai, Japan (1995), pp. 1064–1070.

2010 (2)

S. N. Sinha and M. Pollefeys, “Camera network calibration and synchronization from silhouettes in archived video,” Int. J. Comput. Vision87, 266–283 (2010).
[CrossRef]

J. Kassebaum, N. Bulusu, and W.-C. Feng, “3-d target-based distributed smart camera network localization,” IEEE Trans. Image Process.19, 2530–2539 (2010).
[CrossRef] [PubMed]

2005 (2)

M. Wilczkowiak, P. Sturm, and E. Boyer, “Using geometric constraints through parallelepipeds for calibration and 3D modelling,” IEEE Trans. Pattern Anal. Mach. Intell.27, 194–207 (2005).
[CrossRef] [PubMed]

T. Svoboda, D. Martinec, and T. Pajdla, “A convenient multi-camera selfcalibration for virtual environments,” Presence: Teleop. Virt. Environ.14, 407–422 (2005).
[CrossRef]

1999 (1)

A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Trans. Pattern Anal. Mach. Intell.21, 476–480 (1999).
[CrossRef]

1992 (1)

C. Tomasi and T. Kanade, “Shape and motion from image streams under orthography: a factorization method,” Int. J. Comput. Vision9, 137–154 (1992).
[CrossRef]

1987 (1)

K. S. Arun, T. S. Huang, and S. D. Blosten, “Least-squares fitting of two 3-D point sets,” IEEE Trans. Pattern Anal. Mach. Intell.PAMI-9, 698–700 (1987).
[CrossRef]

Arun, K. S.

K. S. Arun, T. S. Huang, and S. D. Blosten, “Least-squares fitting of two 3-D point sets,” IEEE Trans. Pattern Anal. Mach. Intell.PAMI-9, 698–700 (1987).
[CrossRef]

Bajcsy, R.

G. Kurillo, Z. Li, and R. Bajcsy, “Wide-area external multi-camera calibration using vision graphs and virtual calibration object,” in “Proc. ACM/IEEE International Conference on Distributed Smart Cameras,” (2008), pp. 1–9.

Blosten, S. D.

K. S. Arun, T. S. Huang, and S. D. Blosten, “Least-squares fitting of two 3-D point sets,” IEEE Trans. Pattern Anal. Mach. Intell.PAMI-9, 698–700 (1987).
[CrossRef]

Boyer, E.

M. Wilczkowiak, P. Sturm, and E. Boyer, “Using geometric constraints through parallelepipeds for calibration and 3D modelling,” IEEE Trans. Pattern Anal. Mach. Intell.27, 194–207 (2005).
[CrossRef] [PubMed]

E. Boyer, “On using silhouettes for camera calibration,” in “Proc. Asian Conference on Computer Vision,” Hyderabad, India (2006), pp. 1–10.

Bulusu, N.

J. Kassebaum, N. Bulusu, and W.-C. Feng, “3-d target-based distributed smart camera network localization,” IEEE Trans. Image Process.19, 2530–2539 (2010).
[CrossRef] [PubMed]

Chen, X.

X. Chen, J. Davis, and P. Slusallek, “Wide area camera calibration using virtual calibration objects,” in “Proc. IEEE International Conference on Computer Vision and Pattern Recognition,” Hilton Head, SC, USA (2000), pp. 520–527.

Davis, J.

X. Chen, J. Davis, and P. Slusallek, “Wide area camera calibration using virtual calibration objects,” in “Proc. IEEE International Conference on Computer Vision and Pattern Recognition,” Hilton Head, SC, USA (2000), pp. 520–527.

Faugeras, O.

O. Faugeras, Three-Dimensional Computer Vision (The MIT Press, 1993).

Feng, W.-C.

J. Kassebaum, N. Bulusu, and W.-C. Feng, “3-d target-based distributed smart camera network localization,” IEEE Trans. Image Process.19, 2530–2539 (2010).
[CrossRef] [PubMed]

Fisher, R. B.

A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Trans. Pattern Anal. Mach. Intell.21, 476–480 (1999).
[CrossRef]

Fitzgibbon, A.

A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Trans. Pattern Anal. Mach. Intell.21, 476–480 (1999).
[CrossRef]

Hartley, R.

R. Hartley, “In defence of the 8-point algorithm,” in “Proc. International Conference on Computer Vision,” Sendai, Japan (1995), pp. 1064–1070.

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

Huang, T. S.

K. S. Arun, T. S. Huang, and S. D. Blosten, “Least-squares fitting of two 3-D point sets,” IEEE Trans. Pattern Anal. Mach. Intell.PAMI-9, 698–700 (1987).
[CrossRef]

Iwaki, H.

H. Medeiros, H. Iwaki, and J. Park, “Online distributed calibration of a large network of wireless cameras using dynamic clustering,” in “Proc. ACM/IEEE International Conference on Distributed Smart Cameras,” (2008), pp. 1–10.

Jacobs, D.

D. Jacobs, “Linear fitting with missing data: Applications to structure from motion and to characterizing intensity images,” in “Proc. IEEE International Conference on Computer Vision and Pattern Recognition,” San Juan, Puerto Rico (1997), pp. 206–212.

Kanade, T.

C. Tomasi and T. Kanade, “Shape and motion from image streams under orthography: a factorization method,” Int. J. Comput. Vision9, 137–154 (1992).
[CrossRef]

Kassebaum, J.

J. Kassebaum, N. Bulusu, and W.-C. Feng, “3-d target-based distributed smart camera network localization,” IEEE Trans. Image Process.19, 2530–2539 (2010).
[CrossRef] [PubMed]

Kurillo, G.

G. Kurillo, Z. Li, and R. Bajcsy, “Wide-area external multi-camera calibration using vision graphs and virtual calibration object,” in “Proc. ACM/IEEE International Conference on Distributed Smart Cameras,” (2008), pp. 1–9.

Li, Z.

G. Kurillo, Z. Li, and R. Bajcsy, “Wide-area external multi-camera calibration using vision graphs and virtual calibration object,” in “Proc. ACM/IEEE International Conference on Distributed Smart Cameras,” (2008), pp. 1–9.

Martinec, D.

T. Svoboda, D. Martinec, and T. Pajdla, “A convenient multi-camera selfcalibration for virtual environments,” Presence: Teleop. Virt. Environ.14, 407–422 (2005).
[CrossRef]

D. Martinec and T. Pajdla, “Structure from many perspective images with occlusions,” in “Proc. European Conference on Computer Vision,” Copenhagen, Denmark, (2002), pp. 355–369.

Medeiros, H.

H. Medeiros, H. Iwaki, and J. Park, “Online distributed calibration of a large network of wireless cameras using dynamic clustering,” in “Proc. ACM/IEEE International Conference on Distributed Smart Cameras,” (2008), pp. 1–10.

Pajdla, T.

T. Svoboda, D. Martinec, and T. Pajdla, “A convenient multi-camera selfcalibration for virtual environments,” Presence: Teleop. Virt. Environ.14, 407–422 (2005).
[CrossRef]

D. Martinec and T. Pajdla, “Structure from many perspective images with occlusions,” in “Proc. European Conference on Computer Vision,” Copenhagen, Denmark, (2002), pp. 355–369.

Park, J.

H. Medeiros, H. Iwaki, and J. Park, “Online distributed calibration of a large network of wireless cameras using dynamic clustering,” in “Proc. ACM/IEEE International Conference on Distributed Smart Cameras,” (2008), pp. 1–10.

Pilu, M.

A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Trans. Pattern Anal. Mach. Intell.21, 476–480 (1999).
[CrossRef]

Pollefeys, M.

S. N. Sinha and M. Pollefeys, “Camera network calibration and synchronization from silhouettes in archived video,” Int. J. Comput. Vision87, 266–283 (2010).
[CrossRef]

Sinha, S. N.

S. N. Sinha and M. Pollefeys, “Camera network calibration and synchronization from silhouettes in archived video,” Int. J. Comput. Vision87, 266–283 (2010).
[CrossRef]

Slusallek, P.

X. Chen, J. Davis, and P. Slusallek, “Wide area camera calibration using virtual calibration objects,” in “Proc. IEEE International Conference on Computer Vision and Pattern Recognition,” Hilton Head, SC, USA (2000), pp. 520–527.

Sturm, P.

M. Wilczkowiak, P. Sturm, and E. Boyer, “Using geometric constraints through parallelepipeds for calibration and 3D modelling,” IEEE Trans. Pattern Anal. Mach. Intell.27, 194–207 (2005).
[CrossRef] [PubMed]

P. Sturm and B. Triggs, “A factorization based algorithm for multi-image projective structure and motion,” in “Proc. European Conference on Computer Vision,” Cambridge, UK (1996), pp. 709–720.

P. Sturm, “Algorithms for plane-based pose estimation,” in “Proc. IEEE International Conference on Computer Vision and Pattern Recognition,” Hilton Head Island, SC, USA, (2000), pp. 706–711.

Svoboda, T.

T. Svoboda, D. Martinec, and T. Pajdla, “A convenient multi-camera selfcalibration for virtual environments,” Presence: Teleop. Virt. Environ.14, 407–422 (2005).
[CrossRef]

Tomasi, C.

C. Tomasi and T. Kanade, “Shape and motion from image streams under orthography: a factorization method,” Int. J. Comput. Vision9, 137–154 (1992).
[CrossRef]

Tomita, F.

T. Ueshiba and F. Tomita, “Plane-based calibration algorithm for multi-camera systems via factorization of homography matrices,” in “Proc. IEEE International Conference on Computer Vision,” (Nice, France, 2003), pp. 966–973.

Triggs, B.

P. Sturm and B. Triggs, “A factorization based algorithm for multi-image projective structure and motion,” in “Proc. European Conference on Computer Vision,” Cambridge, UK (1996), pp. 709–720.

Ueshiba, T.

T. Ueshiba and F. Tomita, “Plane-based calibration algorithm for multi-camera systems via factorization of homography matrices,” in “Proc. IEEE International Conference on Computer Vision,” (Nice, France, 2003), pp. 966–973.

Wilczkowiak, M.

M. Wilczkowiak, P. Sturm, and E. Boyer, “Using geometric constraints through parallelepipeds for calibration and 3D modelling,” IEEE Trans. Pattern Anal. Mach. Intell.27, 194–207 (2005).
[CrossRef] [PubMed]

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” Tech. Rep. MSR-TR-98-71, Microsoft Corporation (1998).

Zisserman, A.

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

IEEE Trans. Image Process. (1)

J. Kassebaum, N. Bulusu, and W.-C. Feng, “3-d target-based distributed smart camera network localization,” IEEE Trans. Image Process.19, 2530–2539 (2010).
[CrossRef] [PubMed]

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

M. Wilczkowiak, P. Sturm, and E. Boyer, “Using geometric constraints through parallelepipeds for calibration and 3D modelling,” IEEE Trans. Pattern Anal. Mach. Intell.27, 194–207 (2005).
[CrossRef] [PubMed]

K. S. Arun, T. S. Huang, and S. D. Blosten, “Least-squares fitting of two 3-D point sets,” IEEE Trans. Pattern Anal. Mach. Intell.PAMI-9, 698–700 (1987).
[CrossRef]

A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Trans. Pattern Anal. Mach. Intell.21, 476–480 (1999).
[CrossRef]

Int. J. Comput. Vision (2)

C. Tomasi and T. Kanade, “Shape and motion from image streams under orthography: a factorization method,” Int. J. Comput. Vision9, 137–154 (1992).
[CrossRef]

S. N. Sinha and M. Pollefeys, “Camera network calibration and synchronization from silhouettes in archived video,” Int. J. Comput. Vision87, 266–283 (2010).
[CrossRef]

Presence: Teleop. Virt. Environ. (1)

T. Svoboda, D. Martinec, and T. Pajdla, “A convenient multi-camera selfcalibration for virtual environments,” Presence: Teleop. Virt. Environ.14, 407–422 (2005).
[CrossRef]

Other (13)

G. Kurillo, Z. Li, and R. Bajcsy, “Wide-area external multi-camera calibration using vision graphs and virtual calibration object,” in “Proc. ACM/IEEE International Conference on Distributed Smart Cameras,” (2008), pp. 1–9.

H. Medeiros, H. Iwaki, and J. Park, “Online distributed calibration of a large network of wireless cameras using dynamic clustering,” in “Proc. ACM/IEEE International Conference on Distributed Smart Cameras,” (2008), pp. 1–10.

X. Chen, J. Davis, and P. Slusallek, “Wide area camera calibration using virtual calibration objects,” in “Proc. IEEE International Conference on Computer Vision and Pattern Recognition,” Hilton Head, SC, USA (2000), pp. 520–527.

E. Boyer, “On using silhouettes for camera calibration,” in “Proc. Asian Conference on Computer Vision,” Hyderabad, India (2006), pp. 1–10.

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

Z. Zhang, “A flexible new technique for camera calibration,” Tech. Rep. MSR-TR-98-71, Microsoft Corporation (1998).

T. Ueshiba and F. Tomita, “Plane-based calibration algorithm for multi-camera systems via factorization of homography matrices,” in “Proc. IEEE International Conference on Computer Vision,” (Nice, France, 2003), pp. 966–973.

P. Sturm and B. Triggs, “A factorization based algorithm for multi-image projective structure and motion,” in “Proc. European Conference on Computer Vision,” Cambridge, UK (1996), pp. 709–720.

D. Jacobs, “Linear fitting with missing data: Applications to structure from motion and to characterizing intensity images,” in “Proc. IEEE International Conference on Computer Vision and Pattern Recognition,” San Juan, Puerto Rico (1997), pp. 206–212.

D. Martinec and T. Pajdla, “Structure from many perspective images with occlusions,” in “Proc. European Conference on Computer Vision,” Copenhagen, Denmark, (2002), pp. 355–369.

P. Sturm, “Algorithms for plane-based pose estimation,” in “Proc. IEEE International Conference on Computer Vision and Pattern Recognition,” Hilton Head Island, SC, USA, (2000), pp. 706–711.

R. Hartley, “In defence of the 8-point algorithm,” in “Proc. International Conference on Computer Vision,” Sendai, Japan (1995), pp. 1064–1070.

O. Faugeras, Three-Dimensional Computer Vision (The MIT Press, 1993).

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