Abstract

Distortion is an undesirable aberration found in optical imaging systems, necessitating numerical calibration. However, the fact that image distortion changes with observation distance can be used for ranging. This study developed a rapid, passive-ranging technique, which is simple, incurs low costs, results in minimal interference, and requires few parameters. After determining the location of reference points, the relationship between the normalized mean distortion of images and observation distance is described using two mathematical models, one of which is based on distortion theory and the other is derived from the curve fitting of the experimental results. Analyzing the instantaneous rate of image distortion can also assist in ranging. The proposed technique demonstrates high sensitivity at closer observation distances, but loses effectiveness as observation distances increase.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  19. Wikipedia, “Fresnel diffraction,” http://en.wikipedia.org/wiki/Fresnel_diffraction .
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    [CrossRef]
  21. J. C. Wyant and K. Creath, Applied Optics and Optical Engineering: Basic Wavefront Aberration Theory (Academic, 1993), pp. 15–18.

2008

J. Wang, F. Shi, J. Zhang, and Y. Liu, “A new calibration model of camera lens distortion,” Pattern Recogn. 41, 607–615 (2008).
[CrossRef]

2004

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging 13, 231–240 (2004).
[CrossRef]

2003

1992

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

1988

P. J. Besl, “Active, optical range imaging sensors,” Mach. Vis. Appl. 1, 127–152 (1988).
[CrossRef]

1987

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]

1978

1971

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

1955

1919

A. Conrady, “Decentered lens systems,” Mon. Not. R. Astron. Soc. 79, 384–390 (1919).

Besl, P. J.

P. J. Besl, “Active, optical range imaging sensors,” Mach. Vis. Appl. 1, 127–152 (1988).
[CrossRef]

Blais, F.

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging 13, 231–240 (2004).
[CrossRef]

Bogunovic, D.

Brown, D. C.

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

D. C. Brown, “The simultaneous determination of the orientation and lens distortion of a photogrammetric camera,” (1956).

Cohen, P.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

Conrady, A.

A. Conrady, “Decentered lens systems,” Mon. Not. R. Astron. Soc. 79, 384–390 (1919).

Creath, K.

J. C. Wyant and K. Creath, Applied Optics and Optical Engineering: Basic Wavefront Aberration Theory (Academic, 1993), pp. 15–18.

Dold, J.

J. Dold, Ein hybrides photogrammetrisches Industriemeßsystem höchster Genauigkeit und seine Überprüfung (Schriftenreihe Studiengang Vermessungswesen, Universität der Bundeswehr, München, 1997).

Faugeras, O.

O. Faugeras, Three-Dimensional Computer Vision: A Geometric Viewpoint (MIT, 1993).

Fitzgibbon, A. W.

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

Harvey, J. E.

Herniou, M.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Clarendon, 1950).

Kostenko, A. A.

A. A. Kostenko, A. I. Nosich, and I. A. Tishchenko, “Radar prehistory, Soviet side: three-coordinate L-band pulse radar developed in Ukraine in the late 30’s,” in Proceedings of IEEE International Symposium on Antenna and Propagating Society (IEEE, 2001), pp. 44–47.

Krywonos, A.

Liu, Y.

J. Wang, F. Shi, J. Zhang, and Y. Liu, “A new calibration model of camera lens distortion,” Pattern Recogn. 41, 607–615 (2008).
[CrossRef]

Magill, A. A.

Mahajan, V. N.

V. N. Mahajan, Optical Imaging and Aberrations: Part I. Ray Geometrical Optics, Vol. PM45 of the SPIE Monographs (SPIE, 1998).

Nosich, A. I.

A. A. Kostenko, A. I. Nosich, and I. A. Tishchenko, “Radar prehistory, Soviet side: three-coordinate L-band pulse radar developed in Ukraine in the late 30’s,” in Proceedings of IEEE International Symposium on Antenna and Propagating Society (IEEE, 2001), pp. 44–47.

Shack, R. V.

Shi, F.

J. Wang, F. Shi, J. Zhang, and Y. Liu, “A new calibration model of camera lens distortion,” Pattern Recogn. 41, 607–615 (2008).
[CrossRef]

Stein, G. P.

G. P. Stein, “Lens distortion calibration using point correspondences,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 602–608.

Tishchenko, I. A.

A. A. Kostenko, A. I. Nosich, and I. A. Tishchenko, “Radar prehistory, Soviet side: three-coordinate L-band pulse radar developed in Ukraine in the late 30’s,” in Proceedings of IEEE International Symposium on Antenna and Propagating Society (IEEE, 2001), pp. 44–47.

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]

Wang, J.

J. Wang, F. Shi, J. Zhang, and Y. Liu, “A new calibration model of camera lens distortion,” Pattern Recogn. 41, 607–615 (2008).
[CrossRef]

Weng, J.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

Wyant, J. C.

J. C. Wyant and K. Creath, Applied Optics and Optical Engineering: Basic Wavefront Aberration Theory (Academic, 1993), pp. 15–18.

Zhang, J.

J. Wang, F. Shi, J. Zhang, and Y. Liu, “A new calibration model of camera lens distortion,” Pattern Recogn. 41, 607–615 (2008).
[CrossRef]

Zhang, Z.

Z. Zhang, “On the epipolar geometry between two images with lens distortion,” in 13th International Conference on Pattern Recognition, (IEEE, 1996), pp. 407–411.

Appl. Opt.

IEEE J. Robot. Autom.

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. Pattern Anal. Mach. Intell.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

J. Electron. Imaging

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging 13, 231–240 (2004).
[CrossRef]

J. Opt. Soc. Am.

Mach. Vis. Appl.

P. J. Besl, “Active, optical range imaging sensors,” Mach. Vis. Appl. 1, 127–152 (1988).
[CrossRef]

Mon. Not. R. Astron. Soc.

A. Conrady, “Decentered lens systems,” Mon. Not. R. Astron. Soc. 79, 384–390 (1919).

Pattern Recogn.

J. Wang, F. Shi, J. Zhang, and Y. Liu, “A new calibration model of camera lens distortion,” Pattern Recogn. 41, 607–615 (2008).
[CrossRef]

Photo. Eng.

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

Other

A. A. Kostenko, A. I. Nosich, and I. A. Tishchenko, “Radar prehistory, Soviet side: three-coordinate L-band pulse radar developed in Ukraine in the late 30’s,” in Proceedings of IEEE International Symposium on Antenna and Propagating Society (IEEE, 2001), pp. 44–47.

V. N. Mahajan, Optical Imaging and Aberrations: Part I. Ray Geometrical Optics, Vol. PM45 of the SPIE Monographs (SPIE, 1998).

H. H. Hopkins, Wave Theory of Aberrations (Clarendon, 1950).

Wikipedia, “Fresnel diffraction,” http://en.wikipedia.org/wiki/Fresnel_diffraction .

J. Dold, Ein hybrides photogrammetrisches Industriemeßsystem höchster Genauigkeit und seine Überprüfung (Schriftenreihe Studiengang Vermessungswesen, Universität der Bundeswehr, München, 1997).

J. C. Wyant and K. Creath, Applied Optics and Optical Engineering: Basic Wavefront Aberration Theory (Academic, 1993), pp. 15–18.

D. C. Brown, “The simultaneous determination of the orientation and lens distortion of a photogrammetric camera,” (1956).

Z. Zhang, “On the epipolar geometry between two images with lens distortion,” in 13th International Conference on Pattern Recognition, (IEEE, 1996), pp. 407–411.

G. P. Stein, “Lens distortion calibration using point correspondences,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 602–608.

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

O. Faugeras, Three-Dimensional Computer Vision: A Geometric Viewpoint (MIT, 1993).

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Figures (15)

Fig. 1.
Fig. 1.

Perspective model for distortion analysis.

Fig. 2.
Fig. 2.

(a) Printed checkerboard sample and (b) setup of camera, showing sample, tripods, and slide for distortion imaging at various distances.

Fig. 3.
Fig. 3.

Measurement range of camera and intervals between shots along the z axis.

Fig. 4.
Fig. 4.

Sample image used for distortion analysis at (a) z=20cm and (b) z=70cm. The red-dashed square indicates the observation range for the fixed point.

Fig. 5.
Fig. 5.

Normalized mean distortion curves for fixed-point observation.

Fig. 6.
Fig. 6.

Sample image used for distortion analysis at (a) z=20cm and (b) z=70cm. The light blue dashed square indicates the observation range for fixed angle of view.

Fig. 7.
Fig. 7.

Normalized mean distortion curves for fixed-angle-of-view observations (60°).

Fig. 8.
Fig. 8.

Relationship between normalized mean distortion and radial distance at various observation distances.

Fig. 9.
Fig. 9.

Distortion contribution curves of Term 1 and Term 2 in Eq. (9).

Fig. 10.
Fig. 10.

Distortion contribution curves of Term 1 and Term 2 in Eq. (10).

Fig. 11.
Fig. 11.

Distortion-distance curves obtained experimentally as calculated using Eq. (8) or Eq. (9) and Eq. (11) for fixed-point observation.

Fig. 12.
Fig. 12.

Distortion-distance curves obtained experimentally as calculated using Eqs. (8) and (11) for fixed-angle-of-view observation.

Fig. 13.
Fig. 13.

Relationship between deviations in distortion and observation distance: (a) fixed-point observation and (b) fixed-angle-of-view observation.

Fig. 14.
Fig. 14.

Instantaneous rate of distortion using Eqs. (14)–(16) for fixed-point observation.

Fig. 15.
Fig. 15.

Instantaneous rate of distortion using Eqs. (14)–(16) for fixed angle-of-view observation.

Equations (17)

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

[xuyu]=[xdyd][1+k1s2+k2s4+].
[xuyu]=(ss1)[xdx0ydy0],
s=s1+k0+k1s2+k2s4+,
[xuyuf]=fz0·[xpypz0].
Dz=1z[U1s(s2s2)+U2(s4s4)+U3(s6s6)].
Fd2z·λ,
W^d=d^4·(S^z^)3,
d¯=i=1n(lili)li·n,
d¯=αz+βz3+γ,
d¯p=[13.13z]T1+[15482.14z3]T2+[0.05],
da¯=[16.64z]T1+[13191.94z3]T2+[0.04],
d¯=1σ+μ·z,
z=13.9+16.95d¯p,
z=12.82+18.18d¯a,
|Vd|=|d¯z|=μ(σ+μ·z)2,
|Vd|=|d¯z|=αz2+3βz4+γ.
|Vd|=d¯zd¯z+δuδu,

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