Abstract

A vision-based method is proposed to measure the 3D shape of external and internal surfaces (not accessible) of smooth transparent objects. Looking at the reflections of point sources on a specular surface with a polarimetric camera, we combine the measurements of two techniques: shape from distortion and shape from polarization. It permits us to recover the position and orientation of the specular surface for each detected point. The internal surface of transparent objects exhibiting as well a specular component, the same technique is used on the highlights coming from the back surface, taking into account the refraction by using polarimetric ray tracing.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, in STAR Eurographics (Eurographics Association, 2008).
  2. A. C. Sanderson, L. E. Weiss, and S. K. Nayar, IEEE Trans. Pattern Anal. Mach Intell. 10, 44 (1988).
  3. M. Tarini, H. P. A. Lensch, M. Goesele, and H.-P. Seidel, Graph. Models 67, 233 (2005).
  4. D. Miyazaki, M. Saito, Y. Sato, and K. Ikeuchi, J. Opt. Soc. Am. 19, 687 (2002).
    [CrossRef]
  5. M. Ferraton, C. Stolz, and F. Mériaudeau, Opt. Express 17, 21077 (2009).
    [CrossRef]
  6. N. J. W. Morris and K. N. Kutulakos, in IEEE ICCV (IEEE, 2007), pp. 1–8.
  7. G. Wetzstein, D. Roodnick, W. Heidrich, and R. Raskar, in IEEE ICCV (IEEE, 2011), pp. 1180–1186.
  8. K. N. Kutulakos and E. Steger, Int. J. Comput. Vis. 76, 13 (2008).
  9. B. Trifonov, D. Bradley, and W. Heidrich, in Proceedings of the Eurographics Symposium on Rendering (Eurographics Association, 2006), pp. 51–60.
  10. M. B. Hullin, M. Fuchs, I. Ihrke, H.-P. Seidel, and H. P. A. Lensch, ACM Trans. Graph. 27, 87 (2008).
  11. M. Ben-Ezra and S. K. Nayar, in IEEE ICCV (IEEE, 2003), Vol. 2, pp. 1025–1032.
  12. S. Savarese and P. Perona, in ECCV (Springer, 2002), Vol. 2351, pp. 759–774.
  13. R. Longhurst, Optics, 3rd ed. (Addison-Wesley, 1973).
  14. M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).
  15. C. Stolz, M. Ferraton, and F. Mériaudeau, Opt. Lett. 37, 4218 (2012).
    [CrossRef]
  16. G. Glaeser and H.-P. Schröcker, J. Geom. Graph. 4, 1 (2000).
  17. S. B. Howell, Astron. Soc. Pac. Conf. 101, 616 (1989).
    [CrossRef]

2012 (1)

2009 (1)

2008 (2)

K. N. Kutulakos and E. Steger, Int. J. Comput. Vis. 76, 13 (2008).

M. B. Hullin, M. Fuchs, I. Ihrke, H.-P. Seidel, and H. P. A. Lensch, ACM Trans. Graph. 27, 87 (2008).

2005 (1)

M. Tarini, H. P. A. Lensch, M. Goesele, and H.-P. Seidel, Graph. Models 67, 233 (2005).

2002 (1)

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

2000 (1)

G. Glaeser and H.-P. Schröcker, J. Geom. Graph. 4, 1 (2000).

1989 (1)

S. B. Howell, Astron. Soc. Pac. Conf. 101, 616 (1989).
[CrossRef]

1988 (1)

A. C. Sanderson, L. E. Weiss, and S. K. Nayar, IEEE Trans. Pattern Anal. Mach Intell. 10, 44 (1988).

Ben-Ezra, M.

M. Ben-Ezra and S. K. Nayar, in IEEE ICCV (IEEE, 2003), Vol. 2, pp. 1025–1032.

Born, M.

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

Bradley, D.

B. Trifonov, D. Bradley, and W. Heidrich, in Proceedings of the Eurographics Symposium on Rendering (Eurographics Association, 2006), pp. 51–60.

Ferraton, M.

Fuchs, M.

M. B. Hullin, M. Fuchs, I. Ihrke, H.-P. Seidel, and H. P. A. Lensch, ACM Trans. Graph. 27, 87 (2008).

Glaeser, G.

G. Glaeser and H.-P. Schröcker, J. Geom. Graph. 4, 1 (2000).

Goesele, M.

M. Tarini, H. P. A. Lensch, M. Goesele, and H.-P. Seidel, Graph. Models 67, 233 (2005).

Heidrich, W.

I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, in STAR Eurographics (Eurographics Association, 2008).

B. Trifonov, D. Bradley, and W. Heidrich, in Proceedings of the Eurographics Symposium on Rendering (Eurographics Association, 2006), pp. 51–60.

G. Wetzstein, D. Roodnick, W. Heidrich, and R. Raskar, in IEEE ICCV (IEEE, 2011), pp. 1180–1186.

Howell, S. B.

S. B. Howell, Astron. Soc. Pac. Conf. 101, 616 (1989).
[CrossRef]

Hullin, M. B.

M. B. Hullin, M. Fuchs, I. Ihrke, H.-P. Seidel, and H. P. A. Lensch, ACM Trans. Graph. 27, 87 (2008).

Ihrke, I.

M. B. Hullin, M. Fuchs, I. Ihrke, H.-P. Seidel, and H. P. A. Lensch, ACM Trans. Graph. 27, 87 (2008).

I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, in STAR Eurographics (Eurographics Association, 2008).

Ikeuchi, K.

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

Kutulakos, K. N.

K. N. Kutulakos and E. Steger, Int. J. Comput. Vis. 76, 13 (2008).

N. J. W. Morris and K. N. Kutulakos, in IEEE ICCV (IEEE, 2007), pp. 1–8.

I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, in STAR Eurographics (Eurographics Association, 2008).

Lensch, H. P. A.

M. B. Hullin, M. Fuchs, I. Ihrke, H.-P. Seidel, and H. P. A. Lensch, ACM Trans. Graph. 27, 87 (2008).

M. Tarini, H. P. A. Lensch, M. Goesele, and H.-P. Seidel, Graph. Models 67, 233 (2005).

I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, in STAR Eurographics (Eurographics Association, 2008).

Longhurst, R.

R. Longhurst, Optics, 3rd ed. (Addison-Wesley, 1973).

Magnor, M.

I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, in STAR Eurographics (Eurographics Association, 2008).

Mériaudeau, F.

Miyazaki, D.

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

Morris, N. J. W.

N. J. W. Morris and K. N. Kutulakos, in IEEE ICCV (IEEE, 2007), pp. 1–8.

Nayar, S. K.

A. C. Sanderson, L. E. Weiss, and S. K. Nayar, IEEE Trans. Pattern Anal. Mach Intell. 10, 44 (1988).

M. Ben-Ezra and S. K. Nayar, in IEEE ICCV (IEEE, 2003), Vol. 2, pp. 1025–1032.

Perona, P.

S. Savarese and P. Perona, in ECCV (Springer, 2002), Vol. 2351, pp. 759–774.

Raskar, R.

G. Wetzstein, D. Roodnick, W. Heidrich, and R. Raskar, in IEEE ICCV (IEEE, 2011), pp. 1180–1186.

Roodnick, D.

G. Wetzstein, D. Roodnick, W. Heidrich, and R. Raskar, in IEEE ICCV (IEEE, 2011), pp. 1180–1186.

Saito, M.

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

Sanderson, A. C.

A. C. Sanderson, L. E. Weiss, and S. K. Nayar, IEEE Trans. Pattern Anal. Mach Intell. 10, 44 (1988).

Sato, Y.

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

Savarese, S.

S. Savarese and P. Perona, in ECCV (Springer, 2002), Vol. 2351, pp. 759–774.

Schröcker, H.-P.

G. Glaeser and H.-P. Schröcker, J. Geom. Graph. 4, 1 (2000).

Seidel, H.-P.

M. B. Hullin, M. Fuchs, I. Ihrke, H.-P. Seidel, and H. P. A. Lensch, ACM Trans. Graph. 27, 87 (2008).

M. Tarini, H. P. A. Lensch, M. Goesele, and H.-P. Seidel, Graph. Models 67, 233 (2005).

Steger, E.

K. N. Kutulakos and E. Steger, Int. J. Comput. Vis. 76, 13 (2008).

Stolz, C.

Tarini, M.

M. Tarini, H. P. A. Lensch, M. Goesele, and H.-P. Seidel, Graph. Models 67, 233 (2005).

Trifonov, B.

B. Trifonov, D. Bradley, and W. Heidrich, in Proceedings of the Eurographics Symposium on Rendering (Eurographics Association, 2006), pp. 51–60.

Weiss, L. E.

A. C. Sanderson, L. E. Weiss, and S. K. Nayar, IEEE Trans. Pattern Anal. Mach Intell. 10, 44 (1988).

Wetzstein, G.

G. Wetzstein, D. Roodnick, W. Heidrich, and R. Raskar, in IEEE ICCV (IEEE, 2011), pp. 1180–1186.

Wolf, E.

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

ACM Trans. Graph. (1)

M. B. Hullin, M. Fuchs, I. Ihrke, H.-P. Seidel, and H. P. A. Lensch, ACM Trans. Graph. 27, 87 (2008).

Astron. Soc. Pac. Conf. (1)

S. B. Howell, Astron. Soc. Pac. Conf. 101, 616 (1989).
[CrossRef]

Graph. Models (1)

M. Tarini, H. P. A. Lensch, M. Goesele, and H.-P. Seidel, Graph. Models 67, 233 (2005).

IEEE Trans. Pattern Anal. Mach Intell. (1)

A. C. Sanderson, L. E. Weiss, and S. K. Nayar, IEEE Trans. Pattern Anal. Mach Intell. 10, 44 (1988).

Int. J. Comput. Vis. (1)

K. N. Kutulakos and E. Steger, Int. J. Comput. Vis. 76, 13 (2008).

J. Geom. Graph. (1)

G. Glaeser and H.-P. Schröcker, J. Geom. Graph. 4, 1 (2000).

J. Opt. Soc. Am. (1)

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

Opt. Express (1)

Opt. Lett. (1)

Other (8)

M. Ben-Ezra and S. K. Nayar, in IEEE ICCV (IEEE, 2003), Vol. 2, pp. 1025–1032.

S. Savarese and P. Perona, in ECCV (Springer, 2002), Vol. 2351, pp. 759–774.

R. Longhurst, Optics, 3rd ed. (Addison-Wesley, 1973).

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

N. J. W. Morris and K. N. Kutulakos, in IEEE ICCV (IEEE, 2007), pp. 1–8.

G. Wetzstein, D. Roodnick, W. Heidrich, and R. Raskar, in IEEE ICCV (IEEE, 2011), pp. 1180–1186.

B. Trifonov, D. Bradley, and W. Heidrich, in Proceedings of the Eurographics Symposium on Rendering (Eurographics Association, 2006), pp. 51–60.

I. Ihrke, K. N. Kutulakos, H. P. A. Lensch, M. Magnor, and W. Heidrich, in STAR Eurographics (Eurographics Association, 2008).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Specular behavior of the two surfaces of a transparent object. (a) Ray tracing for the reflection of a point source. (b) Observation of the reflections of a regular grid on a transparent planar plate.

Fig. 2.
Fig. 2.

(a) Shape from distortion ambiguity for the external surface. (b) Degree of polarization ρ1 as a function of the incidence angle on the external surface θ1r.

Fig. 3.
Fig. 3.

Shape from distortion ambiguity for the internal surface. (a) Given the position of point P2 along the ray r⃗2t, we cannot directly compute the normal n⃗2, as we do not know either the ray i⃗2t or i⃗2. (b) Placing into the plane of incidence Π2i, we can compute the path of light by using Fermat’s principle. (c) Once the point I position is computed, it is possible to get the normal n⃗2. The reverse, computation of P2 position from the normal n⃗2, is straightforward using Snell’s law and triangulation.

Fig. 4.
Fig. 4.

Shape from polarization for the internal surface in the coplanar case. (a) Degree of polarization ρ2 as a function of the incident angle on the internal surface θ2r, for three values of θ2si. (b) Geometry in the coplanar case.

Fig. 5.
Fig. 5.

Experimental results. (a) Our setup with a Plexiglas planar plate. (b) Image of the plate taken with the polarizer oriented at 0°. (c) Reconstruction result on the plate. For each reconstructed points, tangent plane, and normal vector are plotted. (d) Reconstruction result on a Plexiglass cylinder.

Equations (4)

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

S1r=C(φ)R1n(θ1r)C(φ)Si,
S2r=C(φs)Tn1(θ2s)C(φs)C(φr)Rn1(θ2r)C(φr)C(φi)T1n(θ2i)C(φi)Si.
S2r=C(φs)Tn1(θ2s)Rn1(θ2r)T1n(θ2i)C(φi)Si.
f(d2)=ρ2Mρ(d2).

Metrics