Abstract

Techniques for modeling an object through observation are very important in object recognition and virtual reality. A wide variety of techniques have been developed for modeling objects with opaque surfaces, whereas less attention has been paid to objects with transparent surfaces. A transparent surface has only surface reflection; it has little body reflection. We present a new method for obtaining surface orientations of transparent surfaces through analysis of the degree of polarization in surface reflection and emission in visible and far-infrared wavelengths, respectively. This parameter, the polarization degree of reflected light at the visible wavelengths, is used for determining the surface orientation at a surface point. The polarization degree at visible wavelengths provides two possible solutions, and the proposed method uses the polarization degree at far-infrared wavelengths to resolve this ambiguity.

© 2002 Optical Society of America

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  1. K. Ikeuchi, “Determining surface orientations of specular surfaces by using the photometric stereo method,” IEEE Trans. Pattern Anal. Mach. Intell. 3, 661–669 (1981).
    [CrossRef] [PubMed]
  2. 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]
  3. Y. Sato, M. D. Wheeler, K. Ikeuchi, “Object shape and reflectance modeling from observation,” in Proceedings of SIGGRAPH 97 (Addison-Wesley, Boston, Mass., 1997), pp. 379–387.
  4. M. Oren, S. K. Nayar, “A theory of specular surface geometry,” Int. J. Comput. Vis. 24, 105–124 (1997).
    [CrossRef]
  5. K. Koshikawa, “A polarimetric approach to shape understanding of glossy objects,” in Proceedings of the International Joint Conference on Artificial Intelligence (Morgan Kaufmann, Los Altos, Calif., 1979), pp. 493–495.
  6. K. Koshikawa, Y. Shirai, “A model-based recognition of glossy objects using their polarimetrical properties,” Adv. Robot. 2, 137–147 (1987).
    [CrossRef]
  7. L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 1059–1071 (1990).
    [CrossRef]
  8. 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]
  9. S. Rahmann, “Polarization images: a geometric interpretation of shape analysis,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 2000), pp. 542–546.
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  14. Y. Schechner, J. Shamir, N. Kiryuati, “Polarization-based decorrelation of transparent layers: the inclination angle of an invisible surface,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 814–819.
  15. D. E. Zongker, D. M. Warner, B. Curless, D. H. Salesin, “Environmental matting and compositing,” in Proceedings of SIGGRAPH 99 (Addison-Wesley, Boston, Mass., 1999), pp. 205–214.
  16. M. Saito, Y. Sato, K. Ikeuchi, H. Kashiwagi, “Measurement of surface orientations of transparent objects using polarization in highlight,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 381–386.
  17. M. Saito, Y. Sato, K. Ikeuchi, H. Kashiwagi, “Measurement of surface orientations of transparent objects by use of polarization in highlight,” J. Opt. Soc. Am. A 16, 2286–2293 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. K. Ikeuchi, “Reconstructing a depth map from intensity maps,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 1984), pp. 736–738.

1999 (1)

1997 (1)

M. Oren, S. K. Nayar, “A theory of specular surface geometry,” Int. J. Comput. Vis. 24, 105–124 (1997).
[CrossRef]

1996 (1)

1994 (1)

1991 (1)

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]

1990 (2)

L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 1059–1071 (1990).
[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]

1987 (1)

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

1981 (1)

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

1970 (1)

1967 (1)

1965 (2)

Anandan, P.

R. Szeliski, S. Avidan, P. Anandan, “Layer extraction from multiple images containing reflections and transparency,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 2000), pp. 246–253.

Avidan, S.

R. Szeliski, S. Avidan, P. Anandan, “Layer extraction from multiple images containing reflections and transparency,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 2000), pp. 246–253.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

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]

Curless, B.

D. E. Zongker, D. M. Warner, B. Curless, D. H. Salesin, “Environmental matting and compositing,” in Proceedings of SIGGRAPH 99 (Addison-Wesley, Boston, Mass., 1999), pp. 205–214.

Ikeuchi, K.

M. Saito, Y. Sato, K. Ikeuchi, H. Kashiwagi, “Measurement of surface orientations of transparent objects by use of polarization in highlight,” J. Opt. Soc. Am. A 16, 2286–2293 (1999).
[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 photometric stereo method,” IEEE Trans. Pattern Anal. Mach. Intell. 3, 661–669 (1981).
[CrossRef] [PubMed]

M. Saito, Y. Sato, K. Ikeuchi, H. Kashiwagi, “Measurement of surface orientations of transparent objects using polarization in highlight,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 381–386.

Y. Sato, M. D. Wheeler, K. Ikeuchi, “Object shape and reflectance modeling from observation,” in Proceedings of SIGGRAPH 97 (Addison-Wesley, Boston, Mass., 1997), pp. 379–387.

K. Ikeuchi, “Reconstructing a depth map from intensity maps,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 1984), pp. 736–738.

Jakeman, E.

Jordan, D. L.

Kanade, T.

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]

Kashiwagi, H.

M. Saito, Y. Sato, K. Ikeuchi, H. Kashiwagi, “Measurement of surface orientations of transparent objects by use of polarization in highlight,” J. Opt. Soc. Am. A 16, 2286–2293 (1999).
[CrossRef]

M. Saito, Y. Sato, K. Ikeuchi, H. Kashiwagi, “Measurement of surface orientations of transparent objects using polarization in highlight,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 381–386.

Kiryuati, N.

Y. Schechner, J. Shamir, N. Kiryuati, “Polarization-based decorrelation of transparent layers: the inclination angle of an invisible surface,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 814–819.

Koshikawa, K.

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

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

Lewis, G. D.

Lundberg, A.

L. B. Wolff, A. Lundberg, R. Tang, “Image understanding from thermal emission polarization,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos Calif., 1998), pp. 625–631.

Nayar, S. K.

M. Oren, S. K. Nayar, “A theory of specular surface geometry,” Int. J. Comput. Vis. 24, 105–124 (1997).
[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]

Nicodemus, F. E.

Oren, M.

M. Oren, S. K. Nayar, “A theory of specular surface geometry,” Int. J. Comput. Vis. 24, 105–124 (1997).
[CrossRef]

Rahmann, S.

S. Rahmann, “Polarization images: a geometric interpretation of shape analysis,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 2000), pp. 542–546.

Saito, M.

M. Saito, Y. Sato, K. Ikeuchi, H. Kashiwagi, “Measurement of surface orientations of transparent objects by use of polarization in highlight,” J. Opt. Soc. Am. A 16, 2286–2293 (1999).
[CrossRef]

M. Saito, Y. Sato, K. Ikeuchi, H. Kashiwagi, “Measurement of surface orientations of transparent objects using polarization in highlight,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 381–386.

Salesin, D. H.

D. E. Zongker, D. M. Warner, B. Curless, D. H. Salesin, “Environmental matting and compositing,” in Proceedings of SIGGRAPH 99 (Addison-Wesley, Boston, Mass., 1999), pp. 205–214.

Sandus, O.

Sato, Y.

M. Saito, Y. Sato, K. Ikeuchi, H. Kashiwagi, “Measurement of surface orientations of transparent objects by use of polarization in highlight,” J. Opt. Soc. Am. A 16, 2286–2293 (1999).
[CrossRef]

Y. Sato, M. D. Wheeler, K. Ikeuchi, “Object shape and reflectance modeling from observation,” in Proceedings of SIGGRAPH 97 (Addison-Wesley, Boston, Mass., 1997), pp. 379–387.

M. Saito, Y. Sato, K. Ikeuchi, H. Kashiwagi, “Measurement of surface orientations of transparent objects using polarization in highlight,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 381–386.

Schechner, Y.

Y. Schechner, J. Shamir, N. Kiryuati, “Polarization-based decorrelation of transparent layers: the inclination angle of an invisible surface,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 814–819.

Shamir, J.

Y. Schechner, J. Shamir, N. Kiryuati, “Polarization-based decorrelation of transparent layers: the inclination angle of an invisible surface,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 814–819.

Shirai, Y.

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

Sparrow, E. M.

Szeliski, R.

R. Szeliski, S. Avidan, P. Anandan, “Layer extraction from multiple images containing reflections and transparency,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 2000), pp. 246–253.

Tang, R.

L. B. Wolff, A. Lundberg, R. Tang, “Image understanding from thermal emission polarization,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos Calif., 1998), pp. 625–631.

Torrance, K. E.

Warner, D. M.

D. E. Zongker, D. M. Warner, B. Curless, D. H. Salesin, “Environmental matting and compositing,” in Proceedings of SIGGRAPH 99 (Addison-Wesley, Boston, Mass., 1999), pp. 205–214.

Wheeler, M. D.

Y. Sato, M. D. Wheeler, K. Ikeuchi, “Object shape and reflectance modeling from observation,” in Proceedings of SIGGRAPH 97 (Addison-Wesley, Boston, Mass., 1997), pp. 379–387.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

Wolff, L. B.

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]

L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 1059–1071 (1990).
[CrossRef]

L. B. Wolff, A. Lundberg, R. Tang, “Image understanding from thermal emission polarization,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos Calif., 1998), pp. 625–631.

Zongker, D. E.

D. E. Zongker, D. M. Warner, B. Curless, D. H. Salesin, “Environmental matting and compositing,” in Proceedings of SIGGRAPH 99 (Addison-Wesley, Boston, Mass., 1999), pp. 205–214.

Adv. Robot. (1)

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

Appl. Opt. (4)

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

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

L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 1059–1071 (1990).
[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]

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]

Int. J. Comput. Vis. (1)

M. Oren, S. K. Nayar, “A theory of specular surface geometry,” Int. J. Comput. Vis. 24, 105–124 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Other (10)

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

Y. Sato, M. D. Wheeler, K. Ikeuchi, “Object shape and reflectance modeling from observation,” in Proceedings of SIGGRAPH 97 (Addison-Wesley, Boston, Mass., 1997), pp. 379–387.

S. Rahmann, “Polarization images: a geometric interpretation of shape analysis,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 2000), pp. 542–546.

L. B. Wolff, A. Lundberg, R. Tang, “Image understanding from thermal emission polarization,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos Calif., 1998), pp. 625–631.

R. Szeliski, S. Avidan, P. Anandan, “Layer extraction from multiple images containing reflections and transparency,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 2000), pp. 246–253.

Y. Schechner, J. Shamir, N. Kiryuati, “Polarization-based decorrelation of transparent layers: the inclination angle of an invisible surface,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 814–819.

D. E. Zongker, D. M. Warner, B. Curless, D. H. Salesin, “Environmental matting and compositing,” in Proceedings of SIGGRAPH 99 (Addison-Wesley, Boston, Mass., 1999), pp. 205–214.

M. Saito, Y. Sato, K. Ikeuchi, H. Kashiwagi, “Measurement of surface orientations of transparent objects using polarization in highlight,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 381–386.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

K. Ikeuchi, “Reconstructing a depth map from intensity maps,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 1984), pp. 736–738.

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Figures (8)

Fig. 1
Fig. 1

Fresnel reflection.

Fig. 2
Fig. 2

Surface normal of object.

Fig. 3
Fig. 3

Relation between the degree of polarization and the incident angle (n=1.5).

Fig. 4
Fig. 4

Energy distribution of a blackbody.

Fig. 5
Fig. 5

Polarization degree of (a) infrared light (n=1.5), (b) visible light (n=1.5).

Fig. 6
Fig. 6

Experimental setup: (a) apparatus for visible light, (b) apparatus for infrared light.

Fig. 7
Fig. 7

Error characteristics of the spherical object.

Fig. 8
Fig. 8

Derived shape of shellfish-shaped object: (a) acrylic object, (b) derived image.

Equations (15)

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

Fp=IrpIap=tan2(ϕ1-ϕ2)tan2(ϕ1+ϕ2)
Fs=IrsIas=sin2(ϕ1-ϕ2)sin2(ϕ1+ϕ2),
tan ϕB=n2/n1.
Imax=FsFp+FsIspec,Imin=FpFp+FsIspec.
ρ=Imax-IminImax+Imin.
ρ=2 sin ϕ tan ϕn2-sin2 ϕn2-sin2 ϕ+sin2 ϕ tan2 ϕ.
W=σT4,
ϵp(T, λ, ϕ)=1-Fp,
ϵs(T, λ, ϕ)=1-Fs.
ρIR=Imax-IminImax+Imin=ϵpW-ϵsWϵpW+ϵsW=Fs-Fp2-Fp-Fs,
Tp=ItpIap=sin 2ϕ1 sin 2ϕ2sin2(ϕ1+ϕ2) cos2(ϕ1-ϕ2),
Ts=ItsIas=sin 2ϕ1 sin 2ϕ2sin2(ϕ1+ϕ2),
Imax=TpTp+TsW,Imin=TsTp+TsW.
ρIR=Imax-IminImax+Imin=Tp-TsTp+Ts=s2-s,
s=sin2 ϕ1+1n2-2n2 sin2 ϕ-2n(1-sin2 ϕ)1-1n2 sin2 ϕ1/2.

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