Abstract

A method is proposed for obtaining surface orientations of transparent objects by use of polarization in highlight. Since the highlight, the specular component of light reflected from objects, is observed only near the specular direction, it reveals only limited parts of an object’s surface. To obtain the orientations of the whole surface of an object, we employ a spherical extended light source. We report the experimental apparatus, a shape recovery algorithm, and a performance evaluation.

© 1999 Optical Society of America

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References

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  1. T. Tanitagai, Applied Optics: Guide of Optical Measurement (Maruzen, Tokyo, 1988).
  2. K. Ikeuchi, “Determining surface orientations of specular surfaces by using the the photometric stereo method,” IEEE Trans. Pattern. Anal. Mach. Intell. 3, 661–669 (1981).
    [CrossRef] [PubMed]
  3. S. K. Nayar, K. Ikeuchi, T. Kanade, “Determining shape and reflectance of hybrid surface by photometric sampling,” IEEE Trans. Rob. Autom. 6, 418–431 (1990).
    [CrossRef]
  4. K. Koshikawa, “A polarimetric approach to shape understanding of glossy objects,” in Proceedings of International Joint Conference on Artificial Intelligence (Morgan Kaufmann, San Mateo, Calif., 1979), pp. 493–495.
  5. L. B. Wolff, T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Pattern. Anal. Mach. Intell. 13, 167–189 (1991).
    [CrossRef]
  6. L. B. Wolff, “Spectral and polarization stereo methods using a single light source,” in Proceedings of International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 708–715.
  7. K. E. Torrance, E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105–1114 (1967).
    [CrossRef]
  8. S. K. Nayar, K. Ikeuchi, T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern. Anal. Mach. Intell. 13, 611–634 (1991).
    [CrossRef]
  9. S. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
    [CrossRef]
  10. M. Ohtsu, Modern Optical Science (Asakura, Tokyo, 1994).

1991 (2)

L. B. Wolff, T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Pattern. Anal. Mach. Intell. 13, 167–189 (1991).
[CrossRef]

S. K. Nayar, K. Ikeuchi, T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern. Anal. Mach. Intell. 13, 611–634 (1991).
[CrossRef]

1990 (1)

S. K. Nayar, K. Ikeuchi, T. Kanade, “Determining shape and reflectance of hybrid surface by photometric sampling,” IEEE Trans. Rob. Autom. 6, 418–431 (1990).
[CrossRef]

1985 (1)

S. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

1981 (1)

K. Ikeuchi, “Determining surface orientations of specular surfaces by using the the photometric stereo method,” IEEE Trans. Pattern. Anal. Mach. Intell. 3, 661–669 (1981).
[CrossRef] [PubMed]

1967 (1)

Boult, T. E.

L. B. Wolff, T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Pattern. Anal. Mach. Intell. 13, 167–189 (1991).
[CrossRef]

Ikeuchi, K.

S. K. Nayar, K. Ikeuchi, T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern. Anal. Mach. Intell. 13, 611–634 (1991).
[CrossRef]

S. K. Nayar, K. Ikeuchi, T. Kanade, “Determining shape and reflectance of hybrid surface by photometric sampling,” IEEE Trans. Rob. Autom. 6, 418–431 (1990).
[CrossRef]

K. Ikeuchi, “Determining surface orientations of specular surfaces by using the the photometric stereo method,” IEEE Trans. Pattern. Anal. Mach. Intell. 3, 661–669 (1981).
[CrossRef] [PubMed]

Kanade, T.

S. K. Nayar, K. Ikeuchi, T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern. Anal. Mach. Intell. 13, 611–634 (1991).
[CrossRef]

S. K. Nayar, K. Ikeuchi, T. Kanade, “Determining shape and reflectance of hybrid surface by photometric sampling,” IEEE Trans. Rob. Autom. 6, 418–431 (1990).
[CrossRef]

Koshikawa, K.

K. Koshikawa, “A polarimetric approach to shape understanding of glossy objects,” in Proceedings of International Joint Conference on Artificial Intelligence (Morgan Kaufmann, San Mateo, Calif., 1979), pp. 493–495.

Nayar, S. K.

S. K. Nayar, K. Ikeuchi, T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern. Anal. Mach. Intell. 13, 611–634 (1991).
[CrossRef]

S. K. Nayar, K. Ikeuchi, T. Kanade, “Determining shape and reflectance of hybrid surface by photometric sampling,” IEEE Trans. Rob. Autom. 6, 418–431 (1990).
[CrossRef]

Ohtsu, M.

M. Ohtsu, Modern Optical Science (Asakura, Tokyo, 1994).

Shafer, S.

S. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

Sparrow, E. M.

Tanitagai, T.

T. Tanitagai, Applied Optics: Guide of Optical Measurement (Maruzen, Tokyo, 1988).

Torrance, K. E.

Wolff, L. B.

L. B. Wolff, T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Pattern. Anal. Mach. Intell. 13, 167–189 (1991).
[CrossRef]

L. B. Wolff, “Spectral and polarization stereo methods using a single light source,” in Proceedings of International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 708–715.

Color Res. Appl. (1)

S. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

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

K. Ikeuchi, “Determining surface orientations of specular surfaces by using the the photometric stereo method,” IEEE Trans. Pattern. Anal. Mach. Intell. 3, 661–669 (1981).
[CrossRef] [PubMed]

L. B. Wolff, T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Pattern. Anal. Mach. Intell. 13, 167–189 (1991).
[CrossRef]

S. K. Nayar, K. Ikeuchi, T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern. Anal. Mach. Intell. 13, 611–634 (1991).
[CrossRef]

IEEE Trans. Rob. Autom. (1)

S. K. Nayar, K. Ikeuchi, T. Kanade, “Determining shape and reflectance of hybrid surface by photometric sampling,” IEEE Trans. Rob. Autom. 6, 418–431 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (4)

T. Tanitagai, Applied Optics: Guide of Optical Measurement (Maruzen, Tokyo, 1988).

M. Ohtsu, Modern Optical Science (Asakura, Tokyo, 1994).

K. Koshikawa, “A polarimetric approach to shape understanding of glossy objects,” in Proceedings of International Joint Conference on Artificial Intelligence (Morgan Kaufmann, San Mateo, Calif., 1979), pp. 493–495.

L. B. Wolff, “Spectral and polarization stereo methods using a single light source,” in Proceedings of International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 708–715.

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Figures (9)

Fig. 1
Fig. 1

Mechanism of reflection.

Fig. 2
Fig. 2

Fresnel reflection.

Fig. 3
Fig. 3

Surface normal of object.

Fig. 4
Fig. 4

Simulation result.

Fig. 5
Fig. 5

Experimental setup.

Fig. 6
Fig. 6

Experimental results: (a) orientation of the plane of incidence; (b) angle of incidence.

Fig. 7
Fig. 7

Experimental setup.

Fig. 8
Fig. 8

Result of measurement of the object shape.

Fig. 9
Fig. 9

Result of flaw inspection.

Equations (14)

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

Ea=A exp{i[ωt-k1(x sin ϕ1+z cos ϕ1)]},
Er=R exp{i[ωt-k1(x sin ϕ1-z cos ϕ1)]},
Et=T exp{i[ωt-k2(x sin ϕ2+z cos ϕ2)]},
n1 sin ϕ1=n2 sin ϕ2.
Eaj+Erj=Etj,Haj+Hrj=Htj(j=x, y),
r=ErEa=tan(ϕ1-ϕ2)tan(ϕ1+ϕ2),
r=ErEa=-sin(ϕ1-ϕ2)sin(ϕ1+ϕ2).
I=nE2/2μ0,
F=tan2(ϕ1-ϕ2)tan2(ϕ1+ϕ2),
F=sin2(ϕ1-ϕ2)sin2(ϕ1+ϕ2).
ϕb=arctan(n2/n1).
Imax=FF+F Is,Imin=FF+F Is.
ρ=Imax-IminImax+Imin.
ρ=2 sin ϕ tan ϕ(n2-sin2 ϕ)1/2n2-sin2 ϕ+sin2 ϕ tan2 ϕ.

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