Abstract

The Lambertian model for diffuse reflection is widely used for the sake of its simplicity. Nevertheless, this model is known to be inaccurate in describing a lot of real-world objects, including those that present a matte surface. To overcome this difficulty, we propose a photometric model where the surfaces are described as a distribution of facets where each facet consists of a flat interface on a Lambertian background. Compared to the Lambertian model, it includes two additional physical parameters: an interface roughness parameter and the ratio between the refractive indices of the background binder and of the upper medium. The Torrance-Sparrow model--distribution of strictly specular facets--and the Oren-Nayar model--distribution of strictly Lambertian facets--appear as special cases.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. L. Simonot, M. Hébert, and R. Hersch, “Extension of the Williams-Clapper model to stacked nondiffusing colored layers with different refractive indices,” J. Opt. Soc. Am. A 23, 1432-1441 (2006).
    [CrossRef]
  7. L. Simonot and G. Obein, “Geometrical considerations in analyzing isotropic or anisotropic surface reflections,” Appl. Opt. 46, 2615-2623 (2007).
    [CrossRef]
  8. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsber, and T. Limperis, “Geometrical consideration and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, 1-52 (1977).
  9. W. R. McCluney, Introduction to Radiometry and Photometry (Artech, 1994).
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    [CrossRef]
  14. J. L. Saunderson, “Calculation of the color pigmented plastics,” J. Opt. Soc. Am. 32, 727-729 (1942).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley Interscience, 1982).
  18. Commission of Illumination, “Colorimetry,” 3rd ed., Tech. Rep. CIE 15:2004 (CIE, 2004).
  19. L. Simonot and M. Elias, “Color change due to surface state modification,” Color Res. Appl. 28, 45-49 (2003).
    [CrossRef]
  20. L. Simonot and M. Elias, “Color change due to a varnish layer,” Color Res. Appl. 29, 196-204 (2004).
    [CrossRef]
  21. M. Elias and L. Simonot, “Bi-directional reflectance of a varnished painting Part 1: influence of the refractive indices without using the approximations of Saunderson correction--exact computation,” Opt. Commun. 231, 17-24 (2004).
    [CrossRef]
  22. M. Elias, L. Simonot, M. Thoury, J. M. Frigerio, “Bi-directional reflectance of a varnished painting Part 2: comparison between the effects of the refractive indices of the surface states and of the absorption of the varnish--experiments and simulations,” Opt. Commun. 231, 25-33 (2004).
    [CrossRef]

2007 (1)

2006 (1)

2005 (1)

H. Ragheb and E. R. Hancock, “Surface radiance correction for shape shading,” Pattern Recogn. 38, 1574-1595 (2005).
[CrossRef]

2004 (4)

M. Hébert and R. D. Hersch, “Classical print reflection models: a radiometric approach,” J. Imaging Sci. Technol. 48, 363-374 (2004).

L. Simonot and M. Elias, “Color change due to a varnish layer,” Color Res. Appl. 29, 196-204 (2004).
[CrossRef]

M. Elias and L. Simonot, “Bi-directional reflectance of a varnished painting Part 1: influence of the refractive indices without using the approximations of Saunderson correction--exact computation,” Opt. Commun. 231, 17-24 (2004).
[CrossRef]

M. Elias, L. Simonot, M. Thoury, J. M. Frigerio, “Bi-directional reflectance of a varnished painting Part 2: comparison between the effects of the refractive indices of the surface states and of the absorption of the varnish--experiments and simulations,” Opt. Commun. 231, 25-33 (2004).
[CrossRef]

2003 (1)

L. Simonot and M. Elias, “Color change due to surface state modification,” Color Res. Appl. 28, 45-49 (2003).
[CrossRef]

2001 (2)

C. Bruegge, N. Chrien, and D. Haner, “A spectralon BRF data base for MISR calibration applications,” Remote Sens. Environ. 77, 354-366 (2001).
[CrossRef]

M. Elias, L. Simonot, and M. Menu, “Bidirectional reflectance of a diffuse background covered by a partly absorbing layer,” Opt. Commun. 191, 1-7 (2001).
[CrossRef]

1999 (1)

1995 (1)

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

1994 (1)

1977 (1)

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsber, and T. Limperis, “Geometrical consideration and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, 1-52 (1977).

1967 (1)

1942 (2)

D. B. Judd, “Fresnel Reflection of Diffusely Incident Light,” J. Res. Natl. Bur. Stand. 29, 329-332 (1942).

J. L. Saunderson, “Calculation of the color pigmented plastics,” J. Opt. Soc. Am. 32, 727-729 (1942).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principle of Optics, 7th ed. (Pergamon, 1999).

Bruegge, C.

C. Bruegge, N. Chrien, and D. Haner, “A spectralon BRF data base for MISR calibration applications,” Remote Sens. Environ. 77, 354-366 (2001).
[CrossRef]

D. Haner, B. McGuckin, and C. Bruegge, “Polarization characteristics of spectralon illuminated by coherent light,” Appl. Opt. 38, 6350-6356 (1999).
[CrossRef]

Chrien, N.

C. Bruegge, N. Chrien, and D. Haner, “A spectralon BRF data base for MISR calibration applications,” Remote Sens. Environ. 77, 354-366 (2001).
[CrossRef]

Elias, M.

M. Elias, L. Simonot, M. Thoury, J. M. Frigerio, “Bi-directional reflectance of a varnished painting Part 2: comparison between the effects of the refractive indices of the surface states and of the absorption of the varnish--experiments and simulations,” Opt. Commun. 231, 25-33 (2004).
[CrossRef]

M. Elias and L. Simonot, “Bi-directional reflectance of a varnished painting Part 1: influence of the refractive indices without using the approximations of Saunderson correction--exact computation,” Opt. Commun. 231, 17-24 (2004).
[CrossRef]

L. Simonot and M. Elias, “Color change due to a varnish layer,” Color Res. Appl. 29, 196-204 (2004).
[CrossRef]

L. Simonot and M. Elias, “Color change due to surface state modification,” Color Res. Appl. 28, 45-49 (2003).
[CrossRef]

M. Elias, L. Simonot, and M. Menu, “Bidirectional reflectance of a diffuse background covered by a partly absorbing layer,” Opt. Commun. 191, 1-7 (2001).
[CrossRef]

Frigerio, J. M.

M. Elias, L. Simonot, M. Thoury, J. M. Frigerio, “Bi-directional reflectance of a varnished painting Part 2: comparison between the effects of the refractive indices of the surface states and of the absorption of the varnish--experiments and simulations,” Opt. Commun. 231, 25-33 (2004).
[CrossRef]

Ginsber, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsber, and T. Limperis, “Geometrical consideration and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, 1-52 (1977).

Hancock, E. R.

H. Ragheb and E. R. Hancock, “Surface radiance correction for shape shading,” Pattern Recogn. 38, 1574-1595 (2005).
[CrossRef]

Haner, D.

C. Bruegge, N. Chrien, and D. Haner, “A spectralon BRF data base for MISR calibration applications,” Remote Sens. Environ. 77, 354-366 (2001).
[CrossRef]

D. Haner, B. McGuckin, and C. Bruegge, “Polarization characteristics of spectralon illuminated by coherent light,” Appl. Opt. 38, 6350-6356 (1999).
[CrossRef]

Hébert, M.

Hersch, R.

Hersch, R. D.

M. Hébert and R. D. Hersch, “Classical print reflection models: a radiometric approach,” J. Imaging Sci. Technol. 48, 363-374 (2004).

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsber, and T. Limperis, “Geometrical consideration and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, 1-52 (1977).

Judd, D. B.

D. B. Judd, “Fresnel Reflection of Diffusely Incident Light,” J. Res. Natl. Bur. Stand. 29, 329-332 (1942).

Lambert, J. H.

J. H. Lambert, Photometria Sive de Mensure de Gratibus Luminis, Colorum Umbrae (Eberhard Klett, 1760).

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsber, and T. Limperis, “Geometrical consideration and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, 1-52 (1977).

McCluney, W. R.

W. R. McCluney, Introduction to Radiometry and Photometry (Artech, 1994).

McGuckin, B.

Menu, M.

M. Elias, L. Simonot, and M. Menu, “Bidirectional reflectance of a diffuse background covered by a partly absorbing layer,” Opt. Commun. 191, 1-7 (2001).
[CrossRef]

Nayar, S. K.

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

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsber, and T. Limperis, “Geometrical consideration and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, 1-52 (1977).

Obein, G.

Oren, M.

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

Ragheb, H.

H. Ragheb and E. R. Hancock, “Surface radiance correction for shape shading,” Pattern Recogn. 38, 1574-1595 (2005).
[CrossRef]

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsber, and T. Limperis, “Geometrical consideration and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, 1-52 (1977).

Saunderson, J. L.

Simonot, L.

L. Simonot and G. Obein, “Geometrical considerations in analyzing isotropic or anisotropic surface reflections,” Appl. Opt. 46, 2615-2623 (2007).
[CrossRef]

L. Simonot, M. Hébert, and R. Hersch, “Extension of the Williams-Clapper model to stacked nondiffusing colored layers with different refractive indices,” J. Opt. Soc. Am. A 23, 1432-1441 (2006).
[CrossRef]

L. Simonot and M. Elias, “Color change due to a varnish layer,” Color Res. Appl. 29, 196-204 (2004).
[CrossRef]

M. Elias, L. Simonot, M. Thoury, J. M. Frigerio, “Bi-directional reflectance of a varnished painting Part 2: comparison between the effects of the refractive indices of the surface states and of the absorption of the varnish--experiments and simulations,” Opt. Commun. 231, 25-33 (2004).
[CrossRef]

M. Elias and L. Simonot, “Bi-directional reflectance of a varnished painting Part 1: influence of the refractive indices without using the approximations of Saunderson correction--exact computation,” Opt. Commun. 231, 17-24 (2004).
[CrossRef]

L. Simonot and M. Elias, “Color change due to surface state modification,” Color Res. Appl. 28, 45-49 (2003).
[CrossRef]

M. Elias, L. Simonot, and M. Menu, “Bidirectional reflectance of a diffuse background covered by a partly absorbing layer,” Opt. Commun. 191, 1-7 (2001).
[CrossRef]

Sparrow, E. M.

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley Interscience, 1982).

Thoury, M.

M. Elias, L. Simonot, M. Thoury, J. M. Frigerio, “Bi-directional reflectance of a varnished painting Part 2: comparison between the effects of the refractive indices of the surface states and of the absorption of the varnish--experiments and simulations,” Opt. Commun. 231, 25-33 (2004).
[CrossRef]

Torrance, K. E.

Wolf, E.

M. Born and E. Wolf, Principle of Optics, 7th ed. (Pergamon, 1999).

Wolff, L. B.

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley Interscience, 1982).

Appl. Opt. (2)

Color Res. Appl. (2)

L. Simonot and M. Elias, “Color change due to surface state modification,” Color Res. Appl. 28, 45-49 (2003).
[CrossRef]

L. Simonot and M. Elias, “Color change due to a varnish layer,” Color Res. Appl. 29, 196-204 (2004).
[CrossRef]

Int. J. Comput. Vis. (1)

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

J. Imaging Sci. Technol. (1)

M. Hébert and R. D. Hersch, “Classical print reflection models: a radiometric approach,” J. Imaging Sci. Technol. 48, 363-374 (2004).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

J. Res. Natl. Bur. Stand. (1)

D. B. Judd, “Fresnel Reflection of Diffusely Incident Light,” J. Res. Natl. Bur. Stand. 29, 329-332 (1942).

Natl. Bur. Stand. Monogr. (1)

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsber, and T. Limperis, “Geometrical consideration and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, 1-52 (1977).

Opt. Commun. (3)

M. Elias, L. Simonot, and M. Menu, “Bidirectional reflectance of a diffuse background covered by a partly absorbing layer,” Opt. Commun. 191, 1-7 (2001).
[CrossRef]

M. Elias and L. Simonot, “Bi-directional reflectance of a varnished painting Part 1: influence of the refractive indices without using the approximations of Saunderson correction--exact computation,” Opt. Commun. 231, 17-24 (2004).
[CrossRef]

M. Elias, L. Simonot, M. Thoury, J. M. Frigerio, “Bi-directional reflectance of a varnished painting Part 2: comparison between the effects of the refractive indices of the surface states and of the absorption of the varnish--experiments and simulations,” Opt. Commun. 231, 25-33 (2004).
[CrossRef]

Pattern Recogn. (1)

H. Ragheb and E. R. Hancock, “Surface radiance correction for shape shading,” Pattern Recogn. 38, 1574-1595 (2005).
[CrossRef]

Remote Sens. Environ. (1)

C. Bruegge, N. Chrien, and D. Haner, “A spectralon BRF data base for MISR calibration applications,” Remote Sens. Environ. 77, 354-366 (2001).
[CrossRef]

Other (5)

J. H. Lambert, Photometria Sive de Mensure de Gratibus Luminis, Colorum Umbrae (Eberhard Klett, 1760).

W. R. McCluney, Introduction to Radiometry and Photometry (Artech, 1994).

M. Born and E. Wolf, Principle of Optics, 7th ed. (Pergamon, 1999).

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley Interscience, 1982).

Commission of Illumination, “Colorimetry,” 3rd ed., Tech. Rep. CIE 15:2004 (CIE, 2004).

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