Abstract

We report a multispectral based method that permits the evolution of shape from polarization setup applied to 3D shape estimation of transparent objects. The setup is based on a polarization imaging technique which is a recent imaging method based on the analysis of the polarization state of the light in the observed scene. The technique has rapidly evolved with the development of electro-optic components and some polarization cameras are now available on the market. Shape from polarization consists in measuring the azimuthal and zenithal angles characterizing the normal of each point of the observed surface. We focus on the ambiguity in the measurement of the zenithal angle and propose a general multispectral approach for estimating the appropriate value of this angle.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2012

R. Rantoson, C. Stolz, D. Fofi, and F. Meriaudeau, Opt. Eng. 51, 033601 (2012).
[CrossRef]

2011

R. Jolivot, P. Vabres, and F. Marzani, Comput. Med. Imag. Graph. 35, 85 (2011).
[CrossRef]

2010

I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, Comput. Graph. Forum 29, 2400 (2010).
[CrossRef]

F. Meriaudeau, L. A. Sanchez-Secades, G. Eren, A. Erçil, F. Truchetet, O. Aubreton, and D. Fofi, IEEE Trans. Instrum. Meas. 592898 (2010).
[CrossRef]

F. Goudail and A. Bénière, Appl. Opt. 49, 683 (2010).
[CrossRef]

2009

2007

F. Meriaudeau, Image Vis. Comput. 25, 1124 (2007).
[CrossRef]

2006

2004

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, IEEE Trans. Pattern Anal. Mach Intell. 26, 73 (2004).
[CrossRef]

2002

1997

L. B. Wolff, Image Vis. Comp. 15, 81 (1997).
[CrossRef]

Aubreton, O.

F. Meriaudeau, L. A. Sanchez-Secades, G. Eren, A. Erçil, F. Truchetet, O. Aubreton, and D. Fofi, IEEE Trans. Instrum. Meas. 592898 (2010).
[CrossRef]

Bénière, A.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed.(Pergamon, Oxford, 1999), p. 952.

Chenault, D. B.

Erçil, A.

F. Meriaudeau, L. A. Sanchez-Secades, G. Eren, A. Erçil, F. Truchetet, O. Aubreton, and D. Fofi, IEEE Trans. Instrum. Meas. 592898 (2010).
[CrossRef]

Eren, G.

F. Meriaudeau, L. A. Sanchez-Secades, G. Eren, A. Erçil, F. Truchetet, O. Aubreton, and D. Fofi, IEEE Trans. Instrum. Meas. 592898 (2010).
[CrossRef]

Ferraton, M.

M. Ferraton, C. Stolz, and F. Mériaudeau, Opt. Express 17, 21077 (2009).
[CrossRef]

O. Morel, M. Ferraton, C. Stolz, and P. Gorria, in ICIP (IEEE, 2006), p. 2285.

Fofi, D.

R. Rantoson, C. Stolz, D. Fofi, and F. Meriaudeau, Opt. Eng. 51, 033601 (2012).
[CrossRef]

F. Meriaudeau, L. A. Sanchez-Secades, G. Eren, A. Erçil, F. Truchetet, O. Aubreton, and D. Fofi, IEEE Trans. Instrum. Meas. 592898 (2010).
[CrossRef]

Goldstein, D. L.

Gorria, P.

O. Morel, C. Stolz, F. Meriaudeau, and P. Gorria, Appl. Opt. 45, 4062 (2006).
[CrossRef]

O. Morel, M. Ferraton, C. Stolz, and P. Gorria, in ICIP (IEEE, 2006), p. 2285.

O. Morel, C. Stolz, P. Gorria, and R. Seulin, “Eclairage sectorisé pour la reconstruction tridimensionnelle par imagerie polarimétrique,” French 05.11674 (November 17, 2005).

Goudail, F.

Heidrich, W.

I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, Comput. Graph. Forum 29, 2400 (2010).
[CrossRef]

Ihrke, I.

I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, Comput. Graph. Forum 29, 2400 (2010).
[CrossRef]

Ikecuhi, K.

Ikeuchi, K.

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, IEEE Trans. Pattern Anal. Mach Intell. 26, 73 (2004).
[CrossRef]

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, IAPR (IEEE, 2002), pp. 26–31.

Jolivot, R.

R. Jolivot, P. Vabres, and F. Marzani, Comput. Med. Imag. Graph. 35, 85 (2011).
[CrossRef]

Kagesawa, M.

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, IEEE Trans. Pattern Anal. Mach Intell. 26, 73 (2004).
[CrossRef]

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, IAPR (IEEE, 2002), pp. 26–31.

Kutulakos, K. N.

I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, Comput. Graph. Forum 29, 2400 (2010).
[CrossRef]

Lensch, H. P. A.

I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, Comput. Graph. Forum 29, 2400 (2010).
[CrossRef]

Magnor, M.

I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, Comput. Graph. Forum 29, 2400 (2010).
[CrossRef]

Marzani, F.

R. Jolivot, P. Vabres, and F. Marzani, Comput. Med. Imag. Graph. 35, 85 (2011).
[CrossRef]

Meriaudeau, F.

R. Rantoson, C. Stolz, D. Fofi, and F. Meriaudeau, Opt. Eng. 51, 033601 (2012).
[CrossRef]

F. Meriaudeau, L. A. Sanchez-Secades, G. Eren, A. Erçil, F. Truchetet, O. Aubreton, and D. Fofi, IEEE Trans. Instrum. Meas. 592898 (2010).
[CrossRef]

F. Meriaudeau, Image Vis. Comput. 25, 1124 (2007).
[CrossRef]

O. Morel, C. Stolz, F. Meriaudeau, and P. Gorria, Appl. Opt. 45, 4062 (2006).
[CrossRef]

Mériaudeau, F.

Miyazaki, D.

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, IEEE Trans. Pattern Anal. Mach Intell. 26, 73 (2004).
[CrossRef]

D. Miyazaki, M. Saito, Y. Sato, and K. Ikecuhi, J. Opt. Soc. Am. A 19, 687 (2002).
[CrossRef]

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, IAPR (IEEE, 2002), pp. 26–31.

Morel, O.

O. Morel, C. Stolz, F. Meriaudeau, and P. Gorria, Appl. Opt. 45, 4062 (2006).
[CrossRef]

O. Morel, M. Ferraton, C. Stolz, and P. Gorria, in ICIP (IEEE, 2006), p. 2285.

O. Morel, C. Stolz, P. Gorria, and R. Seulin, “Eclairage sectorisé pour la reconstruction tridimensionnelle par imagerie polarimétrique,” French 05.11674 (November 17, 2005).

Rahmann, S.

S. Rahmann, Iberian Conference on Pattern Recognition and Image Analysis (IbPRIA03) (Springer, 2003), pp. 810–820.

Rantoson, R.

R. Rantoson, C. Stolz, D. Fofi, and F. Meriaudeau, Opt. Eng. 51, 033601 (2012).
[CrossRef]

Saito, M.

Sanchez-Secades, L. A.

F. Meriaudeau, L. A. Sanchez-Secades, G. Eren, A. Erçil, F. Truchetet, O. Aubreton, and D. Fofi, IEEE Trans. Instrum. Meas. 592898 (2010).
[CrossRef]

Sato, Y.

Seulin, R.

O. Morel, C. Stolz, P. Gorria, and R. Seulin, “Eclairage sectorisé pour la reconstruction tridimensionnelle par imagerie polarimétrique,” French 05.11674 (November 17, 2005).

Shaw, J. A.

Stolz, C.

R. Rantoson, C. Stolz, D. Fofi, and F. Meriaudeau, Opt. Eng. 51, 033601 (2012).
[CrossRef]

M. Ferraton, C. Stolz, and F. Mériaudeau, Opt. Express 17, 21077 (2009).
[CrossRef]

O. Morel, C. Stolz, F. Meriaudeau, and P. Gorria, Appl. Opt. 45, 4062 (2006).
[CrossRef]

O. Morel, M. Ferraton, C. Stolz, and P. Gorria, in ICIP (IEEE, 2006), p. 2285.

O. Morel, C. Stolz, P. Gorria, and R. Seulin, “Eclairage sectorisé pour la reconstruction tridimensionnelle par imagerie polarimétrique,” French 05.11674 (November 17, 2005).

Truchetet, F.

F. Meriaudeau, L. A. Sanchez-Secades, G. Eren, A. Erçil, F. Truchetet, O. Aubreton, and D. Fofi, IEEE Trans. Instrum. Meas. 592898 (2010).
[CrossRef]

Tyo, S. J.

Vabres, P.

R. Jolivot, P. Vabres, and F. Marzani, Comput. Med. Imag. Graph. 35, 85 (2011).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed.(Pergamon, Oxford, 1999), p. 952.

Wolff, L. B.

L. B. Wolff, Image Vis. Comp. 15, 81 (1997).
[CrossRef]

Appl. Opt.

Comput. Graph. Forum

I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, Comput. Graph. Forum 29, 2400 (2010).
[CrossRef]

Comput. Med. Imag. Graph.

R. Jolivot, P. Vabres, and F. Marzani, Comput. Med. Imag. Graph. 35, 85 (2011).
[CrossRef]

IEEE Trans. Instrum. Meas.

F. Meriaudeau, L. A. Sanchez-Secades, G. Eren, A. Erçil, F. Truchetet, O. Aubreton, and D. Fofi, IEEE Trans. Instrum. Meas. 592898 (2010).
[CrossRef]

IEEE Trans. Pattern Anal. Mach Intell.

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, IEEE Trans. Pattern Anal. Mach Intell. 26, 73 (2004).
[CrossRef]

Image Vis. Comp.

L. B. Wolff, Image Vis. Comp. 15, 81 (1997).
[CrossRef]

Image Vis. Comput.

F. Meriaudeau, Image Vis. Comput. 25, 1124 (2007).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

R. Rantoson, C. Stolz, D. Fofi, and F. Meriaudeau, Opt. Eng. 51, 033601 (2012).
[CrossRef]

Opt. Express

Other

M. Born and E. Wolf, Principles of Optics, 7th ed.(Pergamon, Oxford, 1999), p. 952.

O. Morel, M. Ferraton, C. Stolz, and P. Gorria, in ICIP (IEEE, 2006), p. 2285.

O. Morel, C. Stolz, P. Gorria, and R. Seulin, “Eclairage sectorisé pour la reconstruction tridimensionnelle par imagerie polarimétrique,” French 05.11674 (November 17, 2005).

S. Rahmann, Iberian Conference on Pattern Recognition and Image Analysis (IbPRIA03) (Springer, 2003), pp. 810–820.

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, IAPR (IEEE, 2002), pp. 26–31.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Geometry of the specular reflection on a surface. The light source and the detector are not sketched here. (b) Partial Stokes polarization setups with LCD based polarization rotator.

Fig. 2.
Fig. 2.

Two degree of polarization curves simulated for two wavelengths (scale emphasized for better reading). For two possible angles θ 1 and θ 2 corresponding to one degree of polarization we apply the disambiguation.

Fig. 3.
Fig. 3.

Partial reconstruction of an acrylic sphere evaluated by considering zenithal angles greater than the Brewster angle with pseudo index of 1.5 + 2.5 i .

Fig. 4.
Fig. 4.

Partial reconstruction of a transparent object having high slopes. The significant part is only where the slope varies a lot. (a) Intensity image. (b) Difference map of the DOP. (c) View of the 3D reconstruction.

Equations (2)

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{ I p ( α ) = 1 2 ( s 0 + s 1 cos 2 α + s 2 sin 2 α ) , I p ( α ) = I 2 ( 1 + ρ cos ( 2 α 2 ϕ ) ) ,
n⃗ = ( f ( x , y ) x f ( x , y ) y 1 ) = ( p = tan θ cos ϕ q = tan θ sin ϕ 1 ) .

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