Abstract

We present herein a technique to calibrate fisheye lenses using cross diffractive optical elements. The setup generated a robust and accurate virtual calibration grid, and the calibration was performed by rotating the camera around two axes. We propose a comparison of three fisheye mathematical models and an evaluation of the number of images in the calibration process. The comparison of our experimental data according to the 3D calibration object results showed that our technique is efficient and reliable.

© 2013 Optical Society of America

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References

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  1. R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw-Hill, 1995).
  2. A. Basu and S. Licardie, “Modeling fish-eye lenses,” in International Conference on Intelligent Robots and Systems ’93, Yokohama, Japan, 26–30 July (IEEE, 1993), pp. 1822–1828.
  3. A. W. Fitzgibbon, “Simultaneous linear estimation of multiple view geometry and lens distortion,” in Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2001), pp. 125–132.
  4. 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]
  5. C. Hughes, P. Denny, M. Glavin, and E. Jones, “Equidistant fish-eye calibration and rectification by vanishing point extraction,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 2289–2296 (2010).
    [CrossRef]
  6. S. K. Nayar, “Catadioptric omnidirectional camera,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 482–488.
  7. M. M. Fleck, “Perspective projection: the wrong imaging model,” Technical report 95-01 (University of Iowa, 1995).
  8. A. Basuand and S. Licardie, “Alternative models for fish-eye lenses,” Pattern Recogn. Lett. 16, 433–441 (1995).
    [CrossRef]
  9. F. Devernay and O. Faugeras, “Straight lines have to be straight,” Mach. Vis. Appl. 13, 14–24 (2001).
    [CrossRef]
  10. E. Schwalbe, “Geometric modelling and calibration of fisheye lens camera systems,” in Proceedings of 2nd Panoramic Photogrammetry Workshop, International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences 36, Part 5/W8 (2005).
  11. J. Kannala and S. S. Brandt, “A generic camera calibration method for fish-eye lenses,” in International Conference on Pattern Recognition, 2004 (Cambridge, 2004), pp. 10–13.
  12. B. Micusik and T. Pajdla, “Structure from motion with wide circular field of view cameras,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 1135–1149 (2006).
    [CrossRef]
  13. H. Li and R. Hartley, “Plane-based calibration and auto-calibration of a fish-eye camera,” in 7th Asian Conference on Computer Vision (Springer, 2006), Vol. 3851, pp. 21–30.
  14. 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. Mach. Intell. 28, 1335–1340 (2006).
    [CrossRef]
  15. C. Hughes, P. Denny, E. Jones, and M. Glavin, “Accuracy of fish-eye lens models,” Appl. Opt. 49, 3338–3347 (2010).
    [CrossRef]
  16. J. Yang and Z. Liu, “Fisheye camera calibration with two pairs of vanishing points,” in International Conference on Information Technology and Computer Science 2009 (IEEE, 2009), Vol. 1, pp. 321–324.
  17. S. Thibault, A. Arfaoui, and P. Désaulniers, “Cross-diffractive optical elements for wide angle geometric camera calibration,” Opt. Lett. 36, 4770–4772 (2011).
    [CrossRef]
  18. M. Bauer, D. Grießbach, A. Hermerschmidt, S. Krüger, M. Scheele, and A. Schischmanow, “Geometrical camera calibration with diffractive optical elements,” Opt. Express 16, 20241–20248 (2008).
    [CrossRef]
  19. A. Arfaoui and F. Plante, “Camera calibration using composed cubic splines,” Geomatica 65, 189–197 (2011).
    [CrossRef]
  20. A. Vyas, M. B. Roopashree, and B. R. Prasad, “Centroid detection by Gaussian pattern matching in adaptive optics,” Int. J. Comput. Appl. 1, 30–35 (2010).
    [CrossRef]

2011

2010

C. Hughes, P. Denny, E. Jones, and M. Glavin, “Accuracy of fish-eye lens models,” Appl. Opt. 49, 3338–3347 (2010).
[CrossRef]

A. Vyas, M. B. Roopashree, and B. R. Prasad, “Centroid detection by Gaussian pattern matching in adaptive optics,” Int. J. Comput. Appl. 1, 30–35 (2010).
[CrossRef]

C. Hughes, P. Denny, M. Glavin, and E. Jones, “Equidistant fish-eye calibration and rectification by vanishing point extraction,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 2289–2296 (2010).
[CrossRef]

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

2006

B. Micusik and T. Pajdla, “Structure from motion with wide circular field of view cameras,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 1135–1149 (2006).
[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. Mach. Intell. 28, 1335–1340 (2006).
[CrossRef]

2001

F. Devernay and O. Faugeras, “Straight lines have to be straight,” Mach. Vis. Appl. 13, 14–24 (2001).
[CrossRef]

1995

A. Basuand and S. Licardie, “Alternative models for fish-eye lenses,” Pattern Recogn. Lett. 16, 433–441 (1995).
[CrossRef]

Arfaoui, A.

Basu, A.

A. Basu and S. Licardie, “Modeling fish-eye lenses,” in International Conference on Intelligent Robots and Systems ’93, Yokohama, Japan, 26–30 July (IEEE, 1993), pp. 1822–1828.

Basuand, A.

A. Basuand and S. Licardie, “Alternative models for fish-eye lenses,” Pattern Recogn. Lett. 16, 433–441 (1995).
[CrossRef]

Bauer, M.

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. Mach. Intell. 28, 1335–1340 (2006).
[CrossRef]

J. Kannala and S. S. Brandt, “A generic camera calibration method for fish-eye lenses,” in International Conference on Pattern Recognition, 2004 (Cambridge, 2004), pp. 10–13.

Denny, P.

C. Hughes, P. Denny, M. Glavin, and E. Jones, “Equidistant fish-eye calibration and rectification by vanishing point extraction,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 2289–2296 (2010).
[CrossRef]

C. Hughes, P. Denny, E. Jones, and M. Glavin, “Accuracy of fish-eye lens models,” Appl. Opt. 49, 3338–3347 (2010).
[CrossRef]

Désaulniers, P.

Devernay, F.

F. Devernay and O. Faugeras, “Straight lines have to be straight,” Mach. Vis. Appl. 13, 14–24 (2001).
[CrossRef]

Faugeras, O.

F. Devernay and O. Faugeras, “Straight lines have to be straight,” Mach. Vis. Appl. 13, 14–24 (2001).
[CrossRef]

Fitzgibbon, A. W.

A. W. Fitzgibbon, “Simultaneous linear estimation of multiple view geometry and lens distortion,” in Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2001), pp. 125–132.

Fleck, M. M.

M. M. Fleck, “Perspective projection: the wrong imaging model,” Technical report 95-01 (University of Iowa, 1995).

Glavin, M.

C. Hughes, P. Denny, M. Glavin, and E. Jones, “Equidistant fish-eye calibration and rectification by vanishing point extraction,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 2289–2296 (2010).
[CrossRef]

C. Hughes, P. Denny, E. Jones, and M. Glavin, “Accuracy of fish-eye lens models,” Appl. Opt. 49, 3338–3347 (2010).
[CrossRef]

Grießbach, D.

Hartley, R.

H. Li and R. Hartley, “Plane-based calibration and auto-calibration of a fish-eye camera,” in 7th Asian Conference on Computer Vision (Springer, 2006), Vol. 3851, pp. 21–30.

Hermerschmidt, A.

Hughes, C.

C. Hughes, P. Denny, M. Glavin, and E. Jones, “Equidistant fish-eye calibration and rectification by vanishing point extraction,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 2289–2296 (2010).
[CrossRef]

C. Hughes, P. Denny, E. Jones, and M. Glavin, “Accuracy of fish-eye lens models,” Appl. Opt. 49, 3338–3347 (2010).
[CrossRef]

Jain, R.

R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw-Hill, 1995).

Jones, E.

C. Hughes, P. Denny, M. Glavin, and E. Jones, “Equidistant fish-eye calibration and rectification by vanishing point extraction,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 2289–2296 (2010).
[CrossRef]

C. Hughes, P. Denny, E. Jones, and M. Glavin, “Accuracy of fish-eye lens models,” Appl. Opt. 49, 3338–3347 (2010).
[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. Mach. Intell. 28, 1335–1340 (2006).
[CrossRef]

J. Kannala and S. S. Brandt, “A generic camera calibration method for fish-eye lenses,” in International Conference on Pattern Recognition, 2004 (Cambridge, 2004), pp. 10–13.

Kasturi, R.

R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw-Hill, 1995).

Krüger, S.

Li, H.

H. Li and R. Hartley, “Plane-based calibration and auto-calibration of a fish-eye camera,” in 7th Asian Conference on Computer Vision (Springer, 2006), Vol. 3851, pp. 21–30.

Licardie, S.

A. Basuand and S. Licardie, “Alternative models for fish-eye lenses,” Pattern Recogn. Lett. 16, 433–441 (1995).
[CrossRef]

A. Basu and S. Licardie, “Modeling fish-eye lenses,” in International Conference on Intelligent Robots and Systems ’93, Yokohama, Japan, 26–30 July (IEEE, 1993), pp. 1822–1828.

Liu, Z.

J. Yang and Z. Liu, “Fisheye camera calibration with two pairs of vanishing points,” in International Conference on Information Technology and Computer Science 2009 (IEEE, 2009), Vol. 1, pp. 321–324.

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]

Micusik, B.

B. Micusik and T. Pajdla, “Structure from motion with wide circular field of view cameras,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 1135–1149 (2006).
[CrossRef]

Nayar, S. K.

S. K. Nayar, “Catadioptric omnidirectional camera,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 482–488.

Pajdla, T.

B. Micusik and T. Pajdla, “Structure from motion with wide circular field of view cameras,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 1135–1149 (2006).
[CrossRef]

Plante, F.

A. Arfaoui and F. Plante, “Camera calibration using composed cubic splines,” Geomatica 65, 189–197 (2011).
[CrossRef]

Prasad, B. R.

A. Vyas, M. B. Roopashree, and B. R. Prasad, “Centroid detection by Gaussian pattern matching in adaptive optics,” Int. J. Comput. Appl. 1, 30–35 (2010).
[CrossRef]

Roopashree, M. B.

A. Vyas, M. B. Roopashree, and B. R. Prasad, “Centroid detection by Gaussian pattern matching in adaptive optics,” Int. J. Comput. Appl. 1, 30–35 (2010).
[CrossRef]

Scheele, M.

Schischmanow, A.

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]

Schunck, B. G.

R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw-Hill, 1995).

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]

E. Schwalbe, “Geometric modelling and calibration of fisheye lens camera systems,” in Proceedings of 2nd Panoramic Photogrammetry Workshop, International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences 36, Part 5/W8 (2005).

Thibault, S.

Vyas, A.

A. Vyas, M. B. Roopashree, and B. R. Prasad, “Centroid detection by Gaussian pattern matching in adaptive optics,” Int. J. Comput. Appl. 1, 30–35 (2010).
[CrossRef]

Yang, J.

J. Yang and Z. Liu, “Fisheye camera calibration with two pairs of vanishing points,” in International Conference on Information Technology and Computer Science 2009 (IEEE, 2009), Vol. 1, pp. 321–324.

Appl. Opt.

Geomatica

A. Arfaoui and F. Plante, “Camera calibration using composed cubic splines,” Geomatica 65, 189–197 (2011).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

B. Micusik and T. Pajdla, “Structure from motion with wide circular field of view cameras,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 1135–1149 (2006).
[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. Mach. Intell. 28, 1335–1340 (2006).
[CrossRef]

C. Hughes, P. Denny, M. Glavin, and E. Jones, “Equidistant fish-eye calibration and rectification by vanishing point extraction,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 2289–2296 (2010).
[CrossRef]

Int. J. Comput. Appl.

A. Vyas, M. B. Roopashree, and B. R. Prasad, “Centroid detection by Gaussian pattern matching in adaptive optics,” Int. J. Comput. Appl. 1, 30–35 (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]

Mach. Vis. Appl.

F. Devernay and O. Faugeras, “Straight lines have to be straight,” Mach. Vis. Appl. 13, 14–24 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Pattern Recogn. Lett.

A. Basuand and S. Licardie, “Alternative models for fish-eye lenses,” Pattern Recogn. Lett. 16, 433–441 (1995).
[CrossRef]

Other

E. Schwalbe, “Geometric modelling and calibration of fisheye lens camera systems,” in Proceedings of 2nd Panoramic Photogrammetry Workshop, International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences 36, Part 5/W8 (2005).

J. Kannala and S. S. Brandt, “A generic camera calibration method for fish-eye lenses,” in International Conference on Pattern Recognition, 2004 (Cambridge, 2004), pp. 10–13.

S. K. Nayar, “Catadioptric omnidirectional camera,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 482–488.

M. M. Fleck, “Perspective projection: the wrong imaging model,” Technical report 95-01 (University of Iowa, 1995).

R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw-Hill, 1995).

A. Basu and S. Licardie, “Modeling fish-eye lenses,” in International Conference on Intelligent Robots and Systems ’93, Yokohama, Japan, 26–30 July (IEEE, 1993), pp. 1822–1828.

A. W. Fitzgibbon, “Simultaneous linear estimation of multiple view geometry and lens distortion,” in Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2001), pp. 125–132.

J. Yang and Z. Liu, “Fisheye camera calibration with two pairs of vanishing points,” in International Conference on Information Technology and Computer Science 2009 (IEEE, 2009), Vol. 1, pp. 321–324.

H. Li and R. Hartley, “Plane-based calibration and auto-calibration of a fish-eye camera,” in 7th Asian Conference on Computer Vision (Springer, 2006), Vol. 3851, pp. 21–30.

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Figures (7)

Fig. 1.
Fig. 1.

Calibration setup with rotatable camera.

Fig. 2.
Fig. 2.

Layout of the grid images recorded by fisheye camera in nine different orientations.

Fig. 3.
Fig. 3.

Fisheye projection.

Fig. 4.
Fig. 4.

Diagram of calibration algorithm.

Fig. 5.
Fig. 5.

Pixel coordinates for all images computed by centroid algorithm.

Fig. 6.
Fig. 6.

Remaining residuals for all images after calibration (in pixels).

Fig. 7.
Fig. 7.

Targets of the 3D calibration object.

Tables (5)

Tables Icon

Table 1. Calibration Results Using the Equidistant Model

Tables Icon

Table 2. Calibration Results Using the Third-Order Model

Tables Icon

Table 3. Calibration Results Using the Fifth-Order Model

Tables Icon

Table 4. Calibration Comparison

Tables Icon

Table 5. RMSE for Fisheye Camera Calibration Using CDOE and 3D Object

Equations (10)

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

P=[X,Y,Z,0]T,
X=λfx+rx+(λfy+ry)sin(α),
Y=(λfy+ry)cos(α),
Z=(1(X2+Y2))1/2,
r=fθ,
r=k1θ+k2θ3+k3θ5+,
P=(R3×3001)·P.
p=[sinθcosφ,sinθsinφ,cosθ]T.
(uv)=(αu00αv)(xy)+(u0v0),
Etot=k=1Nj=1M(rcjkrojk)2,

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