Abstract

A simple method is proposed to calibrate the fisheye distortion center, which synthesizes the algorithms of the ellipse fitting and Gaussian surface fitting. Through analyzing the imaging projection of the equidistant fisheye lens, the calibration principle is introduced in detail. From the experimental results, we find that ellipse fitting error and the relative error of Gaussian surface fitting are less than 0.06 pixels and 1.5%, respectively, and the proposed method has a higher calibration precision and stability compared with the methods in the inferences. Besides, the proposed method does not rely on any particular distortion model and other fisheye parameters, and only the image information of the calibration board is utilized, which reduces the calibration complexity and is suitable for the center calibration of any equidistant fisheye camera.

© 2012 Optical Society of America

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References

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  1. L. Wang and H. H. Ju, “Extrinsic calibration of a fisheye camera and inertial measurement unit,” in Proceedings of IEEE Conference on Machine Learning and Cybernetics (IEEE, 2009), pp. 2427–2432.
  2. J. Courbon, Y. Mezouar, N. Guénard, and P. Martinet, “Vision-based navigation of unmanned aerial vehicles,” Control Engineering Practice 18, 789–799 (2010).
    [CrossRef]
  3. C. R. Baxter, M. A. Massie, and T. J Bartolac, “Operational testing and applications of the AIRS FPA with infrared fisheye optics,” Proc. SPIE 4820, 515–524 (2003).
    [CrossRef]
  4. Y. Z. Wang, “Biomimetic staring infrared imaging omnidirectional detection technology,” Chinese Sci. Bull. 55, 3073–3080 (2010).
    [CrossRef]
  5. G. Q. Yang, “The calibration algorithm of fish-eye image,” Image Technology 3, 16 (2010).
  6. S. Shah and J. K. Aggarwal, “Intrinsic parameter calibration procedure for a (high-distortion) fish-eye lens camera with distortion model and accuracy estimation,” Pattern Recogn. 29, 1775–1788 (1996).
    [CrossRef]
  7. J. Kannala and S. S. Brandt, “A generic camera model and calibration method for conventional, wide-angle, and fish-eye lenses,” IEEE Trans. Pattern Anal. Machine Intell. 28, 1335–1340 (2006).
    [CrossRef]
  8. C. Hughes, R. McFeely, P. Denny, M. Glavin, and E. Jones, “Equidistant (fθ) fish-eye perspective with application in distortion centre estimation,” Image Vis. Comput. 28, 538–551 (2010).
    [CrossRef]
  9. D. Wang and M. Zhu, “Camera’s image center measurement method based of distorted symmetry,” Chin. J. Electron Dev. 30, 103 (2007).
  10. R. Hartley and S. S. Kang, “Parameter-free radial distortion correction with center of distortion estimation,” IEEE Trans. Pattern Anal. Machine Intell. 29, 1309–1321 (2007).
    [CrossRef]
  11. L. Krüger and C. Wöhler, “Accurate chequerboard corner localisation for camera calibration,” Pattern Recogn. Lett. 32, 1428–1430 (2011).
    [CrossRef]
  12. D. Schneider, E. Schwalbe, and H. G. Maas, “Validation of geometric models for fisheye lenses,” ISPRS J. Photogramm. Remote Sens. 64, 259–266 (2009).
    [CrossRef]
  13. Y. Z. Wang, Fish-Eye Lens Optics (Academic, 2006).
  14. L. S. An, Applied Optics (Academic, 2006).
  15. W. J. Feng, B. F. Zhang, and Z. L. Cao, “Omni-directional vision parameter calibration and rectification based on fish-eye lens,” J. Tianjin Univ. 44, 417 (2011).
  16. J. J. Kumler and M. Bauer, “Fish-eye lens designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).
    [CrossRef]
  17. R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLA (Academic, 2008).
  18. A. Ray and D. C. Srivastava, “Non-linear least squares ellipse fitting using the genetic algorithm with applications to strain analysis,” J. Struct. Geol. 30, 1593–1602 (2008).
    [CrossRef]
  19. K. Kanatani and P. Rangarajan, “Hyper least squares fitting of circles and ellipses,” Comput. Stat. Data Anal. 55, 2197–2208 (2011).
    [CrossRef]
  20. W. M. Li, Q. Y. Yu, H. Z. Hu, Q. Wang, and W. P. Deng, “Iteration algorithm of surface fitting in the detection of light-spot position,” Opt. Tech. 30, 33 (2004).
  21. X. Zhang and L. S. Ge, “Application and research on pre-calibration of image center,” Comput. Technol. Development 17, 44 (2007).
  22. R. K. Lenz and R. Y. Tsai, “Techniques for calibration of the scale factor and image center for high accuracy 3-D machine vision metrology,” IEEE Trans. Pattern Anal. Machine Intell. 10, 713–720 (1988).
    [CrossRef]
  23. H. W. Gao, C. D. Cheng, and B. Li, “Camera calibration method for optical center,” Opto-Electron. Eng. 33, 68(2006).

2011

L. Krüger and C. Wöhler, “Accurate chequerboard corner localisation for camera calibration,” Pattern Recogn. Lett. 32, 1428–1430 (2011).
[CrossRef]

W. J. Feng, B. F. Zhang, and Z. L. Cao, “Omni-directional vision parameter calibration and rectification based on fish-eye lens,” J. Tianjin Univ. 44, 417 (2011).

K. Kanatani and P. Rangarajan, “Hyper least squares fitting of circles and ellipses,” Comput. Stat. Data Anal. 55, 2197–2208 (2011).
[CrossRef]

2010

C. Hughes, R. McFeely, P. Denny, M. Glavin, and E. Jones, “Equidistant (fθ) fish-eye perspective with application in distortion centre estimation,” Image Vis. Comput. 28, 538–551 (2010).
[CrossRef]

J. Courbon, Y. Mezouar, N. Guénard, and P. Martinet, “Vision-based navigation of unmanned aerial vehicles,” Control Engineering Practice 18, 789–799 (2010).
[CrossRef]

Y. Z. Wang, “Biomimetic staring infrared imaging omnidirectional detection technology,” Chinese Sci. Bull. 55, 3073–3080 (2010).
[CrossRef]

G. Q. Yang, “The calibration algorithm of fish-eye image,” Image Technology 3, 16 (2010).

2009

D. Schneider, E. Schwalbe, and H. G. Maas, “Validation of geometric models for fisheye lenses,” ISPRS J. Photogramm. Remote Sens. 64, 259–266 (2009).
[CrossRef]

2008

A. Ray and D. C. Srivastava, “Non-linear least squares ellipse fitting using the genetic algorithm with applications to strain analysis,” J. Struct. Geol. 30, 1593–1602 (2008).
[CrossRef]

2007

X. Zhang and L. S. Ge, “Application and research on pre-calibration of image center,” Comput. Technol. Development 17, 44 (2007).

D. Wang and M. Zhu, “Camera’s image center measurement method based of distorted symmetry,” Chin. J. Electron Dev. 30, 103 (2007).

R. Hartley and S. S. Kang, “Parameter-free radial distortion correction with center of distortion estimation,” IEEE Trans. Pattern Anal. Machine Intell. 29, 1309–1321 (2007).
[CrossRef]

2006

J. Kannala and S. S. Brandt, “A generic camera model and calibration method for conventional, wide-angle, and fish-eye lenses,” IEEE Trans. Pattern Anal. Machine Intell. 28, 1335–1340 (2006).
[CrossRef]

H. W. Gao, C. D. Cheng, and B. Li, “Camera calibration method for optical center,” Opto-Electron. Eng. 33, 68(2006).

2004

W. M. Li, Q. Y. Yu, H. Z. Hu, Q. Wang, and W. P. Deng, “Iteration algorithm of surface fitting in the detection of light-spot position,” Opt. Tech. 30, 33 (2004).

2003

C. R. Baxter, M. A. Massie, and T. J Bartolac, “Operational testing and applications of the AIRS FPA with infrared fisheye optics,” Proc. SPIE 4820, 515–524 (2003).
[CrossRef]

2000

J. J. Kumler and M. Bauer, “Fish-eye lens designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).
[CrossRef]

1996

S. Shah and J. K. Aggarwal, “Intrinsic parameter calibration procedure for a (high-distortion) fish-eye lens camera with distortion model and accuracy estimation,” Pattern Recogn. 29, 1775–1788 (1996).
[CrossRef]

1988

R. K. Lenz and R. Y. Tsai, “Techniques for calibration of the scale factor and image center for high accuracy 3-D machine vision metrology,” IEEE Trans. Pattern Anal. Machine Intell. 10, 713–720 (1988).
[CrossRef]

Aggarwal, J. K.

S. Shah and J. K. Aggarwal, “Intrinsic parameter calibration procedure for a (high-distortion) fish-eye lens camera with distortion model and accuracy estimation,” Pattern Recogn. 29, 1775–1788 (1996).
[CrossRef]

An, L. S.

L. S. An, Applied Optics (Academic, 2006).

Bartolac, T. J

C. R. Baxter, M. A. Massie, and T. J Bartolac, “Operational testing and applications of the AIRS FPA with infrared fisheye optics,” Proc. SPIE 4820, 515–524 (2003).
[CrossRef]

Bauer, M.

J. J. Kumler and M. Bauer, “Fish-eye lens designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).
[CrossRef]

Baxter, C. R.

C. R. Baxter, M. A. Massie, and T. J Bartolac, “Operational testing and applications of the AIRS FPA with infrared fisheye optics,” Proc. SPIE 4820, 515–524 (2003).
[CrossRef]

Brandt, S. S.

J. Kannala and S. S. Brandt, “A generic camera model and calibration method for conventional, wide-angle, and fish-eye lenses,” IEEE Trans. Pattern Anal. Machine Intell. 28, 1335–1340 (2006).
[CrossRef]

Cao, Z. L.

W. J. Feng, B. F. Zhang, and Z. L. Cao, “Omni-directional vision parameter calibration and rectification based on fish-eye lens,” J. Tianjin Univ. 44, 417 (2011).

Cheng, C. D.

H. W. Gao, C. D. Cheng, and B. Li, “Camera calibration method for optical center,” Opto-Electron. Eng. 33, 68(2006).

Courbon, J.

J. Courbon, Y. Mezouar, N. Guénard, and P. Martinet, “Vision-based navigation of unmanned aerial vehicles,” Control Engineering Practice 18, 789–799 (2010).
[CrossRef]

Deng, W. P.

W. M. Li, Q. Y. Yu, H. Z. Hu, Q. Wang, and W. P. Deng, “Iteration algorithm of surface fitting in the detection of light-spot position,” Opt. Tech. 30, 33 (2004).

Denny, P.

C. Hughes, R. McFeely, P. Denny, M. Glavin, and E. Jones, “Equidistant (fθ) fish-eye perspective with application in distortion centre estimation,” Image Vis. Comput. 28, 538–551 (2010).
[CrossRef]

Eddins, S. L.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLA (Academic, 2008).

Feng, W. J.

W. J. Feng, B. F. Zhang, and Z. L. Cao, “Omni-directional vision parameter calibration and rectification based on fish-eye lens,” J. Tianjin Univ. 44, 417 (2011).

Gao, H. W.

H. W. Gao, C. D. Cheng, and B. Li, “Camera calibration method for optical center,” Opto-Electron. Eng. 33, 68(2006).

Ge, L. S.

X. Zhang and L. S. Ge, “Application and research on pre-calibration of image center,” Comput. Technol. Development 17, 44 (2007).

Glavin, M.

C. Hughes, R. McFeely, P. Denny, M. Glavin, and E. Jones, “Equidistant (fθ) fish-eye perspective with application in distortion centre estimation,” Image Vis. Comput. 28, 538–551 (2010).
[CrossRef]

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLA (Academic, 2008).

Guénard, N.

J. Courbon, Y. Mezouar, N. Guénard, and P. Martinet, “Vision-based navigation of unmanned aerial vehicles,” Control Engineering Practice 18, 789–799 (2010).
[CrossRef]

Hartley, R.

R. Hartley and S. S. Kang, “Parameter-free radial distortion correction with center of distortion estimation,” IEEE Trans. Pattern Anal. Machine Intell. 29, 1309–1321 (2007).
[CrossRef]

Hu, H. Z.

W. M. Li, Q. Y. Yu, H. Z. Hu, Q. Wang, and W. P. Deng, “Iteration algorithm of surface fitting in the detection of light-spot position,” Opt. Tech. 30, 33 (2004).

Hughes, C.

C. Hughes, R. McFeely, P. Denny, M. Glavin, and E. Jones, “Equidistant (fθ) fish-eye perspective with application in distortion centre estimation,” Image Vis. Comput. 28, 538–551 (2010).
[CrossRef]

Jones, E.

C. Hughes, R. McFeely, P. Denny, M. Glavin, and E. Jones, “Equidistant (fθ) fish-eye perspective with application in distortion centre estimation,” Image Vis. Comput. 28, 538–551 (2010).
[CrossRef]

Ju, H. H.

L. Wang and H. H. Ju, “Extrinsic calibration of a fisheye camera and inertial measurement unit,” in Proceedings of IEEE Conference on Machine Learning and Cybernetics (IEEE, 2009), pp. 2427–2432.

Kanatani, K.

K. Kanatani and P. Rangarajan, “Hyper least squares fitting of circles and ellipses,” Comput. Stat. Data Anal. 55, 2197–2208 (2011).
[CrossRef]

Kang, S. S.

R. Hartley and S. S. Kang, “Parameter-free radial distortion correction with center of distortion estimation,” IEEE Trans. Pattern Anal. Machine Intell. 29, 1309–1321 (2007).
[CrossRef]

Kannala, J.

J. Kannala and S. S. Brandt, “A generic camera model and calibration method for conventional, wide-angle, and fish-eye lenses,” IEEE Trans. Pattern Anal. Machine Intell. 28, 1335–1340 (2006).
[CrossRef]

Krüger, L.

L. Krüger and C. Wöhler, “Accurate chequerboard corner localisation for camera calibration,” Pattern Recogn. Lett. 32, 1428–1430 (2011).
[CrossRef]

Kumler, J. J.

J. J. Kumler and M. Bauer, “Fish-eye lens designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).
[CrossRef]

Lenz, R. K.

R. K. Lenz and R. Y. Tsai, “Techniques for calibration of the scale factor and image center for high accuracy 3-D machine vision metrology,” IEEE Trans. Pattern Anal. Machine Intell. 10, 713–720 (1988).
[CrossRef]

Li, B.

H. W. Gao, C. D. Cheng, and B. Li, “Camera calibration method for optical center,” Opto-Electron. Eng. 33, 68(2006).

Li, W. M.

W. M. Li, Q. Y. Yu, H. Z. Hu, Q. Wang, and W. P. Deng, “Iteration algorithm of surface fitting in the detection of light-spot position,” Opt. Tech. 30, 33 (2004).

Maas, H. G.

D. Schneider, E. Schwalbe, and H. G. Maas, “Validation of geometric models for fisheye lenses,” ISPRS J. Photogramm. Remote Sens. 64, 259–266 (2009).
[CrossRef]

Martinet, P.

J. Courbon, Y. Mezouar, N. Guénard, and P. Martinet, “Vision-based navigation of unmanned aerial vehicles,” Control Engineering Practice 18, 789–799 (2010).
[CrossRef]

Massie, M. A.

C. R. Baxter, M. A. Massie, and T. J Bartolac, “Operational testing and applications of the AIRS FPA with infrared fisheye optics,” Proc. SPIE 4820, 515–524 (2003).
[CrossRef]

McFeely, R.

C. Hughes, R. McFeely, P. Denny, M. Glavin, and E. Jones, “Equidistant (fθ) fish-eye perspective with application in distortion centre estimation,” Image Vis. Comput. 28, 538–551 (2010).
[CrossRef]

Mezouar, Y.

J. Courbon, Y. Mezouar, N. Guénard, and P. Martinet, “Vision-based navigation of unmanned aerial vehicles,” Control Engineering Practice 18, 789–799 (2010).
[CrossRef]

Rangarajan, P.

K. Kanatani and P. Rangarajan, “Hyper least squares fitting of circles and ellipses,” Comput. Stat. Data Anal. 55, 2197–2208 (2011).
[CrossRef]

Ray, A.

A. Ray and D. C. Srivastava, “Non-linear least squares ellipse fitting using the genetic algorithm with applications to strain analysis,” J. Struct. Geol. 30, 1593–1602 (2008).
[CrossRef]

Schneider, D.

D. Schneider, E. Schwalbe, and H. G. Maas, “Validation of geometric models for fisheye lenses,” ISPRS J. Photogramm. Remote Sens. 64, 259–266 (2009).
[CrossRef]

Schwalbe, E.

D. Schneider, E. Schwalbe, and H. G. Maas, “Validation of geometric models for fisheye lenses,” ISPRS J. Photogramm. Remote Sens. 64, 259–266 (2009).
[CrossRef]

Shah, S.

S. Shah and J. K. Aggarwal, “Intrinsic parameter calibration procedure for a (high-distortion) fish-eye lens camera with distortion model and accuracy estimation,” Pattern Recogn. 29, 1775–1788 (1996).
[CrossRef]

Srivastava, D. C.

A. Ray and D. C. Srivastava, “Non-linear least squares ellipse fitting using the genetic algorithm with applications to strain analysis,” J. Struct. Geol. 30, 1593–1602 (2008).
[CrossRef]

Tsai, R. Y.

R. K. Lenz and R. Y. Tsai, “Techniques for calibration of the scale factor and image center for high accuracy 3-D machine vision metrology,” IEEE Trans. Pattern Anal. Machine Intell. 10, 713–720 (1988).
[CrossRef]

Wang, D.

D. Wang and M. Zhu, “Camera’s image center measurement method based of distorted symmetry,” Chin. J. Electron Dev. 30, 103 (2007).

Wang, L.

L. Wang and H. H. Ju, “Extrinsic calibration of a fisheye camera and inertial measurement unit,” in Proceedings of IEEE Conference on Machine Learning and Cybernetics (IEEE, 2009), pp. 2427–2432.

Wang, Q.

W. M. Li, Q. Y. Yu, H. Z. Hu, Q. Wang, and W. P. Deng, “Iteration algorithm of surface fitting in the detection of light-spot position,” Opt. Tech. 30, 33 (2004).

Wang, Y. Z.

Y. Z. Wang, “Biomimetic staring infrared imaging omnidirectional detection technology,” Chinese Sci. Bull. 55, 3073–3080 (2010).
[CrossRef]

Y. Z. Wang, Fish-Eye Lens Optics (Academic, 2006).

Wöhler, C.

L. Krüger and C. Wöhler, “Accurate chequerboard corner localisation for camera calibration,” Pattern Recogn. Lett. 32, 1428–1430 (2011).
[CrossRef]

Woods, R. E.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLA (Academic, 2008).

Yang, G. Q.

G. Q. Yang, “The calibration algorithm of fish-eye image,” Image Technology 3, 16 (2010).

Yu, Q. Y.

W. M. Li, Q. Y. Yu, H. Z. Hu, Q. Wang, and W. P. Deng, “Iteration algorithm of surface fitting in the detection of light-spot position,” Opt. Tech. 30, 33 (2004).

Zhang, B. F.

W. J. Feng, B. F. Zhang, and Z. L. Cao, “Omni-directional vision parameter calibration and rectification based on fish-eye lens,” J. Tianjin Univ. 44, 417 (2011).

Zhang, X.

X. Zhang and L. S. Ge, “Application and research on pre-calibration of image center,” Comput. Technol. Development 17, 44 (2007).

Zhu, M.

D. Wang and M. Zhu, “Camera’s image center measurement method based of distorted symmetry,” Chin. J. Electron Dev. 30, 103 (2007).

Chin. J. Electron Dev.

D. Wang and M. Zhu, “Camera’s image center measurement method based of distorted symmetry,” Chin. J. Electron Dev. 30, 103 (2007).

Chinese Sci. Bull.

Y. Z. Wang, “Biomimetic staring infrared imaging omnidirectional detection technology,” Chinese Sci. Bull. 55, 3073–3080 (2010).
[CrossRef]

Comput. Stat. Data Anal.

K. Kanatani and P. Rangarajan, “Hyper least squares fitting of circles and ellipses,” Comput. Stat. Data Anal. 55, 2197–2208 (2011).
[CrossRef]

Comput. Technol. Development

X. Zhang and L. S. Ge, “Application and research on pre-calibration of image center,” Comput. Technol. Development 17, 44 (2007).

Control Engineering Practice

J. Courbon, Y. Mezouar, N. Guénard, and P. Martinet, “Vision-based navigation of unmanned aerial vehicles,” Control Engineering Practice 18, 789–799 (2010).
[CrossRef]

IEEE Trans. Pattern Anal. Machine Intell.

R. Hartley and S. S. Kang, “Parameter-free radial distortion correction with center of distortion estimation,” IEEE Trans. Pattern Anal. Machine Intell. 29, 1309–1321 (2007).
[CrossRef]

J. Kannala and S. S. Brandt, “A generic camera model and calibration method for conventional, wide-angle, and fish-eye lenses,” IEEE Trans. Pattern Anal. Machine Intell. 28, 1335–1340 (2006).
[CrossRef]

R. K. Lenz and R. Y. Tsai, “Techniques for calibration of the scale factor and image center for high accuracy 3-D machine vision metrology,” IEEE Trans. Pattern Anal. Machine Intell. 10, 713–720 (1988).
[CrossRef]

Image Technology

G. Q. Yang, “The calibration algorithm of fish-eye image,” Image Technology 3, 16 (2010).

Image Vis. Comput.

C. Hughes, R. McFeely, P. Denny, M. Glavin, and E. Jones, “Equidistant (fθ) fish-eye perspective with application in distortion centre estimation,” Image Vis. Comput. 28, 538–551 (2010).
[CrossRef]

ISPRS J. Photogramm. Remote Sens.

D. Schneider, E. Schwalbe, and H. G. Maas, “Validation of geometric models for fisheye lenses,” ISPRS J. Photogramm. Remote Sens. 64, 259–266 (2009).
[CrossRef]

J. Struct. Geol.

A. Ray and D. C. Srivastava, “Non-linear least squares ellipse fitting using the genetic algorithm with applications to strain analysis,” J. Struct. Geol. 30, 1593–1602 (2008).
[CrossRef]

J. Tianjin Univ.

W. J. Feng, B. F. Zhang, and Z. L. Cao, “Omni-directional vision parameter calibration and rectification based on fish-eye lens,” J. Tianjin Univ. 44, 417 (2011).

Opt. Tech.

W. M. Li, Q. Y. Yu, H. Z. Hu, Q. Wang, and W. P. Deng, “Iteration algorithm of surface fitting in the detection of light-spot position,” Opt. Tech. 30, 33 (2004).

Opto-Electron. Eng.

H. W. Gao, C. D. Cheng, and B. Li, “Camera calibration method for optical center,” Opto-Electron. Eng. 33, 68(2006).

Pattern Recogn.

S. Shah and J. K. Aggarwal, “Intrinsic parameter calibration procedure for a (high-distortion) fish-eye lens camera with distortion model and accuracy estimation,” Pattern Recogn. 29, 1775–1788 (1996).
[CrossRef]

Pattern Recogn. Lett.

L. Krüger and C. Wöhler, “Accurate chequerboard corner localisation for camera calibration,” Pattern Recogn. Lett. 32, 1428–1430 (2011).
[CrossRef]

Proc. SPIE

C. R. Baxter, M. A. Massie, and T. J Bartolac, “Operational testing and applications of the AIRS FPA with infrared fisheye optics,” Proc. SPIE 4820, 515–524 (2003).
[CrossRef]

J. J. Kumler and M. Bauer, “Fish-eye lens designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).
[CrossRef]

Other

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLA (Academic, 2008).

Y. Z. Wang, Fish-Eye Lens Optics (Academic, 2006).

L. S. An, Applied Optics (Academic, 2006).

L. Wang and H. H. Ju, “Extrinsic calibration of a fisheye camera and inertial measurement unit,” in Proceedings of IEEE Conference on Machine Learning and Cybernetics (IEEE, 2009), pp. 2427–2432.

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Figures (8)

Fig. 1.
Fig. 1.

Illustration of the fisheye image (a) and the example (b) as the fisheye image fills a circular area inside the image frame.

Fig. 2.
Fig. 2.

Illustration of the fisheye image (a) and the example (b) as the area of the image frame is less than the fisheye image.

Fig. 3.
Fig. 3.

Object-image relationship of the fisheye camera.

Fig. 4.
Fig. 4.

Calibration board (a) and its image captured by the fisheye camera (b).

Fig. 5.
Fig. 5.

Edges extracted from the calibration image (a) and the shapes fitted by ellipse algorithm (b).

Fig. 6.
Fig. 6.

Actual imaging area of the projection ellipse (a) and its fitting shape by Gaussian algorithm (b).

Fig. 7.
Fig. 7.

Board images with the labelled distortion center.

Fig. 8.
Fig. 8.

Error of ellipse fitting (a) and the relative error of Gaussian surface fitting (b).

Tables (2)

Tables Icon

Table 1. Calibration Results of the Fisheye Distortion Centers

Tables Icon

Table 2. Comparison of Our Method with the Methods in the References

Equations (24)

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

y=fω,
dy=fdω.
βr=dyrdω,
βr=fr.
βt=fr·(ωsinω).
βt=βr·(ωsinω).
Au2+Buv+Cv2+Du+Ev+1=0.
J=1Nij=1Ni[Auj2+Bujvj+Cvj2+Duj+Evj+1]2,
JA=JB=JC=JD=JE=0.
[j=1Niuj4j=1Niuj3vjj=1Niuj2vj2j=1Niuj3j=1Niuj2vjj=1Niuj3vjj=1Niuj2vj2j=1Niujvj3j=1Niuj2vjj=1Niujvj2j=1Niuj2vj2j=1Niujvj3j=1Nivj4j=1Niujvj2j=1Nivj3j=1Niuj3j=1Niuj2vjj=1Niujvj2j=1Niuj2j=1Niujvjj=1Niuj2vjj=1Niujvj2j=1Nivj3j=1Niujvjj=1Nivj2][ABCDE]=[j=1Niuj2j=1Niujvjj=1Nivj2j=1Niujj=1Nivj].
{ueo=BE2CD4ACB2veo=BD2AE4ACB2.
f(u,v)=G·exp[(uu0)22σu2(vv0)22σv2],
f·lnf=(lnGu022σu2v022σv2)·f+u0σu2(uf)+v0σv2(vf)12σu2(u2f)12σv2(v2f).
H=KL,
E=HKL.
MSE=1NE22=1NETE.
K=QR,
QTE=QTHQTKL=QTHRL.
E22=QTE22=QTHRL22.
QTH=[ST],R=[R10],
E22=SR1L22+T22.
u0=l2/2l4,v0=l3/2l5.
MEi=(j=1Ni[Auj2+Bujvj+Cvj2+Duj+Evj+1]2)1/2Ni.
REi=|ft(ui,vi)ff(ui,vi)ft(ui,vi)|×100%,

Metrics