Abstract

A polarimetric vision system yielding a roughness-segmentation-based image is described. As a general principle, the bidirectional reflectance distribution function (BRDF) of a surface is assumed to be related to its local irregularities, i.e., its roughness. This BRDF is seen as the sum of a specular and a diffuse component. In this paper we propose to introduce polarization measurements in order to estimate this roughness parameter without requiring any assumption for the model of the diffuse component, nor is diffuse–specular separation required. Moreover, with the proposed method, the refractive indices of the observed objects are estimated at each pixel. Examples are given for quality control applications.

© 2008 Optical Society of America

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References

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  1. D. J. Whitehouse, "Surface metrology," Meas. Sci. Technol. 8, 955-972 (1997).
    [CrossRef]
  2. J. Liu, K. Ymazaki, and Y. Zhou, "A reflective fiber optic sensor for surface roughness inprocess measurement," J. Manuf. Sci. Eng. 124, 515-522 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. C. Lindner and F. Puente Leon, "Reflection-based surface segmentation using active illumination," in Proceedings of IEEE Instrumentation and Measurement Technical Conference (IEEE, 2006), pp. 157-162.
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  13. D. Kim, S. Lin, K. Hong, and H. Shum, "Variational separation using color and polarization," in Proceedings of Workshop on Machine Vision and Applications (IAPR, 2002), pp. 176-179.
  14. S. K. Nayar, X. Fang, and T. Boult, "Separation of reflection components using color and polarization," Int. J. Comput. Vis. 21, 163-186 (1997).
    [CrossRef]
  15. L. B. Wolff and T. E. Boult, "Constraining object features using a polarization reflectance model," IEEE Trans. Pattern Anal. Mach. Intell. 13, 635-657 (1991).
    [CrossRef]
  16. F. Goudail, P. Terrier, Y. Takakura, L. Bigué, F. Galland, and V. Devlaminck, "Target detection with a liquid crystal-based passive Stokes polarimeter," Appl. Opt. 43, 274-282 (2004).
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  17. J. S. Tyo, "Design of optimal polarimeters: maximization of SNR and minimization of systematic errors," Appl. Opt. 41, 619-630 (2002).
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  20. K. N. Kutulakos and E. Steger, "A theory of refractive and specular 3D shape by lightpath triangulation," in Proceedings of IEEE International Conference on Computer Vision (ICCV'05) (IEEE, 2005), Vol. 2, pp. 1448-1455.
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    [CrossRef]

2004 (1)

2003 (1)

2002 (2)

J. Liu, K. Ymazaki, and Y. Zhou, "A reflective fiber optic sensor for surface roughness inprocess measurement," J. Manuf. Sci. Eng. 124, 515-522 (2002).
[CrossRef]

J. S. Tyo, "Design of optimal polarimeters: maximization of SNR and minimization of systematic errors," Appl. Opt. 41, 619-630 (2002).
[CrossRef] [PubMed]

2001 (1)

1998 (1)

H. C. Chen and L. B. Wolff, "Polarization phased-based method for material classification in computer vision," Int. J. Comput. Vis. 28, 73-83 (1998).
[CrossRef]

1997 (2)

S. K. Nayar, X. Fang, and T. Boult, "Separation of reflection components using color and polarization," Int. J. Comput. Vis. 21, 163-186 (1997).
[CrossRef]

D. J. Whitehouse, "Surface metrology," Meas. Sci. Technol. 8, 955-972 (1997).
[CrossRef]

1996 (1)

F. Solomon and K. Ikeuchi, "Extracting the shape and roughness of specular lobe objects using four light photometric stereo," IEEE Trans. Pattern Anal. Mach. Intell. 18, 449-454 (1996).
[CrossRef]

1995 (1)

M. Oren and S. K. Nayar, "Generalization of the Lambertian model and implications for machines vision," Int. J. Comput. Vis. 14, 227-251 (1995).
[CrossRef]

1991 (1)

L. B. Wolff and T. E. Boult, "Constraining object features using a polarization reflectance model," IEEE Trans. Pattern Anal. Mach. Intell. 13, 635-657 (1991).
[CrossRef]

1985 (1)

S. Shafer, "Using color to separate reflection components," Color Res. Appl. 10, 210-218 (1985).
[CrossRef]

1967 (1)

Appl. Opt. (4)

Color Res. Appl. (1)

S. Shafer, "Using color to separate reflection components," Color Res. Appl. 10, 210-218 (1985).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (2)

L. B. Wolff and T. E. Boult, "Constraining object features using a polarization reflectance model," IEEE Trans. Pattern Anal. Mach. Intell. 13, 635-657 (1991).
[CrossRef]

F. Solomon and K. Ikeuchi, "Extracting the shape and roughness of specular lobe objects using four light photometric stereo," IEEE Trans. Pattern Anal. Mach. Intell. 18, 449-454 (1996).
[CrossRef]

Int. J. Comput. Vis. (3)

M. Oren and S. K. Nayar, "Generalization of the Lambertian model and implications for machines vision," Int. J. Comput. Vis. 14, 227-251 (1995).
[CrossRef]

S. K. Nayar, X. Fang, and T. Boult, "Separation of reflection components using color and polarization," Int. J. Comput. Vis. 21, 163-186 (1997).
[CrossRef]

H. C. Chen and L. B. Wolff, "Polarization phased-based method for material classification in computer vision," Int. J. Comput. Vis. 28, 73-83 (1998).
[CrossRef]

J. Manuf. Sci. Eng. (1)

J. Liu, K. Ymazaki, and Y. Zhou, "A reflective fiber optic sensor for surface roughness inprocess measurement," J. Manuf. Sci. Eng. 124, 515-522 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (1)

D. J. Whitehouse, "Surface metrology," Meas. Sci. Technol. 8, 955-972 (1997).
[CrossRef]

Other (8)

D. Miyazaki, R. T. Tan, K. Hara, and K. Ikeuchi, "Polarization-based inverse rendering from a single view," in Proceedings of IEEE Conference on Computer Vision (IEEE, 2003), pp. 982-987.
[CrossRef]

C. Lindner and F. Puente Leon, "Reflection-based surface segmentation using active illumination," in Proceedings of IEEE Instrumentation and Measurement Technical Conference (IEEE, 2006), pp. 157-162.
[CrossRef]

R. L. Cook and K. E. Torrance, "A reflectance model for computer graphics," in Proceedings of Computer Graphics (SIGGRAPH, 1981), Vol. 15, pp. 307-316.
[CrossRef]

S. Lin, Y. Li, S. B. Kang, X. Tong, and H. Shum, "Diffuse-specular separation and depth recovery from image sequences," in Proceedings of European Conference on Computer Vision (ECCV, 2002), Vol. 3, pp. 89-103.

D. Kim, S. Lin, K. Hong, and H. Shum, "Variational separation using color and polarization," in Proceedings of Workshop on Machine Vision and Applications (IAPR, 2002), pp. 176-179.

E. Collet, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1993).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1999).

K. N. Kutulakos and E. Steger, "A theory of refractive and specular 3D shape by lightpath triangulation," in Proceedings of IEEE International Conference on Computer Vision (ICCV'05) (IEEE, 2005), Vol. 2, pp. 1448-1455.

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Figures (11)

Fig. 1
Fig. 1

Geometry of the microfacet model.

Fig. 2
Fig. 2

Geometry of the measurement device.

Fig. 3
Fig. 3

Observed scene (two objects with different roughness).

Fig. 4
Fig. 4

Stokes images for four elevation angles θ S of the light source.

Fig. 5
Fig. 5

Linear regression applied on the two series of points computed for an arbitrary pixel of the triangle region.

Fig. 6
Fig. 6

Linear regression applied on the two series of points computed for an arbitrary pixel of the square region.

Fig. 7
Fig. 7

Intensity image of the observed piece of wood with histogram equalization for contrast enhancement.

Fig. 8
Fig. 8

Estimated s value map for the observed scene.

Fig. 9
Fig. 9

Detection of varnished defect (triangle) on a metallic object (varnish for automobile painting is used). Left, intensity image with histogram equalization for contrast enhancement; right, Δ image.

Fig. 10
Fig. 10

Detection of thin dielectric deposit (text) on a metallic object (the text was written with a lacquer for hair). Left, intensity image with histogram equalization for contrast enhancement; right, Δ image.

Fig. 11
Fig. 11

Detection of oil traces (text) on a metallic object (the text was written with lubrication oil for industrial tools). Left, intensity image with histogram equalization for contrast enhancement; right, Δ image.

Equations (22)

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

D ( a ) = 1 s 2 cos 4 a exp ( tan 2 a s 2 ) .
I C = K D , C cos θ i + K S , C F ( η , θ i ) G ( a , θ i , θ i , θ R ) D ( a ) cos θ R ,
G = min { 1 ; 2 cos a cos θ R cos θ i ; 2 cos a cos θ i cos θ i } .
ρ S = cos θ i η cos γ cos θ i + η cos γ ,
ρ P = η cos θ i cos γ cos γ + η cos θ i .
cos γ = η 2 sin 2 θ i η .
M = 1 2 [ ρ S ρ S + ρ P ρ P ρ S ρ S ρ P ρ P 0 0 ρ S ρ S ρ P ρ P ρ S ρ S + ρ P ρ P 0 0 0 0 ρ S ρ P + ρ P ρ S j ( ρ S ρ P ρ P ρ S ) 0 0 j ( ρ S ρ P ρ P ρ S ) ρ S ρ P + ρ P ρ S ] .
cos a = cos θ N cos θ S 2 + sin θ N sin θ S 2 cos ( φ S φ N ) ,
θ R = θ N ,
cos θ i = cos θ N cos θ S + sin θ N sin θ S cos ( φ S φ N ) ,
θ i = θ S 2 .
S D = S 0 D 0 0 0 = S 0 K D cos θ i 0 0 0 ,
S S = S 0 S S 1 S S 2 S S 3 S = K S G 1 s 2 cos 4 a cos θ R exp ( tan 2 a s 2 ) S 0 M 11 S 0 M 21 S 0 M 33 S 0 M 43 ,
S 2 S S 1 S = M 33 M 21 = ρ S ρ P + ρ P ρ S ρ S ρ S ρ P ρ P = f ( η , θ i ) .
G = θ i ( ( S 2 S S 1 S ) measured f ( η ) modeled ) 2 .
ln ( S 1 or 2 S cos 4 a cos θ R G M 21 or 33 ) = ln ( K S s 2 ) tan 2 a s 2 .
Y 1 = ln ( S 1 S cos 4 a cos θ R G M 21 ) ,
Y 2 = ln ( S 2 S cos 4 a cos θ R G M 33 ) ,
X = tan 2 a .
ρ P ρ S = tan Ψ e i Δ .
M = ρ S 2 2 [ 1 + tan 2 Ψ 1 tan 2 Ψ 0 0 1 tan 2 Ψ 1 + tan 2 Ψ 0 0 0 0 2 tan Ψ cos Δ 2 tan Ψ sin Δ 0 0 2 tan Ψ sin Δ 2 tan Ψ cos Δ ] .
S 3 S 2 = M 43 M 33 = 2 tan Ψ sin Δ 2 tan Ψ cos Δ = tan Δ .

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