Abstract

A method to recover the shape of metallic surfaces that have a directional microstructure is demonstrated. A simple model that shows how surface radiance varies with the azimuth of the light source is described and verified on real surfaces. The model predicts that if a light source is revolved around a flat facet then two peaks in radiance will be observed: tilting the facet against the grain of the material will cause the amplitudes of the peaks to change relative to one another; titling the facet with the grain will change the angles at which the peaks occur. It is shown that by measuring these effects, it is possible to estimate the slope of the facet within a limited range.

© 2009 Optical Society of America

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References

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  1. R. Woodham, “Photometric methods for determining surface orientation from multiple images,” Opt. Eng. (Bellingham) 19, 139-144 (1980).
  2. E. Coleman and R. Jain, “Obtaining 3-dimensional shape of textured and specular surfaces using four-source photometry,” Comput. Graph. Image Process. 18, 309-328 (1982).
    [CrossRef]
  3. S. Barsky and M. Petrou, “The 4-source photometric stereo technique for three-dimensional surfaces in the presence of highlights and shadows,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1239-1252 (2003).
    [CrossRef]
  4. K. Ikeuchi, “Determining surface orientation of specular surfaces by using the photometric stereo method,” IEEE Trans. Pattern Anal. Mach. Intell. 3, 661-669 (1981).
    [CrossRef] [PubMed]
  5. G. Healey and T. Binford, “Local shape from specularity,” Comput. Vis. Graph. Image Process. 42, 62-86 (1988).
    [CrossRef]
  6. S. K. Nayar, A. C. Sanderson, L. E. Weiss, and D. D. Simon, “Specular surface inspection using structured highlight and Gaussian images,” IEEE Trans. Rob. Autom. 6, 208-218 (1990).
    [CrossRef]
  7. J. Wang and K. Dana, “Relief texture from specularities,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 446-457 (2006).
    [CrossRef] [PubMed]
  8. T. Chen, M. Goesele, and H. Seidel, “Mesostructure from specularity,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2006), pp. 1825-1832.
  9. J. T. Kajiya, “Anisotropic reflection models,” in Proceedings of 12th Annual Conference on Computer Graphics and Interactive Techniques (ACM SIGGRAPH, 1985), pp. 15-21.
    [CrossRef]
  10. P. Poulin and A. Fournier, “A model for anisotropic reflection,” ACM SIGGRAPH Comput. Graph. 24, 273-282 (1990).
    [CrossRef]
  11. G. Ward: “Measuring and modeling anisotropic reflection,” ACM SIGGRAPH Comput. Graph. 26, 265-272 (1992).
    [CrossRef]
  12. M. Ashikhmin and P. Shirley, “An anisotropic phong BRDF model,” J. Graph. Tools 5, 25-32 (2000).
  13. M. Holroyd, J. Lawrence, G. Humphreys, and T. Zickler, “A photometric approach for estimating normals and tangents,” in ACM Proceedings of SIGGRAPH Asia 2008 (ACM, 2008), pp. 133-141
  14. G. McGunnigle, “Estimating fibre orientation in spruce using lighting direction,” IET Comput. Vis. 3, 143-158 (2009).
    [CrossRef]

2009 (1)

G. McGunnigle, “Estimating fibre orientation in spruce using lighting direction,” IET Comput. Vis. 3, 143-158 (2009).
[CrossRef]

2006 (1)

J. Wang and K. Dana, “Relief texture from specularities,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 446-457 (2006).
[CrossRef] [PubMed]

2003 (1)

S. Barsky and M. Petrou, “The 4-source photometric stereo technique for three-dimensional surfaces in the presence of highlights and shadows,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1239-1252 (2003).
[CrossRef]

2000 (1)

M. Ashikhmin and P. Shirley, “An anisotropic phong BRDF model,” J. Graph. Tools 5, 25-32 (2000).

1992 (1)

G. Ward: “Measuring and modeling anisotropic reflection,” ACM SIGGRAPH Comput. Graph. 26, 265-272 (1992).
[CrossRef]

1990 (2)

P. Poulin and A. Fournier, “A model for anisotropic reflection,” ACM SIGGRAPH Comput. Graph. 24, 273-282 (1990).
[CrossRef]

S. K. Nayar, A. C. Sanderson, L. E. Weiss, and D. D. Simon, “Specular surface inspection using structured highlight and Gaussian images,” IEEE Trans. Rob. Autom. 6, 208-218 (1990).
[CrossRef]

1988 (1)

G. Healey and T. Binford, “Local shape from specularity,” Comput. Vis. Graph. Image Process. 42, 62-86 (1988).
[CrossRef]

1982 (1)

E. Coleman and R. Jain, “Obtaining 3-dimensional shape of textured and specular surfaces using four-source photometry,” Comput. Graph. Image Process. 18, 309-328 (1982).
[CrossRef]

1981 (1)

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

1980 (1)

R. Woodham, “Photometric methods for determining surface orientation from multiple images,” Opt. Eng. (Bellingham) 19, 139-144 (1980).

Ashikhmin, M.

M. Ashikhmin and P. Shirley, “An anisotropic phong BRDF model,” J. Graph. Tools 5, 25-32 (2000).

Barsky, S.

S. Barsky and M. Petrou, “The 4-source photometric stereo technique for three-dimensional surfaces in the presence of highlights and shadows,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1239-1252 (2003).
[CrossRef]

Binford, T.

G. Healey and T. Binford, “Local shape from specularity,” Comput. Vis. Graph. Image Process. 42, 62-86 (1988).
[CrossRef]

Chen, T.

T. Chen, M. Goesele, and H. Seidel, “Mesostructure from specularity,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2006), pp. 1825-1832.

Coleman, E.

E. Coleman and R. Jain, “Obtaining 3-dimensional shape of textured and specular surfaces using four-source photometry,” Comput. Graph. Image Process. 18, 309-328 (1982).
[CrossRef]

Dana, K.

J. Wang and K. Dana, “Relief texture from specularities,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 446-457 (2006).
[CrossRef] [PubMed]

Fournier, A.

P. Poulin and A. Fournier, “A model for anisotropic reflection,” ACM SIGGRAPH Comput. Graph. 24, 273-282 (1990).
[CrossRef]

Goesele, M.

T. Chen, M. Goesele, and H. Seidel, “Mesostructure from specularity,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2006), pp. 1825-1832.

Healey, G.

G. Healey and T. Binford, “Local shape from specularity,” Comput. Vis. Graph. Image Process. 42, 62-86 (1988).
[CrossRef]

Holroyd, M.

M. Holroyd, J. Lawrence, G. Humphreys, and T. Zickler, “A photometric approach for estimating normals and tangents,” in ACM Proceedings of SIGGRAPH Asia 2008 (ACM, 2008), pp. 133-141

Humphreys, G.

M. Holroyd, J. Lawrence, G. Humphreys, and T. Zickler, “A photometric approach for estimating normals and tangents,” in ACM Proceedings of SIGGRAPH Asia 2008 (ACM, 2008), pp. 133-141

Ikeuchi, K.

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

Jain, R.

E. Coleman and R. Jain, “Obtaining 3-dimensional shape of textured and specular surfaces using four-source photometry,” Comput. Graph. Image Process. 18, 309-328 (1982).
[CrossRef]

Kajiya, J. T.

J. T. Kajiya, “Anisotropic reflection models,” in Proceedings of 12th Annual Conference on Computer Graphics and Interactive Techniques (ACM SIGGRAPH, 1985), pp. 15-21.
[CrossRef]

Lawrence, J.

M. Holroyd, J. Lawrence, G. Humphreys, and T. Zickler, “A photometric approach for estimating normals and tangents,” in ACM Proceedings of SIGGRAPH Asia 2008 (ACM, 2008), pp. 133-141

McGunnigle, G.

G. McGunnigle, “Estimating fibre orientation in spruce using lighting direction,” IET Comput. Vis. 3, 143-158 (2009).
[CrossRef]

Nayar, S. K.

S. K. Nayar, A. C. Sanderson, L. E. Weiss, and D. D. Simon, “Specular surface inspection using structured highlight and Gaussian images,” IEEE Trans. Rob. Autom. 6, 208-218 (1990).
[CrossRef]

Petrou, M.

S. Barsky and M. Petrou, “The 4-source photometric stereo technique for three-dimensional surfaces in the presence of highlights and shadows,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1239-1252 (2003).
[CrossRef]

Poulin, P.

P. Poulin and A. Fournier, “A model for anisotropic reflection,” ACM SIGGRAPH Comput. Graph. 24, 273-282 (1990).
[CrossRef]

Sanderson, A. C.

S. K. Nayar, A. C. Sanderson, L. E. Weiss, and D. D. Simon, “Specular surface inspection using structured highlight and Gaussian images,” IEEE Trans. Rob. Autom. 6, 208-218 (1990).
[CrossRef]

Seidel, H.

T. Chen, M. Goesele, and H. Seidel, “Mesostructure from specularity,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2006), pp. 1825-1832.

Shirley, P.

M. Ashikhmin and P. Shirley, “An anisotropic phong BRDF model,” J. Graph. Tools 5, 25-32 (2000).

Simon, D. D.

S. K. Nayar, A. C. Sanderson, L. E. Weiss, and D. D. Simon, “Specular surface inspection using structured highlight and Gaussian images,” IEEE Trans. Rob. Autom. 6, 208-218 (1990).
[CrossRef]

Wang, J.

J. Wang and K. Dana, “Relief texture from specularities,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 446-457 (2006).
[CrossRef] [PubMed]

Ward, G.

G. Ward: “Measuring and modeling anisotropic reflection,” ACM SIGGRAPH Comput. Graph. 26, 265-272 (1992).
[CrossRef]

Weiss, L. E.

S. K. Nayar, A. C. Sanderson, L. E. Weiss, and D. D. Simon, “Specular surface inspection using structured highlight and Gaussian images,” IEEE Trans. Rob. Autom. 6, 208-218 (1990).
[CrossRef]

Woodham, R.

R. Woodham, “Photometric methods for determining surface orientation from multiple images,” Opt. Eng. (Bellingham) 19, 139-144 (1980).

Zickler, T.

M. Holroyd, J. Lawrence, G. Humphreys, and T. Zickler, “A photometric approach for estimating normals and tangents,” in ACM Proceedings of SIGGRAPH Asia 2008 (ACM, 2008), pp. 133-141

ACM SIGGRAPH Comput. Graph. (2)

P. Poulin and A. Fournier, “A model for anisotropic reflection,” ACM SIGGRAPH Comput. Graph. 24, 273-282 (1990).
[CrossRef]

G. Ward: “Measuring and modeling anisotropic reflection,” ACM SIGGRAPH Comput. Graph. 26, 265-272 (1992).
[CrossRef]

Comput. Graph. Image Process. (1)

E. Coleman and R. Jain, “Obtaining 3-dimensional shape of textured and specular surfaces using four-source photometry,” Comput. Graph. Image Process. 18, 309-328 (1982).
[CrossRef]

Comput. Vis. Graph. Image Process. (1)

G. Healey and T. Binford, “Local shape from specularity,” Comput. Vis. Graph. Image Process. 42, 62-86 (1988).
[CrossRef]

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

S. Barsky and M. Petrou, “The 4-source photometric stereo technique for three-dimensional surfaces in the presence of highlights and shadows,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1239-1252 (2003).
[CrossRef]

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

J. Wang and K. Dana, “Relief texture from specularities,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 446-457 (2006).
[CrossRef] [PubMed]

IEEE Trans. Rob. Autom. (1)

S. K. Nayar, A. C. Sanderson, L. E. Weiss, and D. D. Simon, “Specular surface inspection using structured highlight and Gaussian images,” IEEE Trans. Rob. Autom. 6, 208-218 (1990).
[CrossRef]

IET Comput. Vis. (1)

G. McGunnigle, “Estimating fibre orientation in spruce using lighting direction,” IET Comput. Vis. 3, 143-158 (2009).
[CrossRef]

J. Graph. Tools (1)

M. Ashikhmin and P. Shirley, “An anisotropic phong BRDF model,” J. Graph. Tools 5, 25-32 (2000).

Opt. Eng. (Bellingham) (1)

R. Woodham, “Photometric methods for determining surface orientation from multiple images,” Opt. Eng. (Bellingham) 19, 139-144 (1980).

Other (3)

T. Chen, M. Goesele, and H. Seidel, “Mesostructure from specularity,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2006), pp. 1825-1832.

J. T. Kajiya, “Anisotropic reflection models,” in Proceedings of 12th Annual Conference on Computer Graphics and Interactive Techniques (ACM SIGGRAPH, 1985), pp. 15-21.
[CrossRef]

M. Holroyd, J. Lawrence, G. Humphreys, and T. Zickler, “A photometric approach for estimating normals and tangents,” in ACM Proceedings of SIGGRAPH Asia 2008 (ACM, 2008), pp. 133-141

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Figures (12)

Fig. 1
Fig. 1

Tilting a facet with a directional microstructure against the grain and with the grain.

Fig. 2
Fig. 2

Azimuth function predicted by the model for a flat facet and a facet tilted with the grain (left) and a facet tilted against the grain (right).

Fig. 3
Fig. 3

Azimuth functions of a ground nickel sample ( R a = 1.6 ) lying flat and tilted with the grain (left); tilted against the grain and tilted both with and against the grain (right).

Fig. 4
Fig. 4

Graphical description of the effect. A facet lying flat (left), a facet tilted with the grain (center), and a facet tilted against the grain (right).

Fig. 5
Fig. 5

Samples: F-samples (left) and L- and T-samples (right).

Fig. 6
Fig. 6

Difference between L- and T-samples; exaggerated roughness.

Fig. 7
Fig. 7

Imaging geometry. Note: the ’blind zone’ refers to the range of azimuths for which we could not illuminate the sample (approximately 12° of azimuth).

Fig. 8
Fig. 8

Effect of surface roughness (left) and the zenith of the light source (right) on the azimuthal peak.

Fig. 9
Fig. 9

Phase difference predicted by model plotted against measured phase differences for T-samples.

Fig. 10
Fig. 10

Peak ratio coefficient C predicted by model plotted against measured values for L-samples.

Fig. 11
Fig. 11

Slope estimation for facets tilted with the grain.

Fig. 12
Fig. 12

Slope estimation for facets tilted against the grain.

Tables (3)

Tables Icon

Table 1 Average Arithmetic Roughness of Test Samples

Tables Icon

Table 2 Effect of Roughness on the Width of the Peaks, Samples Lit from a Zenith of 45°

Tables Icon

Table 3 Effect of Zenith of the Light Source on the Width of the Peaks (N7 sample)

Equations (15)

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

I facet ( τ ) = k σ p σ q exp { 1 2 [ ( r cos τ p 0 σ p ) 2 + ( r sin τ q 0 σ q ) 2 ] } ,
p = d z d x , q = d z d y ;
r = ( p sp 2 + q sp 2 ) , k = const. ,
p sp = r cos τ , q sp = r sin τ .
( r cos τ σ p ) 2 + ( r sin τ q 0 σ q ) 2 = 0 .
( r sin τ q 0 σ q ) 2 = 0 ,
q 0 = r sin τ ,
τ = sin 1 ( q 0 r ) .
δ P = 2 τ = 2 sin 1 ( q 0 r ) .
R = i ( τ = 0 ° ) i ( τ = 180 ° ) = exp { 1 2 [ ( r p 0 σ p ) 2 + ( r p 0 σ p ) 2 ] } ,
R = exp { 1 2 ( 4 r p 0 σ p 2 ) } ,
R = exp ( 2 r p 0 σ p 2 ) .
C = i ( τ = 0 ° ) i ( τ = 180 ° ) + i ( τ = 0 ° ) = 1 1 + 1 R .
p 0 = σ p 2 2 r ln ( I 0 I 180 ) ,
q 0 = r sin δ P 2 .

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