Abstract

Estimates of the frequency of metameric surfaces, which appear the same to the eye under one illuminant but different under another, were obtained from 50 hyperspectral images of natural scenes. The degree of metamerism was specified with respect to a color-difference measure after allowing for full chromatic adaptation. The relative frequency of metameric pairs of surfaces, expressed as a proportion of all pairs of surfaces in a scene, was very low. Depending on the criterion degree of metamerism, it ranged from about 106 to 104 for the largest illuminant change tested, which was from a daylight of correlated color temperature 25,000K to one of 4000K. But, given pairs of surfaces that were indistinguishable under one of these illuminants, the conditional relative frequency of metamerism was much higher, from about 102 to 101, sufficiently large to affect visual inferences about material identity.

© 2006 Optical Society of America

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2006 (2)

D. H. Foster, K. Amano, and S. M. C. Nascimento, "Color constancy in natural scenes explained by global image statistics," Visual Neurosci. 23, 341-349 (2006).
[CrossRef]

K. Amano, D. H. Foster, and S. M. C. Nascimento, "Color constancy in natural scenes with and without an explicit illuminant cue," Visual Neurosci. 23, 351-356 (2006).
[CrossRef]

2005 (5)

C. A. Párraga, T. Troscianko, and D. J. Tolhurst, "The effects of amplitude-spectrum statistics on foveal and peripheral discrimination of changes in natural images, and a multiresolution model," Vision Res. 45, 3145-3168 (2005).
[CrossRef] [PubMed]

D. H. Foster, S. M. C. Nascimento, and K. Amano, "Information limits on identification of natural surfaces by apparent colour," Perception 34, 1003-1008 (2005).
[CrossRef] [PubMed]

E. K. Oxtoby and D. H. Foster, "Perceptual limits on low-dimensional models of Munsell reflectance spectra," Perception 34, 961-966 (2005).
[CrossRef] [PubMed]

S. M. C. Nascimento, D. H. Foster, and K. Amano, "Psychophysical estimates of the number of spectral-reflectance basis functions needed to reproduce natural scenes," J. Opt. Soc. Am. A 22, 1017-1022 (2005).
[CrossRef]

G. D. Finayson and P. Morovic, "Metamer sets," J. Opt. Soc. Am. A 22, 810-819 (2005).

2004 (1)

D. H. Foster, S. M. C. Nascimento, and K. Amano, "Information limits on neural identification of colored surfaces in natural scenes," Visual Neurosci. 21, 331-336 (2004).
[CrossRef]

2003 (2)

M. R. Luo, C. J. Li, R. W. G. Hunt, B. Rigg, and K. J. Smith, "CMC 2002 colour inconstancy index: CMCCON02," Coloration Technology 119, 280-285 (2003).
[CrossRef]

D. H. Foster, "Does colour constancy exist?," Trends in Cognitive Science 7, 439-443 (2003).
[CrossRef]

2002 (2)

C.-J. Li, M. R. Luo, B. Rigg, and R. W. G. Hunt, "CMC 2000 chromatic adaptation transform: CMCCAT2000," Color Res. Appl. 27, 49-58 (2002).
[CrossRef]

S. M. C. Nascimento, F. P. Ferreira, and D. H. Foster, "Statistics of spatial cone-excitation ratios in natural scenes," J. Opt. Soc. Am. A 19, 1484-1490 (2002).
[CrossRef]

2001 (1)

M. R. Luo, G. Cui, and B. Rigg, "The development of the CIE 2000 colour-difference formula: CIEDE2000," Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

2000 (1)

M. G. A. Thomson, S. Westland, and J. Shaw, "Spatial resolution and metamerism in coloured natural scenes," Perception 29, 123 (2000).

1998 (1)

P. Lennie, "Single units and visual cortical organization," Perception 27, 889-935 (1998).
[CrossRef]

1997 (2)

S. M. C. Nascimento and D. H. Foster, "Detecting natural changes of cone-excitation ratios in simple and complex coloured images," Proc. R. Soc. London, Ser. B 264, 1395-1402 (1997).
[CrossRef]

M. G. A. Thomson and D. H. Foster, "Role of second- and third-order statistics in the discriminability of natural images," J. Opt. Soc. Am. A 14, 2081-2090 (1997).
[CrossRef]

1994 (3)

D. H. Foster and S. M. C. Nascimento, "Relational colour constancy from invariant cone-excitation ratios," Proc. R. Soc. London, Ser. B 257, 115-121 (1994).
[CrossRef]

T. Jaaskelainen, R. Silvennoinen, J. Hiltunen, and J. P. S. Parkkinen, "Classification of the reflectance spectra of pine, spruce, and birch," Appl. Opt. 33, 2356-2362 (1994).
[CrossRef] [PubMed]

M. J. Vrhel, R. Gershon, and L. S. Iwan, "Measurement and analysis of object reflectance spectra," Color Res. Appl. 19, 4-9 (1994).

1992 (1)

D. J. Tolhurst, Y. Tadmor, and T. Chao, "Amplitude spectra of natural images," Ophthalmic Physiol. Opt. 12, 229-232 (1992).
[CrossRef] [PubMed]

1991 (2)

H. S. Fairman, "Recommended terminology for Matrix R and metamerism," Color Res. Appl. 16, 337-341 (1991).
[CrossRef]

F. W. Billmeyer, Jr., "Notes on indices of metamerism," Color Res. Appl. 16, 342-343 (1991).
[CrossRef]

1990 (1)

1989 (1)

1987 (2)

1984 (1)

1983 (1)

R. G. Kuehni, "Metamerism, exact and approximate," Color Res. Appl. 8, 192-192 (1983).
[CrossRef]

1972 (1)

H. Terstiege, "Chromatic adaptation: A state-of-the-art report," J. Color Appearance 1, 19-23 (cont., p. 40) (1972).

1964 (1)

Amano, K.

D. H. Foster, K. Amano, and S. M. C. Nascimento, "Color constancy in natural scenes explained by global image statistics," Visual Neurosci. 23, 341-349 (2006).
[CrossRef]

K. Amano, D. H. Foster, and S. M. C. Nascimento, "Color constancy in natural scenes with and without an explicit illuminant cue," Visual Neurosci. 23, 351-356 (2006).
[CrossRef]

D. H. Foster, S. M. C. Nascimento, and K. Amano, "Information limits on identification of natural surfaces by apparent colour," Perception 34, 1003-1008 (2005).
[CrossRef] [PubMed]

S. M. C. Nascimento, D. H. Foster, and K. Amano, "Psychophysical estimates of the number of spectral-reflectance basis functions needed to reproduce natural scenes," J. Opt. Soc. Am. A 22, 1017-1022 (2005).
[CrossRef]

D. H. Foster, S. M. C. Nascimento, and K. Amano, "Information limits on neural identification of colored surfaces in natural scenes," Visual Neurosci. 21, 331-336 (2004).
[CrossRef]

Billmeyer, F. W.

F. W. Billmeyer, Jr., "Notes on indices of metamerism," Color Res. Appl. 16, 342-343 (1991).
[CrossRef]

Bridgeman, T.

T. Bridgeman and N. E. Hudson, "Calculation of the degree of metamerism between two colours," in 1st AIC Congress: Color 69 (Muster-Schmidt, 1970) 745-751.

Buchsbaum, G.

Burton, G. J.

Chao, T.

D. J. Tolhurst, Y. Tadmor, and T. Chao, "Amplitude spectra of natural images," Ophthalmic Physiol. Opt. 12, 229-232 (1992).
[CrossRef] [PubMed]

Cui, G.

M. R. Luo, G. Cui, and B. Rigg, "The development of the CIE 2000 colour-difference formula: CIEDE2000," Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

Efron, B.

B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap (Chapman & Hall, 1993).

Fairchild, M. D.

M. D. Fairchild, Color Appearance Models, 2nd ed. (Wiley, 2005).

Fairman, H. S.

H. S. Fairman, "Recommended terminology for Matrix R and metamerism," Color Res. Appl. 16, 337-341 (1991).
[CrossRef]

Ferreira, F. P.

Field, D.

Field, D. J.

Finayson, G. D.

Finlayson, G. D.

G. D. Finlayson and P. M. Morovic, "Metamer crossovers of infinite metamer sets," in Eighth Color Imaging Conference: Color Science and Engineering Systems, Technologies, Applications (Society for Imaging Science and Technology, 2000), pp. 13-17.

G. D. Finlayson and S. Süsstrunk, "Performance of a chromatic adaptation transform based on spectral sharpening," in Eighth Color Imaging Conference: Color Science and Engineering Systems, Technologies, Applications (Society for Imaging Science and Technology, 2000), pp. 49-55.

Foster, D. H.

D. H. Foster, K. Amano, and S. M. C. Nascimento, "Color constancy in natural scenes explained by global image statistics," Visual Neurosci. 23, 341-349 (2006).
[CrossRef]

K. Amano, D. H. Foster, and S. M. C. Nascimento, "Color constancy in natural scenes with and without an explicit illuminant cue," Visual Neurosci. 23, 351-356 (2006).
[CrossRef]

D. H. Foster, S. M. C. Nascimento, and K. Amano, "Information limits on identification of natural surfaces by apparent colour," Perception 34, 1003-1008 (2005).
[CrossRef] [PubMed]

S. M. C. Nascimento, D. H. Foster, and K. Amano, "Psychophysical estimates of the number of spectral-reflectance basis functions needed to reproduce natural scenes," J. Opt. Soc. Am. A 22, 1017-1022 (2005).
[CrossRef]

E. K. Oxtoby and D. H. Foster, "Perceptual limits on low-dimensional models of Munsell reflectance spectra," Perception 34, 961-966 (2005).
[CrossRef] [PubMed]

D. H. Foster, S. M. C. Nascimento, and K. Amano, "Information limits on neural identification of colored surfaces in natural scenes," Visual Neurosci. 21, 331-336 (2004).
[CrossRef]

D. H. Foster, "Does colour constancy exist?," Trends in Cognitive Science 7, 439-443 (2003).
[CrossRef]

S. M. C. Nascimento, F. P. Ferreira, and D. H. Foster, "Statistics of spatial cone-excitation ratios in natural scenes," J. Opt. Soc. Am. A 19, 1484-1490 (2002).
[CrossRef]

S. M. C. Nascimento and D. H. Foster, "Detecting natural changes of cone-excitation ratios in simple and complex coloured images," Proc. R. Soc. London, Ser. B 264, 1395-1402 (1997).
[CrossRef]

M. G. A. Thomson and D. H. Foster, "Role of second- and third-order statistics in the discriminability of natural images," J. Opt. Soc. Am. A 14, 2081-2090 (1997).
[CrossRef]

D. H. Foster and S. M. C. Nascimento, "Relational colour constancy from invariant cone-excitation ratios," Proc. R. Soc. London, Ser. B 257, 115-121 (1994).
[CrossRef]

Gershon, R.

M. J. Vrhel, R. Gershon, and L. S. Iwan, "Measurement and analysis of object reflectance spectra," Color Res. Appl. 19, 4-9 (1994).

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, "Geometrical considerations and nomenclature for reflectance" (Institute for Basic Standards, National Bureau of Standards, Washington, D.C., 1997).

Gottschalk, A.

Hallikainen, J.

Hiltunen, J.

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, "Geometrical considerations and nomenclature for reflectance" (Institute for Basic Standards, National Bureau of Standards, Washington, D.C., 1997).

Hudson, N. E.

T. Bridgeman and N. E. Hudson, "Calculation of the degree of metamerism between two colours," in 1st AIC Congress: Color 69 (Muster-Schmidt, 1970) 745-751.

Hunt, R. W. G.

M. R. Luo, C. J. Li, R. W. G. Hunt, B. Rigg, and K. J. Smith, "CMC 2002 colour inconstancy index: CMCCON02," Coloration Technology 119, 280-285 (2003).
[CrossRef]

C.-J. Li, M. R. Luo, B. Rigg, and R. W. G. Hunt, "CMC 2000 chromatic adaptation transform: CMCCAT2000," Color Res. Appl. 27, 49-58 (2002).
[CrossRef]

R. W. G. Hunt, Measuring Colour, 3rd ed. (Fountain Press, 1998).

Iwan, L. S.

M. J. Vrhel, R. Gershon, and L. S. Iwan, "Measurement and analysis of object reflectance spectra," Color Res. Appl. 19, 4-9 (1994).

Jaaskelainen, T.

Judd, D. B.

Kersten, D.

Knill, D. C.

Kuehni, R. G.

R. G. Kuehni, "Metamerism, exact and approximate," Color Res. Appl. 8, 192-192 (1983).
[CrossRef]

Lennie, P.

P. Lennie, "Single units and visual cortical organization," Perception 27, 889-935 (1998).
[CrossRef]

Li, C. J.

M. R. Luo, C. J. Li, R. W. G. Hunt, B. Rigg, and K. J. Smith, "CMC 2002 colour inconstancy index: CMCCON02," Coloration Technology 119, 280-285 (2003).
[CrossRef]

Li, C.-J.

C.-J. Li, M. R. Luo, B. Rigg, and R. W. G. Hunt, "CMC 2000 chromatic adaptation transform: CMCCAT2000," Color Res. Appl. 27, 49-58 (2002).
[CrossRef]

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, "Geometrical considerations and nomenclature for reflectance" (Institute for Basic Standards, National Bureau of Standards, Washington, D.C., 1997).

Luo, M. R.

M. R. Luo, C. J. Li, R. W. G. Hunt, B. Rigg, and K. J. Smith, "CMC 2002 colour inconstancy index: CMCCON02," Coloration Technology 119, 280-285 (2003).
[CrossRef]

C.-J. Li, M. R. Luo, B. Rigg, and R. W. G. Hunt, "CMC 2000 chromatic adaptation transform: CMCCAT2000," Color Res. Appl. 27, 49-58 (2002).
[CrossRef]

M. R. Luo, G. Cui, and B. Rigg, "The development of the CIE 2000 colour-difference formula: CIEDE2000," Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

MacAdam, D. L.

Moorhead, I. R.

Morovic, P.

G. D. Finayson and P. Morovic, "Metamer sets," J. Opt. Soc. Am. A 22, 810-819 (2005).

P.-L. Sun and P. Morovic, "Inter-relating colour difference metrics," in Tenth Color Imaging Conference: Color Science and Engineering Systems, Technologies, Applications, (Society for Imaging Science and Technology, 2002), pp. 55-60.
[PubMed]

Morovic, P. M.

G. D. Finlayson and P. M. Morovic, "Metamer crossovers of infinite metamer sets," in Eighth Color Imaging Conference: Color Science and Engineering Systems, Technologies, Applications (Society for Imaging Science and Technology, 2000), pp. 13-17.

Nascimento, S. M. C.

D. H. Foster, K. Amano, and S. M. C. Nascimento, "Color constancy in natural scenes explained by global image statistics," Visual Neurosci. 23, 341-349 (2006).
[CrossRef]

K. Amano, D. H. Foster, and S. M. C. Nascimento, "Color constancy in natural scenes with and without an explicit illuminant cue," Visual Neurosci. 23, 351-356 (2006).
[CrossRef]

D. H. Foster, S. M. C. Nascimento, and K. Amano, "Information limits on identification of natural surfaces by apparent colour," Perception 34, 1003-1008 (2005).
[CrossRef] [PubMed]

S. M. C. Nascimento, D. H. Foster, and K. Amano, "Psychophysical estimates of the number of spectral-reflectance basis functions needed to reproduce natural scenes," J. Opt. Soc. Am. A 22, 1017-1022 (2005).
[CrossRef]

D. H. Foster, S. M. C. Nascimento, and K. Amano, "Information limits on neural identification of colored surfaces in natural scenes," Visual Neurosci. 21, 331-336 (2004).
[CrossRef]

S. M. C. Nascimento, F. P. Ferreira, and D. H. Foster, "Statistics of spatial cone-excitation ratios in natural scenes," J. Opt. Soc. Am. A 19, 1484-1490 (2002).
[CrossRef]

S. M. C. Nascimento and D. H. Foster, "Detecting natural changes of cone-excitation ratios in simple and complex coloured images," Proc. R. Soc. London, Ser. B 264, 1395-1402 (1997).
[CrossRef]

D. H. Foster and S. M. C. Nascimento, "Relational colour constancy from invariant cone-excitation ratios," Proc. R. Soc. London, Ser. B 257, 115-121 (1994).
[CrossRef]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, "Geometrical considerations and nomenclature for reflectance" (Institute for Basic Standards, National Bureau of Standards, Washington, D.C., 1997).

Oxtoby, E. K.

E. K. Oxtoby and D. H. Foster, "Perceptual limits on low-dimensional models of Munsell reflectance spectra," Perception 34, 961-966 (2005).
[CrossRef] [PubMed]

Paltridge, R. J.

R. J. Paltridge, M. G. A. Thomson, T. Yates, and S. Westland, "Color spaces for discrimination and categorization in natural scenes," in 9th Congress of the International Colour Association, R.Chung and A.Rodrigues, eds., Proc. SPIE 4421, 877-880 (2002).

Parkkinen, J. P. S.

Párraga, C. A.

C. A. Párraga, T. Troscianko, and D. J. Tolhurst, "The effects of amplitude-spectrum statistics on foveal and peripheral discrimination of changes in natural images, and a multiresolution model," Vision Res. 45, 3145-3168 (2005).
[CrossRef] [PubMed]

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, "Geometrical considerations and nomenclature for reflectance" (Institute for Basic Standards, National Bureau of Standards, Washington, D.C., 1997).

Rigg, B.

M. R. Luo, C. J. Li, R. W. G. Hunt, B. Rigg, and K. J. Smith, "CMC 2002 colour inconstancy index: CMCCON02," Coloration Technology 119, 280-285 (2003).
[CrossRef]

C.-J. Li, M. R. Luo, B. Rigg, and R. W. G. Hunt, "CMC 2000 chromatic adaptation transform: CMCCAT2000," Color Res. Appl. 27, 49-58 (2002).
[CrossRef]

M. R. Luo, G. Cui, and B. Rigg, "The development of the CIE 2000 colour-difference formula: CIEDE2000," Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

Ripamonti, C.

S. Westland and C. Ripamonti, Computational Colour Science Using MATLAB (Wiley, 2004).
[PubMed]

Shaw, J.

M. G. A. Thomson, S. Westland, and J. Shaw, "Spatial resolution and metamerism in coloured natural scenes," Perception 29, 123 (2000).

Silvennoinen, R.

Smith, K. J.

M. R. Luo, C. J. Li, R. W. G. Hunt, B. Rigg, and K. J. Smith, "CMC 2002 colour inconstancy index: CMCCON02," Coloration Technology 119, 280-285 (2003).
[CrossRef]

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P.-L. Sun and P. Morovic, "Inter-relating colour difference metrics," in Tenth Color Imaging Conference: Color Science and Engineering Systems, Technologies, Applications, (Society for Imaging Science and Technology, 2002), pp. 55-60.
[PubMed]

Süsstrunk, S.

G. D. Finlayson and S. Süsstrunk, "Performance of a chromatic adaptation transform based on spectral sharpening," in Eighth Color Imaging Conference: Color Science and Engineering Systems, Technologies, Applications (Society for Imaging Science and Technology, 2000), pp. 49-55.

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D. J. Tolhurst, Y. Tadmor, and T. Chao, "Amplitude spectra of natural images," Ophthalmic Physiol. Opt. 12, 229-232 (1992).
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M. G. A. Thomson, S. Westland, and J. Shaw, "Spatial resolution and metamerism in coloured natural scenes," Perception 29, 123 (2000).

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R. J. Paltridge, M. G. A. Thomson, T. Yates, and S. Westland, "Color spaces for discrimination and categorization in natural scenes," in 9th Congress of the International Colour Association, R.Chung and A.Rodrigues, eds., Proc. SPIE 4421, 877-880 (2002).

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B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap (Chapman & Hall, 1993).

Tolhurst, D. J.

C. A. Párraga, T. Troscianko, and D. J. Tolhurst, "The effects of amplitude-spectrum statistics on foveal and peripheral discrimination of changes in natural images, and a multiresolution model," Vision Res. 45, 3145-3168 (2005).
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C. A. Párraga, T. Troscianko, and D. J. Tolhurst, "The effects of amplitude-spectrum statistics on foveal and peripheral discrimination of changes in natural images, and a multiresolution model," Vision Res. 45, 3145-3168 (2005).
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M. G. A. Thomson, S. Westland, and J. Shaw, "Spatial resolution and metamerism in coloured natural scenes," Perception 29, 123 (2000).

R. J. Paltridge, M. G. A. Thomson, T. Yates, and S. Westland, "Color spaces for discrimination and categorization in natural scenes," in 9th Congress of the International Colour Association, R.Chung and A.Rodrigues, eds., Proc. SPIE 4421, 877-880 (2002).

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Appl. Opt. (2)

Color Res. Appl. (6)

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Coloration Technology (1)

M. R. Luo, C. J. Li, R. W. G. Hunt, B. Rigg, and K. J. Smith, "CMC 2002 colour inconstancy index: CMCCON02," Coloration Technology 119, 280-285 (2003).
[CrossRef]

J. Color Appearance (1)

H. Terstiege, "Chromatic adaptation: A state-of-the-art report," J. Color Appearance 1, 19-23 (cont., p. 40) (1972).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (8)

Ophthalmic Physiol. Opt. (1)

D. J. Tolhurst, Y. Tadmor, and T. Chao, "Amplitude spectra of natural images," Ophthalmic Physiol. Opt. 12, 229-232 (1992).
[CrossRef] [PubMed]

Perception (4)

D. H. Foster, S. M. C. Nascimento, and K. Amano, "Information limits on identification of natural surfaces by apparent colour," Perception 34, 1003-1008 (2005).
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M. G. A. Thomson, S. Westland, and J. Shaw, "Spatial resolution and metamerism in coloured natural scenes," Perception 29, 123 (2000).

E. K. Oxtoby and D. H. Foster, "Perceptual limits on low-dimensional models of Munsell reflectance spectra," Perception 34, 961-966 (2005).
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Proc. R. Soc. London, Ser. B (2)

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Trends in Cognitive Science (1)

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Vision Res. (1)

C. A. Párraga, T. Troscianko, and D. J. Tolhurst, "The effects of amplitude-spectrum statistics on foveal and peripheral discrimination of changes in natural images, and a multiresolution model," Vision Res. 45, 3145-3168 (2005).
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Other (14)

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, "Geometrical considerations and nomenclature for reflectance" (Institute for Basic Standards, National Bureau of Standards, Washington, D.C., 1997).

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

R. W. G. Hunt, Measuring Colour, 3rd ed. (Fountain Press, 1998).

Colorimetry, 3rd ed., CIE Publication 15:2004 (CIE Central Bureau, Vienna, 2004).

R. J. Paltridge, M. G. A. Thomson, T. Yates, and S. Westland, "Color spaces for discrimination and categorization in natural scenes," in 9th Congress of the International Colour Association, R.Chung and A.Rodrigues, eds., Proc. SPIE 4421, 877-880 (2002).

G. D. Finlayson and S. Süsstrunk, "Performance of a chromatic adaptation transform based on spectral sharpening," in Eighth Color Imaging Conference: Color Science and Engineering Systems, Technologies, Applications (Society for Imaging Science and Technology, 2000), pp. 49-55.

S. Westland and C. Ripamonti, Computational Colour Science Using MATLAB (Wiley, 2004).
[PubMed]

M. D. Fairchild, Color Appearance Models, 2nd ed. (Wiley, 2005).

P.-L. Sun and P. Morovic, "Inter-relating colour difference metrics," in Tenth Color Imaging Conference: Color Science and Engineering Systems, Technologies, Applications, (Society for Imaging Science and Technology, 2002), pp. 55-60.
[PubMed]

B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap (Chapman & Hall, 1993).

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Figures (5)

Fig. 1
Fig. 1

Comparison of reflectance spectra estimated by hyperspectral imaging (symbols) and by telespectroradiometry (solid curves). Data shown for two acrylic paint samples. For methods, see text and Ref. [14].

Fig. 2
Fig. 2

Example scenes and corresponding conditional probabilities of color differences. The eight images A–H were drawn from the 50 scenes used in this study. The small neutral spheres or rectangular plates visible in some scenes (bottom left A, F; bottom center G; right B, bottom right D) were used for calibration (or other, psychophysical experiments) and were excluded in the analysis by a mask. The relative-frequency plots a–h show the estimated conditional probabilities of the color difference Δ E between pairs of surfaces under a daylight of correlated color temperature of 4000 K given that Δ E was subthreshold under a daylight of correlated color temperature 25,000 K . Color differences were calculated with CIEDE2000,[3, 27] the adaptation model was CMCCAT2000,[24] and the nominal color-difference threshold[6, 29] Δ E thr = 0.5 .

Fig. 3
Fig. 3

Log relative frequency of metameric pairs as a function of criterion degree of metamerism n, i.e., such that color differences Δ E were at least n times a nominal threshold Δ E thr . The illuminant change was from a daylight of correlated color temperature 25,000 K to one of 4000 K . Data for predominantly vegetated and nonvegetated scenes are shown by solid and open symbols, respectively, offset slightly for clarity. Solid and dashed straight lines are the corresponding linear regressions, excluding data from a simple CIELAB estimate ( ) . Different models of color-difference measure,[3, 27] chromatic adaptation,[24] and nominal threshold[6, 29] are indicated by different symbols (엯 CMCCAT2000, CIEDE2000, Δ E thr = 0.5 ; ⎔ CMCCAT2000, CIEDE2000, Δ E thr = 1.0 ; ◻ CMCCAT2000, CMC ( l : c ) , Δ E thr = 0.5 ; ◇ CMCCAT2000, CMC ( l : c ) , Δ E thr = 1.0 ; ▵ Sharp[25] CMCCAT2000, CIEDE2000, Δ E thr = 0.5 ; ▿ Sharp CMCCAT2000, CIEDE2000, Δ E thr = 1.0 ; ◁ Sharp CMCCAT2000, CMC ( l : c ) , Δ E thr = 0.5 ; ▷ Sharp CMCCAT2000, CMC ( l : c ) , Δ E thr = 1.0 ; ☆ CIELAB, Δ E thr = 1.0 ).

Fig. 4
Fig. 4

Images of blurred reflectance spectra and variations in relative frequencies of metamers with amount of blur. The eight images A–H show for the eight example scenes of Fig. 2 the effects of local spatial averaging of reflectance functions with a fixed kernel of width w = 64 pixels. The corresponding graphs a–h show plotted against w, on a log scale, the log of the estimated relative frequency of pairs of surfaces with nominally subthreshold color differences, i.e., Δ E < Δ E thr , under a daylight of correlated color temperature 25,000 K (dotted curve) and the log of the estimated relative frequency (solid curve) and conditional relative frequency (dashed line) of metameric pairs for a criterion degree of metamerism of n = 1 , i.e., Δ E Δ E thr , under a daylight of 4000 K (with threshold[6, 29] Δ E thr = 0.5 ).

Fig. 5
Fig. 5

Relationship between generalized metamerism and metamerism. The median of the distribution of Δ 2 E for each scene under successive illuminants is plotted against the median of the distribution of Δ 2 E with Δ E 1 < Δ E thr . Color differences Δ E 1 under the first illuminant and second differences Δ 2 E (see text) were calculated with respect to CIEDE2000[3, 27]; the adaptation model was CMCCAT2000,[24] and the illuminant change was from a daylight of correlated color temperature 25,000 K to one of 4000 K . The nominal color-difference threshold[6, 29] Δ E thr = 0.5 . Data from 29 predominantly vegetated scenes are shown by solid circles and from 21 predominantly nonvegetated scenes by open circles. The straight line is a linear regression.

Tables (6)

Tables Icon

Table 1 Centiles of Color Differences Δ E under the Second of Two Illuminants for Pairs of Surfaces with Δ E < 0.5 under the First Illuminant, a Calculated with Color-Difference Formula CIEDE2000[3, 27] and Adaptation Model CMCCAT2000[24]

Tables Icon

Table 2 Relative Frequencies and Conditional Relative Frequencies of Metameric Pairs of Surfaces in Natural Scenes, Calculated with Color-Difference Formula CIEDE2000,[3, 27] Adaptation Model CMCCAT2000,[24] and Nominal Discrimination Threshold Δ E thr = 0.5 a

Tables Icon

Table 3 Relative Frequencies and Conditional Relative Frequencies of Metameric Pairs of Surfaces in Natural Scenes, Calculated with Color-Difference Formula CIEDE2000,[3, 27] Adaptation Model CMCCAT2000,[24] and Nominal Discrimination Threshold Δ E thr = 1.0 a

Tables Icon

Table 4 Relative Frequencies and Conditional Relative Frequencies of Metameric Pairs of Surfaces in Natural Scenes, Calculated with Color-Difference Formula CMC ( l : c ) ,[3, 27] Adaptation Model CMCCAT2000,[24] and Nominal Discrimination Threshold Δ E thr = 0.5 a

Tables Icon

Table 5 Relative Frequencies and Conditional Relative Frequencies of Metameric Pairs of Surfaces in Natural Scenes, Calculated With Color-Difference Formula CMC ( l : c ) , [3, 27] Adaptation Model CMCCAT2000,[24] and Nominal Discrimination Threshold Δ E thr = 1.0 a

Tables Icon

Table 6 Relative Frequencies and Conditional Relative Frequencies of Metameric Pairs of Surfaces in Natural Scenes, Calculated from CIELAB[3] Alone, with Nominal Discrimination Threshold Δ E thr = 1.0

Equations (2)

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c ( λ ; x , y ) = 2 π E ( θ , ϕ ; λ ) R ( θ 0 , ϕ 0 ; θ , ϕ ; λ ; x , y ) d ω .
c ( λ ; x , y ) = 2 π E ( θ , ϕ ; λ ; x , y ) R ( θ 0 , ϕ 0 ; θ , ϕ ; λ ; x , y ) d ω .

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