Abstract

Polarized light carries valuable information about where the light has been and the various physical parameters that have been acting upon it. Thus there are several methods in computer vision that make it possible to obtain information on the observed object by studying the polarization of light reflected on the object. Most studies using this principle are interested in the determination of the object orientation in three-dimensional space. The basis of these studies rests on the estimate of a parameter that connects the orientation of the observed surface and the polarization of the reflected light wave. This parameter is the angle of polarization φ, also called the orientation of polarization. Generally, one using these methods estimates the φ angle by observing the reflected light wave through a linear polarizing filter and grabbing multiple frames for different angular orientations of the polarizer. So, between each acquisition, the polarizer is rotated of an angle θ relative to a horizontal reference axis. The accuracy of the φ estimate is then directly related to the positioning of the polarizer. But, in practice, it is difficult to guarantee the exact value of the rotation of this polarizer. It is all the more difficult to guarantee the reliability of positioning in time. We thus propose a robust and accurate solution, based on the self-calibration principle, for measuring the orientation of partially polarized light using CCD cameras. In contrast to methods generally discussed in computer vision journals, our estimate of the angle of polarization is independent of the reliability of the polarizer positioning.

© 2001 Optical Society of America

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References

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  1. K. Koshikawa, Y. Shirai, “A model-based recognition of glossy objects using their polarimetric properties,” Adv. Rob. 2, 137–147 (1987).
    [CrossRef]
  2. B. F. Jones, P. T. Fairney, “Recognition of shiny dielectric objects by analyzing the polarization of reflected light,” Image Vision Comput. 7, 253–258 (1989).
    [CrossRef]
  3. L. B. Wolff, T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 635–657 (1991).
    [CrossRef]
  4. L. B. Wolff, “Liquid crystal polarization camera,” IEEE Trans. Rob. Autom. 13, 195–203 (1997).
    [CrossRef]
  5. A. M. Wallace, B. Liang, E. Trucco, J. Clark, “Improving depth image acquisition using polarized light,” Int. J. Comput. Vision 32, 87–109 (1999).
    [CrossRef]
  6. E. Collet, Polarized Light: Fundamentals and Applications (Marcel Dekker, New York), 1993.
  7. E. Joubert, P. Miche, R. Debrie, “3-D surface reconstruction using a polarization state analysis,” J. Opt. 26, 2–8 (1995).
    [CrossRef]
  8. S. J. Maybank, O. D. Faugeras, “Theory of self-calibration of a moving camera,” Int. J. Comput. Vision 8, 123–151 (1992).
    [CrossRef]
  9. T. Q. Long, O. D. Faugeras, “Self-calibration of a moving camera from point correspondences and fundamental matrices,” Int. J. Comput. Vision 22, 261–289 (1997).
    [CrossRef]

1999

A. M. Wallace, B. Liang, E. Trucco, J. Clark, “Improving depth image acquisition using polarized light,” Int. J. Comput. Vision 32, 87–109 (1999).
[CrossRef]

1997

T. Q. Long, O. D. Faugeras, “Self-calibration of a moving camera from point correspondences and fundamental matrices,” Int. J. Comput. Vision 22, 261–289 (1997).
[CrossRef]

L. B. Wolff, “Liquid crystal polarization camera,” IEEE Trans. Rob. Autom. 13, 195–203 (1997).
[CrossRef]

1995

E. Joubert, P. Miche, R. Debrie, “3-D surface reconstruction using a polarization state analysis,” J. Opt. 26, 2–8 (1995).
[CrossRef]

1992

S. J. Maybank, O. D. Faugeras, “Theory of self-calibration of a moving camera,” Int. J. Comput. Vision 8, 123–151 (1992).
[CrossRef]

1991

L. B. Wolff, T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 635–657 (1991).
[CrossRef]

1989

B. F. Jones, P. T. Fairney, “Recognition of shiny dielectric objects by analyzing the polarization of reflected light,” Image Vision Comput. 7, 253–258 (1989).
[CrossRef]

1987

K. Koshikawa, Y. Shirai, “A model-based recognition of glossy objects using their polarimetric properties,” Adv. Rob. 2, 137–147 (1987).
[CrossRef]

Boult, T. E.

L. B. Wolff, T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 635–657 (1991).
[CrossRef]

Clark, J.

A. M. Wallace, B. Liang, E. Trucco, J. Clark, “Improving depth image acquisition using polarized light,” Int. J. Comput. Vision 32, 87–109 (1999).
[CrossRef]

Collet, E.

E. Collet, Polarized Light: Fundamentals and Applications (Marcel Dekker, New York), 1993.

Debrie, R.

E. Joubert, P. Miche, R. Debrie, “3-D surface reconstruction using a polarization state analysis,” J. Opt. 26, 2–8 (1995).
[CrossRef]

Fairney, P. T.

B. F. Jones, P. T. Fairney, “Recognition of shiny dielectric objects by analyzing the polarization of reflected light,” Image Vision Comput. 7, 253–258 (1989).
[CrossRef]

Faugeras, O. D.

T. Q. Long, O. D. Faugeras, “Self-calibration of a moving camera from point correspondences and fundamental matrices,” Int. J. Comput. Vision 22, 261–289 (1997).
[CrossRef]

S. J. Maybank, O. D. Faugeras, “Theory of self-calibration of a moving camera,” Int. J. Comput. Vision 8, 123–151 (1992).
[CrossRef]

Jones, B. F.

B. F. Jones, P. T. Fairney, “Recognition of shiny dielectric objects by analyzing the polarization of reflected light,” Image Vision Comput. 7, 253–258 (1989).
[CrossRef]

Joubert, E.

E. Joubert, P. Miche, R. Debrie, “3-D surface reconstruction using a polarization state analysis,” J. Opt. 26, 2–8 (1995).
[CrossRef]

Koshikawa, K.

K. Koshikawa, Y. Shirai, “A model-based recognition of glossy objects using their polarimetric properties,” Adv. Rob. 2, 137–147 (1987).
[CrossRef]

Liang, B.

A. M. Wallace, B. Liang, E. Trucco, J. Clark, “Improving depth image acquisition using polarized light,” Int. J. Comput. Vision 32, 87–109 (1999).
[CrossRef]

Long, T. Q.

T. Q. Long, O. D. Faugeras, “Self-calibration of a moving camera from point correspondences and fundamental matrices,” Int. J. Comput. Vision 22, 261–289 (1997).
[CrossRef]

Maybank, S. J.

S. J. Maybank, O. D. Faugeras, “Theory of self-calibration of a moving camera,” Int. J. Comput. Vision 8, 123–151 (1992).
[CrossRef]

Miche, P.

E. Joubert, P. Miche, R. Debrie, “3-D surface reconstruction using a polarization state analysis,” J. Opt. 26, 2–8 (1995).
[CrossRef]

Shirai, Y.

K. Koshikawa, Y. Shirai, “A model-based recognition of glossy objects using their polarimetric properties,” Adv. Rob. 2, 137–147 (1987).
[CrossRef]

Trucco, E.

A. M. Wallace, B. Liang, E. Trucco, J. Clark, “Improving depth image acquisition using polarized light,” Int. J. Comput. Vision 32, 87–109 (1999).
[CrossRef]

Wallace, A. M.

A. M. Wallace, B. Liang, E. Trucco, J. Clark, “Improving depth image acquisition using polarized light,” Int. J. Comput. Vision 32, 87–109 (1999).
[CrossRef]

Wolff, L. B.

L. B. Wolff, “Liquid crystal polarization camera,” IEEE Trans. Rob. Autom. 13, 195–203 (1997).
[CrossRef]

L. B. Wolff, T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 635–657 (1991).
[CrossRef]

Adv. Rob.

K. Koshikawa, Y. Shirai, “A model-based recognition of glossy objects using their polarimetric properties,” Adv. Rob. 2, 137–147 (1987).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

L. B. Wolff, T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 635–657 (1991).
[CrossRef]

IEEE Trans. Rob. Autom.

L. B. Wolff, “Liquid crystal polarization camera,” IEEE Trans. Rob. Autom. 13, 195–203 (1997).
[CrossRef]

Image Vision Comput.

B. F. Jones, P. T. Fairney, “Recognition of shiny dielectric objects by analyzing the polarization of reflected light,” Image Vision Comput. 7, 253–258 (1989).
[CrossRef]

Int. J. Comput. Vision

S. J. Maybank, O. D. Faugeras, “Theory of self-calibration of a moving camera,” Int. J. Comput. Vision 8, 123–151 (1992).
[CrossRef]

T. Q. Long, O. D. Faugeras, “Self-calibration of a moving camera from point correspondences and fundamental matrices,” Int. J. Comput. Vision 22, 261–289 (1997).
[CrossRef]

A. M. Wallace, B. Liang, E. Trucco, J. Clark, “Improving depth image acquisition using polarized light,” Int. J. Comput. Vision 32, 87–109 (1999).
[CrossRef]

J. Opt.

E. Joubert, P. Miche, R. Debrie, “3-D surface reconstruction using a polarization state analysis,” J. Opt. 26, 2–8 (1995).
[CrossRef]

Other

E. Collet, Polarized Light: Fundamentals and Applications (Marcel Dekker, New York), 1993.

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Figures (13)

Fig. 1
Fig. 1

Principle of determination of the polarization angle φ after specular reflection.

Fig. 2
Fig. 2

Principle of operation of a linear polarizing filter.

Fig. 3
Fig. 3

Projection of the components E and E on the principal axis of the polarizing filter.

Fig. 4
Fig. 4

Principle of the proposed method.

Fig. 5
Fig. 5

Orthogonal decomposition of the E ⊥proj field by the polarizing cube beam splitter.

Fig. 6
Fig. 6

Orthogonal decomposition of the E ‖proj field by the polarizing cube beam splitter.

Fig. 7
Fig. 7

Proposed measurement system with two CCD cameras, a polarizing cube beam splitter, and a linear polarizing filter.

Fig. 8
Fig. 8

Simulation of the error made by the existing methods on the φ estimate when an offset is introduced on the θ values.

Fig. 9
Fig. 9

Simulation of the error made by the proposed method on the φ estimate when an offset is introduced on the θ values.

Fig. 10
Fig. 10

Device allowing estimation of the precision of our measurement system.

Fig. 11
Fig. 11

Comparison between experimental and theoretical values of the intensities I VERTI and I HORI as a function of the angle θ.

Fig. 12
Fig. 12

Experimental accuracy on the phi estimate for a redundancy r = 0.

Fig. 13
Fig. 13

Experimental accuracy on the phi estimate for a redundancy r = 12.

Equations (20)

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

Eproj=E cosθ+π-φ,
Eproj=E cosφ-π2-θ.
Iout=I0cos2θ-φ+β cos2φ-π2-θ+ID2,
Iout=A cos2θ-φ+B,
IVERTI=E2cos2φ-θsin2θ+E2cos2×φ-π2-θsin2θ+ID2sin2θ,
IHORI=E2cos2φ-θcos2θ+E2cos2×φ-π2-θcos2θ+ID2cos2θ.
IVERTI=I01-βsin2θ×cos2φ-θ+βI0+ID/2I01-β,
IHORI=I01-βcos2θ×cos2φ-θ+βI0+ID/2I01-β,
IVERTI=A sin2θcos2φ-θ+B,
IHORI=A cos2θcos2φ-θ+B.
IVERTI=αA sin2θcos2φ-θ+B,
IHORI=A cos2θcos2φ-θ+B.
S=i=1neVERTIi2+eHORIi2,
eVERTI=Pϕ-IVERTIeHORI=Qϕ-IHORI Eϕ.
Vϕ=Eϕ0+Eϕi Δϕi,
Vϕ=L+AΔϕ,
minΔϕnVTWV.
Ωϕ=2VTW Vϕ=2VTWA=0  ATWV=0,ATWL+AΔϕ=ATWL+ATWAΔϕ=0,
Δϕ=-ATWA-1ATWL.
q=trI-AATWA-1AT=rN.

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