Abstract

We present an approach to recovering scenes deteriorated by reflections off a semi-reflecting medium. The approach is based on imaging through a polarizer at two different orientations. We analyze the image-formation process, taking into account changes in reflection and polarization properties owing to internal reflections within the medium. Reconstruction by inverting this process requires estimation of the incidence angle (the inclination of the transparent medium). We estimate this angle by seeking the value that leads to decorrelation of the estimated scenes that are automatically and uniquely labeled reflected–transmitted.

© 1999 Optical Society of America

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References

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  1. H. Fujikake, K. Takizawa, T. Aida, H. Kikuchi, T. Fujii, and M. Kawakita, Opt. Rev. 5, 93 (1998).
    [CrossRef]
  2. Y. Y. Schechner, N. Kiryati, and R. Basri, in IEEE International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York), pp. 1061–1066.
  3. W. A. Shurcliff and S. S. Ballard, Polarized Light (Van Nostrand, Princeton, N.J., 1964), pp. 100–104.
  4. N. Ohnishi, K. Kumaki, T. Yamamura, and T. Tanaka, in Computer Vision-ECCV ’96, R. Buxton and R. Cipolla, eds., Vol. 1065 of Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1996), pp. 636–646.
    [CrossRef]
  5. D. Weinshall, Nature 341, 737 (1989).
    [CrossRef] [PubMed]
  6. L. B. Wolff, J. Opt. Soc. Am. A 11, 2935 (1994).
    [CrossRef]
  7. H. Farid and E. H. Adelson, “Separating reflections from images by use of independent-components analysis,” J. Opt. Soc. Am. A (to be published).
  8. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 38–45.
  9. Link to the raw images through http://www.ee.technion.ac.il/~yoavs/publications .

1998

H. Fujikake, K. Takizawa, T. Aida, H. Kikuchi, T. Fujii, and M. Kawakita, Opt. Rev. 5, 93 (1998).
[CrossRef]

1994

1989

D. Weinshall, Nature 341, 737 (1989).
[CrossRef] [PubMed]

Adelson, E. H.

H. Farid and E. H. Adelson, “Separating reflections from images by use of independent-components analysis,” J. Opt. Soc. Am. A (to be published).

Aida, T.

H. Fujikake, K. Takizawa, T. Aida, H. Kikuchi, T. Fujii, and M. Kawakita, Opt. Rev. 5, 93 (1998).
[CrossRef]

Ballard, S. S.

W. A. Shurcliff and S. S. Ballard, Polarized Light (Van Nostrand, Princeton, N.J., 1964), pp. 100–104.

Basri, R.

Y. Y. Schechner, N. Kiryati, and R. Basri, in IEEE International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York), pp. 1061–1066.

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 38–45.

Farid, H.

H. Farid and E. H. Adelson, “Separating reflections from images by use of independent-components analysis,” J. Opt. Soc. Am. A (to be published).

Fujii, T.

H. Fujikake, K. Takizawa, T. Aida, H. Kikuchi, T. Fujii, and M. Kawakita, Opt. Rev. 5, 93 (1998).
[CrossRef]

Fujikake, H.

H. Fujikake, K. Takizawa, T. Aida, H. Kikuchi, T. Fujii, and M. Kawakita, Opt. Rev. 5, 93 (1998).
[CrossRef]

Kawakita, M.

H. Fujikake, K. Takizawa, T. Aida, H. Kikuchi, T. Fujii, and M. Kawakita, Opt. Rev. 5, 93 (1998).
[CrossRef]

Kikuchi, H.

H. Fujikake, K. Takizawa, T. Aida, H. Kikuchi, T. Fujii, and M. Kawakita, Opt. Rev. 5, 93 (1998).
[CrossRef]

Kiryati, N.

Y. Y. Schechner, N. Kiryati, and R. Basri, in IEEE International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York), pp. 1061–1066.

Kumaki, K.

N. Ohnishi, K. Kumaki, T. Yamamura, and T. Tanaka, in Computer Vision-ECCV ’96, R. Buxton and R. Cipolla, eds., Vol. 1065 of Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1996), pp. 636–646.
[CrossRef]

Ohnishi, N.

N. Ohnishi, K. Kumaki, T. Yamamura, and T. Tanaka, in Computer Vision-ECCV ’96, R. Buxton and R. Cipolla, eds., Vol. 1065 of Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1996), pp. 636–646.
[CrossRef]

Schechner, Y. Y.

Y. Y. Schechner, N. Kiryati, and R. Basri, in IEEE International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York), pp. 1061–1066.

Shurcliff, W. A.

W. A. Shurcliff and S. S. Ballard, Polarized Light (Van Nostrand, Princeton, N.J., 1964), pp. 100–104.

Takizawa, K.

H. Fujikake, K. Takizawa, T. Aida, H. Kikuchi, T. Fujii, and M. Kawakita, Opt. Rev. 5, 93 (1998).
[CrossRef]

Tanaka, T.

N. Ohnishi, K. Kumaki, T. Yamamura, and T. Tanaka, in Computer Vision-ECCV ’96, R. Buxton and R. Cipolla, eds., Vol. 1065 of Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1996), pp. 636–646.
[CrossRef]

Weinshall, D.

D. Weinshall, Nature 341, 737 (1989).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 38–45.

Wolff, L. B.

Yamamura, T.

N. Ohnishi, K. Kumaki, T. Yamamura, and T. Tanaka, in Computer Vision-ECCV ’96, R. Buxton and R. Cipolla, eds., Vol. 1065 of Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1996), pp. 636–646.
[CrossRef]

J. Opt. Soc. Am. A

Nature

D. Weinshall, Nature 341, 737 (1989).
[CrossRef] [PubMed]

Opt. Rev.

H. Fujikake, K. Takizawa, T. Aida, H. Kikuchi, T. Fujii, and M. Kawakita, Opt. Rev. 5, 93 (1998).
[CrossRef]

Other

Y. Y. Schechner, N. Kiryati, and R. Basri, in IEEE International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York), pp. 1061–1066.

W. A. Shurcliff and S. S. Ballard, Polarized Light (Van Nostrand, Princeton, N.J., 1964), pp. 100–104.

N. Ohnishi, K. Kumaki, T. Yamamura, and T. Tanaka, in Computer Vision-ECCV ’96, R. Buxton and R. Cipolla, eds., Vol. 1065 of Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1996), pp. 636–646.
[CrossRef]

H. Farid and E. H. Adelson, “Separating reflections from images by use of independent-components analysis,” J. Opt. Soc. Am. A (to be published).

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 38–45.

Link to the raw images through http://www.ee.technion.ac.il/~yoavs/publications .

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Figures (4)

Fig. 1
Fig. 1

Ratios of the polarizing effects in a single air–glass interface and in a glass window.

Fig. 2
Fig. 2

For each φtrue there are domains (white) where a zero of the correlation exists at a wrongly assumed angle φ (beside the correct one).

Fig. 3
Fig. 3

Top left, f. Top right, the reflection is weaker in f, but the image is still unclear. Middle row, the reconstructed virtual (left) and real (right) scenes, based on the automatic detection of the AOI. Bottom right, the real object imaged without the interfering glass window. Bottom left, the virtual object photographed by a technique that removes the objects behind the window.

Fig. 4
Fig. 4

At the estimated incidence angle of 27° the reconstructions are decorrelated.

Equations (13)

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R˜=R+T2Rl=0R2l=21+RR
fα=f+f2+f+f2cos2α-θ,
f=fθ=IRR˜/2+ITT˜/2,
f=fθ+90°=IRR~/2+ITT~/2.
IˆTφ=2R~φR~φ-R~φf-2R~φR~φ-R~φf,
IˆRφ=2-2R~φR~φ-R~φf-2-2R~φR~φ-R~φf.
IˆTφ=1-ρIT+ρIR,  IˆRφ=1-τIR+τIT,
ρφtrue,φ=R˜φR˜φtrue-R˜φtrueR˜φR˜φ-R˜φ,
τφtrue,φ=T~φT~φtrue-T~φtrueT~φT~φ-T~φ.
φˆ=φ: CorrIˆTφ,IˆRφ=0.
CovIˆT,IˆR=τ1-ρVarIT+ρ1-τVarIR.
CovIˆT,IˆR=τ1-ρVarIRVarITVarIR-η,
fθα=θ,θ+90°=0.

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