Abstract

The paper presents a method aimed at accurately reconstructing transparent objects using the area source. The method called polarized light measurements (PLM) combines two reconstruction techniques: polarization analyses and light-path triangulation. The originality of this study relies on the PLM method that enables to extract the radiometric cues and geometric cues simultaneously during the surface reconstruction. To validate performance, a series of the comparison experiments are developed on different objects for the diverse thickness, material and curvature radius of unit under test. The subsequent error analyses are applied to evaluate the method, and the error distribution can be well observed in the results. The PLM performs an efficient process and a higher accuracy compared with traditional reconstruction on transparent objects made by the polarization analyses and triangulation method used alone.

© 2017 Optical Society of America

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  1. I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, “Transparent and specular object reconstruction,” Comp. Graphics Forum 29(8), 2400–2426 (2010).
  2. M. Benezra and S. K. Nayar, “What does motion reveal about transparency?” IEEE International Conference on Computer Vision (IEEE, 2003), pp. 1025–1032.
  3. N. Alt, P. Rives, and E. Steinbach, “Reconstruction of transparent objects in unstructured scenes with a depth camera,” in IEEE International Conference on Image Processing (IEEE, 2013), pp. 4131–4135.
  4. G. Eren, O. Aubreton, F. Meriaudeau, L. A. Sanchez Secades, D. Fofi, A. T. Naskali, F. Truchetet, and A. Ercil, “Scanning from heating: 3D shape estimation of transparent objects from local surface heating,” Opt. Express 17(14), 11457–11468 (2009).
    [PubMed]
  5. X. Gong and S. Bansmer, “3-D ice shape measurements using mid-infrared laser scanning,” Opt. Express 23(4), 4908–4926 (2015).
    [PubMed]
  6. N. J. W. Morris and K. N. Kutulakos, “Reconstructing the surface of inhomogeneous transparent scenes by scatter-trace photography,” IEEE International Conference on Computer Vision (IEEE, 2007), pp. 1–8.
  7. D. Miyazaki and K. Ikeuchi, “Shape estimation of transparent objects by using polarization analyses,” IPSJ Digital Courier 29(2), 407–427 (2012).
  8. D. Miyazaki, M. Saito, Y. Sato, and K. Ikeuchi, “Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths,” J. Opt. Soc. Am. A 19(4), 687–694 (2002).
    [PubMed]
  9. D. Miyazaki and K. Ikeuchi, “Inverse polarization raytracing: estimating surface shapes of transparent objects,” in Computer Vision and Pattern Recognition (IEEE, 2005), pp. 910–917.
  10. T. Chen, H. P. A. Lensch, C. Fuchs, and H. P. Seidel, “Polarization and phase-shifting for 3D scanning of translucent objects,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.
  11. M. Iqbal, O. Morel, and F. Mériaudeau, “Extract information of polarization imaging from local matching stereo,” International Conference on Intelligent and Advanced Systems (IEEE, 2010), pp. 1–6.
  12. O. Morel, C. Stolz, F. Meriaudeau, and P. Gorria, “Active lighting applied to three-dimensional reconstruction of specular metallic surfaces by polarization imaging,” Appl. Opt. 45(17), 4062–4068 (2006).
    [PubMed]
  13. V. Chari and P. Sturm, “A theory of refractive photo-light-path triangulation,” IEEE International Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 1438–1445.
  14. K. N. Kutulakos and E. Steger, “A theory of refractive and specular 3D shape by light-path triangulation,” Int. J. Comput. Vis. 76(1), 13–29 (2007).
  15. K. Han, K. Y. K. Wong, and M. Liu, “A fixed viewpoint approach for dense reconstruction of transparent objects,” IEEE International Conference on Computer Vision and Pattern Recognition (IEEE, 2015), pp. 4001–4008.
  16. D. E. Zongker, D. M. Werner, B. Curless, and D. H. Salesin, “Environment matting and compositing,” CiteSeer (1999).
  17. M. Yamazaki, S. Iwata, and G. Xu, “Dense 3D reconstruction of specular and transparent objects using stereo cameras and phase-shift method,” in Asian Conference on Computer Vision, (Springer-Verlag, 2007), pp. 570–579.
  18. N. J. W. Morris and K. N. Kutulakos, “Dynamic refraction stereo,” in Tenth IEEE International Conference on Computer Vision (IEEE, 2011), pp. 1573–1580.
  19. P. C. Seitz, “3D measurement with active triangulation for spectacle lens optimization and individualization,” Proc. SPIE 9528, 952806 (2015).
  20. F. Drouet, C. Stolz, O. Laligant, and O. Aubreton, “3D measurement of both front and back surfaces of transparent objects by polarization imaging,” Proc. SPIE 9205, 92050N (2015).
  21. G. A. Atkinson and E. R. Hancock, “Recovery of surface orientation from diffuse polarization,” IEEE Trans. Image Process. 15(6), 1653–1664 (2006).
    [PubMed]
  22. M. Ferraton, C. Stolz, and F. Mériaudeau, “Optimization of a polarization imaging system for 3D measurements of transparent objects,” Opt. Express 17(23), 21077–21082 (2009).
    [PubMed]
  23. L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vis. Comput. 15(2), 81–93 (1997).
  24. M. Vedel, N. Lechocinski, and S. Breugnot, “3D shape reconstruction of optical element using polarization,” Proc. SPIE 7672(1), 92–96 (2010).

2015 (3)

X. Gong and S. Bansmer, “3-D ice shape measurements using mid-infrared laser scanning,” Opt. Express 23(4), 4908–4926 (2015).
[PubMed]

P. C. Seitz, “3D measurement with active triangulation for spectacle lens optimization and individualization,” Proc. SPIE 9528, 952806 (2015).

F. Drouet, C. Stolz, O. Laligant, and O. Aubreton, “3D measurement of both front and back surfaces of transparent objects by polarization imaging,” Proc. SPIE 9205, 92050N (2015).

2012 (1)

D. Miyazaki and K. Ikeuchi, “Shape estimation of transparent objects by using polarization analyses,” IPSJ Digital Courier 29(2), 407–427 (2012).

2010 (1)

M. Vedel, N. Lechocinski, and S. Breugnot, “3D shape reconstruction of optical element using polarization,” Proc. SPIE 7672(1), 92–96 (2010).

2009 (2)

2007 (1)

K. N. Kutulakos and E. Steger, “A theory of refractive and specular 3D shape by light-path triangulation,” Int. J. Comput. Vis. 76(1), 13–29 (2007).

2006 (2)

G. A. Atkinson and E. R. Hancock, “Recovery of surface orientation from diffuse polarization,” IEEE Trans. Image Process. 15(6), 1653–1664 (2006).
[PubMed]

O. Morel, C. Stolz, F. Meriaudeau, and P. Gorria, “Active lighting applied to three-dimensional reconstruction of specular metallic surfaces by polarization imaging,” Appl. Opt. 45(17), 4062–4068 (2006).
[PubMed]

2002 (1)

1997 (1)

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vis. Comput. 15(2), 81–93 (1997).

Alt, N.

N. Alt, P. Rives, and E. Steinbach, “Reconstruction of transparent objects in unstructured scenes with a depth camera,” in IEEE International Conference on Image Processing (IEEE, 2013), pp. 4131–4135.

Atkinson, G. A.

G. A. Atkinson and E. R. Hancock, “Recovery of surface orientation from diffuse polarization,” IEEE Trans. Image Process. 15(6), 1653–1664 (2006).
[PubMed]

Aubreton, O.

F. Drouet, C. Stolz, O. Laligant, and O. Aubreton, “3D measurement of both front and back surfaces of transparent objects by polarization imaging,” Proc. SPIE 9205, 92050N (2015).

G. Eren, O. Aubreton, F. Meriaudeau, L. A. Sanchez Secades, D. Fofi, A. T. Naskali, F. Truchetet, and A. Ercil, “Scanning from heating: 3D shape estimation of transparent objects from local surface heating,” Opt. Express 17(14), 11457–11468 (2009).
[PubMed]

Bansmer, S.

Benezra, M.

M. Benezra and S. K. Nayar, “What does motion reveal about transparency?” IEEE International Conference on Computer Vision (IEEE, 2003), pp. 1025–1032.

Breugnot, S.

M. Vedel, N. Lechocinski, and S. Breugnot, “3D shape reconstruction of optical element using polarization,” Proc. SPIE 7672(1), 92–96 (2010).

Chari, V.

V. Chari and P. Sturm, “A theory of refractive photo-light-path triangulation,” IEEE International Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 1438–1445.

Chen, T.

T. Chen, H. P. A. Lensch, C. Fuchs, and H. P. Seidel, “Polarization and phase-shifting for 3D scanning of translucent objects,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.

Drouet, F.

F. Drouet, C. Stolz, O. Laligant, and O. Aubreton, “3D measurement of both front and back surfaces of transparent objects by polarization imaging,” Proc. SPIE 9205, 92050N (2015).

Ercil, A.

Eren, G.

Ferraton, M.

Fofi, D.

Fuchs, C.

T. Chen, H. P. A. Lensch, C. Fuchs, and H. P. Seidel, “Polarization and phase-shifting for 3D scanning of translucent objects,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.

Gong, X.

Gorria, P.

Han, K.

K. Han, K. Y. K. Wong, and M. Liu, “A fixed viewpoint approach for dense reconstruction of transparent objects,” IEEE International Conference on Computer Vision and Pattern Recognition (IEEE, 2015), pp. 4001–4008.

Hancock, E. R.

G. A. Atkinson and E. R. Hancock, “Recovery of surface orientation from diffuse polarization,” IEEE Trans. Image Process. 15(6), 1653–1664 (2006).
[PubMed]

Ikeuchi, K.

D. Miyazaki and K. Ikeuchi, “Shape estimation of transparent objects by using polarization analyses,” IPSJ Digital Courier 29(2), 407–427 (2012).

D. Miyazaki, M. Saito, Y. Sato, and K. Ikeuchi, “Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths,” J. Opt. Soc. Am. A 19(4), 687–694 (2002).
[PubMed]

Iqbal, M.

M. Iqbal, O. Morel, and F. Mériaudeau, “Extract information of polarization imaging from local matching stereo,” International Conference on Intelligent and Advanced Systems (IEEE, 2010), pp. 1–6.

Iwata, S.

M. Yamazaki, S. Iwata, and G. Xu, “Dense 3D reconstruction of specular and transparent objects using stereo cameras and phase-shift method,” in Asian Conference on Computer Vision, (Springer-Verlag, 2007), pp. 570–579.

Kutulakos, K. N.

K. N. Kutulakos and E. Steger, “A theory of refractive and specular 3D shape by light-path triangulation,” Int. J. Comput. Vis. 76(1), 13–29 (2007).

N. J. W. Morris and K. N. Kutulakos, “Reconstructing the surface of inhomogeneous transparent scenes by scatter-trace photography,” IEEE International Conference on Computer Vision (IEEE, 2007), pp. 1–8.

N. J. W. Morris and K. N. Kutulakos, “Dynamic refraction stereo,” in Tenth IEEE International Conference on Computer Vision (IEEE, 2011), pp. 1573–1580.

Laligant, O.

F. Drouet, C. Stolz, O. Laligant, and O. Aubreton, “3D measurement of both front and back surfaces of transparent objects by polarization imaging,” Proc. SPIE 9205, 92050N (2015).

Lechocinski, N.

M. Vedel, N. Lechocinski, and S. Breugnot, “3D shape reconstruction of optical element using polarization,” Proc. SPIE 7672(1), 92–96 (2010).

Lensch, H. P. A.

T. Chen, H. P. A. Lensch, C. Fuchs, and H. P. Seidel, “Polarization and phase-shifting for 3D scanning of translucent objects,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.

Liu, M.

K. Han, K. Y. K. Wong, and M. Liu, “A fixed viewpoint approach for dense reconstruction of transparent objects,” IEEE International Conference on Computer Vision and Pattern Recognition (IEEE, 2015), pp. 4001–4008.

Meriaudeau, F.

Mériaudeau, F.

M. Ferraton, C. Stolz, and F. Mériaudeau, “Optimization of a polarization imaging system for 3D measurements of transparent objects,” Opt. Express 17(23), 21077–21082 (2009).
[PubMed]

M. Iqbal, O. Morel, and F. Mériaudeau, “Extract information of polarization imaging from local matching stereo,” International Conference on Intelligent and Advanced Systems (IEEE, 2010), pp. 1–6.

Miyazaki, D.

D. Miyazaki and K. Ikeuchi, “Shape estimation of transparent objects by using polarization analyses,” IPSJ Digital Courier 29(2), 407–427 (2012).

D. Miyazaki, M. Saito, Y. Sato, and K. Ikeuchi, “Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths,” J. Opt. Soc. Am. A 19(4), 687–694 (2002).
[PubMed]

Morel, O.

O. Morel, C. Stolz, F. Meriaudeau, and P. Gorria, “Active lighting applied to three-dimensional reconstruction of specular metallic surfaces by polarization imaging,” Appl. Opt. 45(17), 4062–4068 (2006).
[PubMed]

M. Iqbal, O. Morel, and F. Mériaudeau, “Extract information of polarization imaging from local matching stereo,” International Conference on Intelligent and Advanced Systems (IEEE, 2010), pp. 1–6.

Morris, N. J. W.

N. J. W. Morris and K. N. Kutulakos, “Dynamic refraction stereo,” in Tenth IEEE International Conference on Computer Vision (IEEE, 2011), pp. 1573–1580.

N. J. W. Morris and K. N. Kutulakos, “Reconstructing the surface of inhomogeneous transparent scenes by scatter-trace photography,” IEEE International Conference on Computer Vision (IEEE, 2007), pp. 1–8.

Naskali, A. T.

Nayar, S. K.

M. Benezra and S. K. Nayar, “What does motion reveal about transparency?” IEEE International Conference on Computer Vision (IEEE, 2003), pp. 1025–1032.

Rives, P.

N. Alt, P. Rives, and E. Steinbach, “Reconstruction of transparent objects in unstructured scenes with a depth camera,” in IEEE International Conference on Image Processing (IEEE, 2013), pp. 4131–4135.

Saito, M.

Sanchez Secades, L. A.

Sato, Y.

Seidel, H. P.

T. Chen, H. P. A. Lensch, C. Fuchs, and H. P. Seidel, “Polarization and phase-shifting for 3D scanning of translucent objects,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.

Seitz, P. C.

P. C. Seitz, “3D measurement with active triangulation for spectacle lens optimization and individualization,” Proc. SPIE 9528, 952806 (2015).

Steger, E.

K. N. Kutulakos and E. Steger, “A theory of refractive and specular 3D shape by light-path triangulation,” Int. J. Comput. Vis. 76(1), 13–29 (2007).

Steinbach, E.

N. Alt, P. Rives, and E. Steinbach, “Reconstruction of transparent objects in unstructured scenes with a depth camera,” in IEEE International Conference on Image Processing (IEEE, 2013), pp. 4131–4135.

Stolz, C.

Sturm, P.

V. Chari and P. Sturm, “A theory of refractive photo-light-path triangulation,” IEEE International Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 1438–1445.

Truchetet, F.

Vedel, M.

M. Vedel, N. Lechocinski, and S. Breugnot, “3D shape reconstruction of optical element using polarization,” Proc. SPIE 7672(1), 92–96 (2010).

Wolff, L. B.

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vis. Comput. 15(2), 81–93 (1997).

Wong, K. Y. K.

K. Han, K. Y. K. Wong, and M. Liu, “A fixed viewpoint approach for dense reconstruction of transparent objects,” IEEE International Conference on Computer Vision and Pattern Recognition (IEEE, 2015), pp. 4001–4008.

Xu, G.

M. Yamazaki, S. Iwata, and G. Xu, “Dense 3D reconstruction of specular and transparent objects using stereo cameras and phase-shift method,” in Asian Conference on Computer Vision, (Springer-Verlag, 2007), pp. 570–579.

Yamazaki, M.

M. Yamazaki, S. Iwata, and G. Xu, “Dense 3D reconstruction of specular and transparent objects using stereo cameras and phase-shift method,” in Asian Conference on Computer Vision, (Springer-Verlag, 2007), pp. 570–579.

Appl. Opt. (1)

IEEE Trans. Image Process. (1)

G. A. Atkinson and E. R. Hancock, “Recovery of surface orientation from diffuse polarization,” IEEE Trans. Image Process. 15(6), 1653–1664 (2006).
[PubMed]

Image Vis. Comput. (1)

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vis. Comput. 15(2), 81–93 (1997).

Int. J. Comput. Vis. (1)

K. N. Kutulakos and E. Steger, “A theory of refractive and specular 3D shape by light-path triangulation,” Int. J. Comput. Vis. 76(1), 13–29 (2007).

IPSJ Digital Courier (1)

D. Miyazaki and K. Ikeuchi, “Shape estimation of transparent objects by using polarization analyses,” IPSJ Digital Courier 29(2), 407–427 (2012).

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

Opt. Express (3)

Proc. SPIE (3)

M. Vedel, N. Lechocinski, and S. Breugnot, “3D shape reconstruction of optical element using polarization,” Proc. SPIE 7672(1), 92–96 (2010).

P. C. Seitz, “3D measurement with active triangulation for spectacle lens optimization and individualization,” Proc. SPIE 9528, 952806 (2015).

F. Drouet, C. Stolz, O. Laligant, and O. Aubreton, “3D measurement of both front and back surfaces of transparent objects by polarization imaging,” Proc. SPIE 9205, 92050N (2015).

Other (12)

V. Chari and P. Sturm, “A theory of refractive photo-light-path triangulation,” IEEE International Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 1438–1445.

K. Han, K. Y. K. Wong, and M. Liu, “A fixed viewpoint approach for dense reconstruction of transparent objects,” IEEE International Conference on Computer Vision and Pattern Recognition (IEEE, 2015), pp. 4001–4008.

D. E. Zongker, D. M. Werner, B. Curless, and D. H. Salesin, “Environment matting and compositing,” CiteSeer (1999).

M. Yamazaki, S. Iwata, and G. Xu, “Dense 3D reconstruction of specular and transparent objects using stereo cameras and phase-shift method,” in Asian Conference on Computer Vision, (Springer-Verlag, 2007), pp. 570–579.

N. J. W. Morris and K. N. Kutulakos, “Dynamic refraction stereo,” in Tenth IEEE International Conference on Computer Vision (IEEE, 2011), pp. 1573–1580.

N. J. W. Morris and K. N. Kutulakos, “Reconstructing the surface of inhomogeneous transparent scenes by scatter-trace photography,” IEEE International Conference on Computer Vision (IEEE, 2007), pp. 1–8.

I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, “Transparent and specular object reconstruction,” Comp. Graphics Forum 29(8), 2400–2426 (2010).

M. Benezra and S. K. Nayar, “What does motion reveal about transparency?” IEEE International Conference on Computer Vision (IEEE, 2003), pp. 1025–1032.

N. Alt, P. Rives, and E. Steinbach, “Reconstruction of transparent objects in unstructured scenes with a depth camera,” in IEEE International Conference on Image Processing (IEEE, 2013), pp. 4131–4135.

D. Miyazaki and K. Ikeuchi, “Inverse polarization raytracing: estimating surface shapes of transparent objects,” in Computer Vision and Pattern Recognition (IEEE, 2005), pp. 910–917.

T. Chen, H. P. A. Lensch, C. Fuchs, and H. P. Seidel, “Polarization and phase-shifting for 3D scanning of translucent objects,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.

M. Iqbal, O. Morel, and F. Mériaudeau, “Extract information of polarization imaging from local matching stereo,” International Conference on Intelligent and Advanced Systems (IEEE, 2010), pp. 1–6.

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Figures (16)

Fig. 1
Fig. 1 Structure of the 3D reconstruction for transparent objects.
Fig. 2
Fig. 2 Specular reflection for the light wave.
Fig. 3
Fig. 3 Variation curve of the fitting intensity.
Fig. 4
Fig. 4 Schematic of the degree of polarization.
Fig. 5
Fig. 5 Schematic of the normal vector for the measured surface.
Fig. 6
Fig. 6 Experimental system.
Fig. 7
Fig. 7 Reconstructed point cloud for spherical mirror that the radius of curvature was 161.874mm.
Fig. 8
Fig. 8 Analysis diagram of the ISM. (a) Cause of formation for the imaging. (b) Multiple reflections in the transparent object.
Fig. 9
Fig. 9 Separated sinusoid.
Fig. 10
Fig. 10 Working sketches of the ISM. (a) Imaging of the reflected light from back surface. (b), (c) Point cloud including imaging. (d), (e) Point cloud with removing imaging.
Fig. 11
Fig. 11 Error distribution at different thickness.
Fig. 12
Fig. 12 Comparison experiments of thicknesses.
Fig. 13
Fig. 13 Error distribution at different material.
Fig. 14
Fig. 14 Comparison experiments of materials.
Fig. 15
Fig. 15 Error distribution at different curvature radius.
Fig. 16
Fig. 16 Comparison experiments of curvature radii.

Equations (16)

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

R p = tan 2 ( θ 1 θ 2 ) tan 2 ( θ 1 + θ 2 )
R s = sin 2 ( θ 1 θ 2 ) sin 2 ( θ 1 + θ 2 )
I ( θ p o l ) = I max + I min 2 + I max I min 2 cos ( 2 θ p o l 2 φ )
ρ = I max I min I max + I min = R s R p R s + R p
ρ = f ( θ ) = 2 sin θ tan θ n 2 sin 2 θ n 2 sin 2 θ + sin 2 θ tan 2 θ
0 < 2 θ = α < 2 θ B
ϕ = φ ± 90 °
ϕ = 90 ° + θ p o l ± 90 °
n = [ c d 1 ] = [ tan θ cos ϕ tan θ sin ϕ 1 ]
[ c w o r l d d w o r l d e w o r l d ] = R ( ε ) [ c d 1 ]
R 1 R 2 = n ( R 2 ) × | 2 R 2 | × n
R 1 = R 2 2 ( n R 2 ) n
I f r o n t = I f m a x + I f m i n 2 + I f m a x I f m i n 2 cos ( 2 ( θ p o l φ 1 ) )
I b a c k = I b m a x + I b m i n 2 + I b m a x I b m i n 2 cos ( 2 ( θ p o l φ 2 ) )
R = 1 2 ( R s + R p ) = 1 2 ( sin 2 ( θ 1 θ 2 ) sin 2 ( θ 1 + θ 2 ) + tan 2 ( θ 1 θ 2 ) tan 2 ( θ 1 + θ 2 ) )
1 n sin ( θ 1 ) = sin ( θ 2 )

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