Abstract

Cone-excitation ratios for pairs of surfaces are almost invariant under changes in illumination and offer a possible basis for color constancy [Proc. R. Soc. London Ser. B 257, 115 (1994)]. We extend this idea to the perception of transparency on the basis of the close analogy between the changes in color signals that occur for surfaces when the illumination changes and the changes in color signals when the surfaces are covered by a filter. This study presents measurements and simulations to investigate the conditions under which cone-excitation ratios are statistically invariant for physically transparent systems. The invariance breaks down when the spectral transmission of the filters is low at some or all wavelengths. We suggest that cone-excitation ratios might be useful to define the stimulus conditions necessary for the perception of transparency.

© 2000 Optical Society of America

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References

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  1. F. Metelli, “The perception of transparency,” Sci. Am. 230, 91–98 (1974).
    [CrossRef]
  2. J. Beck, “Additive and subtractive color mixture in color transparency,” Percept. Psychophys. 23, 265–267 (1978).
    [CrossRef] [PubMed]
  3. J. Beck, K. Prazdny, R. Ivry, “The perception of transparency with achromatic colors,” Percept. Psychophys. 35, 407–422 (1984).
    [CrossRef] [PubMed]
  4. W. Gerbino, C. I. F. H. J. Stultiens, J. M. Troost, C. M. M. de Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3–20 (1990).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  18. Ihara Electronics Co., Ltd., 2077 Kamitaraga-cho, Kasugai, Aichi 486-0801, Japan.
  19. Eastman Kodak Company, Rochester, N.Y. 14650.
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  25. Munsell Book of Color—Matte Finish Collection (Munsell Color, Baltimore, Md., 1976).
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    [CrossRef]

1999 (1)

C. Ripamonti, S. Westland, “Colour signal constraints for the perception of transparency,” Perception 28 (suppl.), 66, A013 (1999).

1997 (2)

S. M. C. Nascimento, 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. D’Zmura, P. Colantoni, K. Knoblauch, B. Laget, “Color transparency,” Perception 26, 471–492 (1997).
[CrossRef] [PubMed]

1996 (1)

1995 (1)

S. M. Courtney, L. H. Finkel, G. Buchsbaum, “Network simulations of retinal and cortical contributions to color constancy,” Vision Res. 35, 413–434 (1995).
[CrossRef] [PubMed]

1994 (2)

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

M. D’Zmura, G. Iverson, “Color constancy. III. General linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 11, 2389–2400 (1994).
[CrossRef]

1993 (2)

1992 (3)

M. D’Zmura, “Color constancy: surface color from changing illumination,” J. Opt. Soc. Am. A 9, 490–493 (1992).
[CrossRef]

D. H. Foster, B. J. Craven, E. R. H. Sale, “Immediate colour constancy,” Ophthalmic Physiol. Opt. 12, 157–160 (1992).
[CrossRef] [PubMed]

B. J. Craven, D. H. Foster, “An operational approach to colour constancy,” Vision Res. 32, 1359–1366 (1992).
[CrossRef] [PubMed]

1990 (1)

W. Gerbino, C. I. F. H. J. Stultiens, J. M. Troost, C. M. M. de Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3–20 (1990).
[CrossRef] [PubMed]

1989 (2)

1988 (1)

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” Crit. Rev. Neurobiol. 3, 333–400 (1988).
[PubMed]

1986 (2)

1984 (1)

J. Beck, K. Prazdny, R. Ivry, “The perception of transparency with achromatic colors,” Percept. Psychophys. 35, 407–422 (1984).
[CrossRef] [PubMed]

1978 (1)

J. Beck, “Additive and subtractive color mixture in color transparency,” Percept. Psychophys. 23, 265–267 (1978).
[CrossRef] [PubMed]

1975 (1)

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

1974 (1)

F. Metelli, “The perception of transparency,” Sci. Am. 230, 91–98 (1974).
[CrossRef]

Beck, J.

J. Beck, K. Prazdny, R. Ivry, “The perception of transparency with achromatic colors,” Percept. Psychophys. 35, 407–422 (1984).
[CrossRef] [PubMed]

J. Beck, “Additive and subtractive color mixture in color transparency,” Percept. Psychophys. 23, 265–267 (1978).
[CrossRef] [PubMed]

Buchsbaum, G.

S. M. Courtney, L. H. Finkel, G. Buchsbaum, “Network simulations of retinal and cortical contributions to color constancy,” Vision Res. 35, 413–434 (1995).
[CrossRef] [PubMed]

Colantoni, P.

M. D’Zmura, P. Colantoni, K. Knoblauch, B. Laget, “Color transparency,” Perception 26, 471–492 (1997).
[CrossRef] [PubMed]

Courtney, S. M.

S. M. Courtney, L. H. Finkel, G. Buchsbaum, “Network simulations of retinal and cortical contributions to color constancy,” Vision Res. 35, 413–434 (1995).
[CrossRef] [PubMed]

Craven, B. J.

D. H. Foster, B. J. Craven, E. R. H. Sale, “Immediate colour constancy,” Ophthalmic Physiol. Opt. 12, 157–160 (1992).
[CrossRef] [PubMed]

B. J. Craven, D. H. Foster, “An operational approach to colour constancy,” Vision Res. 32, 1359–1366 (1992).
[CrossRef] [PubMed]

D’Zmura, M.

de Weert, C. M. M.

W. Gerbino, C. I. F. H. J. Stultiens, J. M. Troost, C. M. M. de Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3–20 (1990).
[CrossRef] [PubMed]

Finkel, L. H.

S. M. Courtney, L. H. Finkel, G. Buchsbaum, “Network simulations of retinal and cortical contributions to color constancy,” Vision Res. 35, 413–434 (1995).
[CrossRef] [PubMed]

Foster, D. H.

S. M. C. Nascimento, 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, S. M. C. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” Proc. R. Soc. London Ser. B 257, 115–121 (1994).
[CrossRef]

B. J. Craven, D. H. Foster, “An operational approach to colour constancy,” Vision Res. 32, 1359–1366 (1992).
[CrossRef] [PubMed]

D. H. Foster, B. J. Craven, E. R. H. Sale, “Immediate colour constancy,” Ophthalmic Physiol. Opt. 12, 157–160 (1992).
[CrossRef] [PubMed]

Gerbino, W.

W. Gerbino, C. I. F. H. J. Stultiens, J. M. Troost, C. M. M. de Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3–20 (1990).
[CrossRef] [PubMed]

Hallikainen, J.

Hiltunen, T.

Hurvich, L. M.

D. Jameson, L. M. Hurvich, “Essay concerning color constancy,” Annu. Rev. Psychol. 40, 1–22 (1989).
[CrossRef] [PubMed]

Iverson, G.

Ivry, R.

J. Beck, K. Prazdny, R. Ivry, “The perception of transparency with achromatic colors,” Percept. Psychophys. 35, 407–422 (1984).
[CrossRef] [PubMed]

Jaaskelainen, T.

Jameson, D.

D. Jameson, L. M. Hurvich, “Essay concerning color constancy,” Annu. Rev. Psychol. 40, 1–22 (1989).
[CrossRef] [PubMed]

Knoblauch, K.

M. D’Zmura, P. Colantoni, K. Knoblauch, B. Laget, “Color transparency,” Perception 26, 471–492 (1997).
[CrossRef] [PubMed]

Laget, B.

M. D’Zmura, P. Colantoni, K. Knoblauch, B. Laget, “Color transparency,” Perception 26, 471–492 (1997).
[CrossRef] [PubMed]

Lennie, P.

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” Crit. Rev. Neurobiol. 3, 333–400 (1988).
[PubMed]

Lenz, R.

Maloney, L. T.

Metelli, F.

F. Metelli, “The perception of transparency,” Sci. Am. 230, 91–98 (1974).
[CrossRef]

Nascimento, S. M. C.

S. M. C. Nascimento, 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, S. M. C. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” Proc. R. Soc. London Ser. B 257, 115–121 (1994).
[CrossRef]

Nassau, K.

K. Nassau, The Physics and Chemistry of Color: the Fifteen Causes of Color (Wiley, New York, 1983).

Osterberg, M.

Parkkinen, J. P. S.

Parkkinen, T.

Pokorny, J.

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

Prazdny, K.

J. Beck, K. Prazdny, R. Ivry, “The perception of transparency with achromatic colors,” Percept. Psychophys. 35, 407–422 (1984).
[CrossRef] [PubMed]

Ripamonti, C.

C. Ripamonti, S. Westland, “Colour signal constraints for the perception of transparency,” Perception 28 (suppl.), 66, A013 (1999).

Sale, E. R. H.

D. H. Foster, B. J. Craven, E. R. H. Sale, “Immediate colour constancy,” Ophthalmic Physiol. Opt. 12, 157–160 (1992).
[CrossRef] [PubMed]

Smith, V. C.

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

Stiles, W. S.

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

Stultiens, C. I. F. H. J.

W. Gerbino, C. I. F. H. J. Stultiens, J. M. Troost, C. M. M. de Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3–20 (1990).
[CrossRef] [PubMed]

Troost, J. M.

W. Gerbino, C. I. F. H. J. Stultiens, J. M. Troost, C. M. M. de Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3–20 (1990).
[CrossRef] [PubMed]

Wandell, B. A.

Westland, S.

C. Ripamonti, S. Westland, “Colour signal constraints for the perception of transparency,” Perception 28 (suppl.), 66, A013 (1999).

S. Westland, “The optical properties of printing inks,” Ph.D. dissertation (University of Leeds, Leeds, UK, 1988).

Wyszecki, G.

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

Annu. Rev. Psychol. (1)

D. Jameson, L. M. Hurvich, “Essay concerning color constancy,” Annu. Rev. Psychol. 40, 1–22 (1989).
[CrossRef] [PubMed]

Crit. Rev. Neurobiol. (1)

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” Crit. Rev. Neurobiol. 3, 333–400 (1988).
[PubMed]

J. Exp. Psychol. Hum. Percept. Perform. (1)

W. Gerbino, C. I. F. H. J. Stultiens, J. M. Troost, C. M. M. de Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3–20 (1990).
[CrossRef] [PubMed]

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

Ophthalmic Physiol. Opt. (1)

D. H. Foster, B. J. Craven, E. R. H. Sale, “Immediate colour constancy,” Ophthalmic Physiol. Opt. 12, 157–160 (1992).
[CrossRef] [PubMed]

Percept. Psychophys. (2)

J. Beck, “Additive and subtractive color mixture in color transparency,” Percept. Psychophys. 23, 265–267 (1978).
[CrossRef] [PubMed]

J. Beck, K. Prazdny, R. Ivry, “The perception of transparency with achromatic colors,” Percept. Psychophys. 35, 407–422 (1984).
[CrossRef] [PubMed]

Perception (2)

M. D’Zmura, P. Colantoni, K. Knoblauch, B. Laget, “Color transparency,” Perception 26, 471–492 (1997).
[CrossRef] [PubMed]

C. Ripamonti, S. Westland, “Colour signal constraints for the perception of transparency,” Perception 28 (suppl.), 66, A013 (1999).

Proc. R. Soc. London Ser. B (2)

S. M. C. Nascimento, 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, S. M. C. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” Proc. R. Soc. London Ser. B 257, 115–121 (1994).
[CrossRef]

Sci. Am. (1)

F. Metelli, “The perception of transparency,” Sci. Am. 230, 91–98 (1974).
[CrossRef]

Vision Res. (3)

B. J. Craven, D. H. Foster, “An operational approach to colour constancy,” Vision Res. 32, 1359–1366 (1992).
[CrossRef] [PubMed]

S. M. Courtney, L. H. Finkel, G. Buchsbaum, “Network simulations of retinal and cortical contributions to color constancy,” Vision Res. 35, 413–434 (1995).
[CrossRef] [PubMed]

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

Other (6)

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

S. Westland, “The optical properties of printing inks,” Ph.D. dissertation (University of Leeds, Leeds, UK, 1988).

Munsell Book of Color—Matte Finish Collection (Munsell Color, Baltimore, Md., 1976).

K. Nassau, The Physics and Chemistry of Color: the Fifteen Causes of Color (Wiley, New York, 1983).

Ihara Electronics Co., Ltd., 2077 Kamitaraga-cho, Kasugai, Aichi 486-0801, Japan.

Eastman Kodak Company, Rochester, N.Y. 14650.

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Figures (5)

Fig. 1
Fig. 1

Invariant cone-excitation-ratio model. The two surfaces (j=1, 2) are partially covered by a transparent layer. The ratio of cone excitations ei,1/ei,2 for the surfaces seen directly is equal to the ratio ei,1/ei,2 when the surfaces are seen through a transparent layer.

Fig. 2
Fig. 2

Scatterplot of ratios of cone excitations for each of the three cone classes (circles, short-wavelength; crosses, medium wavelength; stars, long-wavelength) for (a) N.D. 0.1 filter, (b) N.D. 0.3 filter, and (c) N.D. 0.6 filter. Each point represents a pair of ratios produced by light (under simulated natural daylight at 6500 K) from two surfaces viewed directly e and through a transparent filter e.

Fig. 3
Fig. 3

(a) Spectral reflectance data for two typical surfaces from the Munsell set; (b) typical filter with λmax=670 nm,σ=100 nm, and r=0; (c) spectral reflectance data for the two surfaces in (a) covered by the filter in (b).

Fig. 4
Fig. 4

Scatterplot of ratios of cone excitations for (a) short-, (b) medium-, and long-wavelength-sensitive cone classes for a filter with σ=50 nm, and r=0. Each point represents a pair of ratios produced by light (under simulated natural daylight at 6500 K) from two surfaces viewed directly e and through a transparent filter e. Based on 1000 iterations.

Fig. 5
Fig. 5

Scatterplot of ratios of cone excitations for (a) short-, (b) medium-, and long-wavelength-sensitive cone classes randomly selected Wratten filters with r=0. Each point represents a pair of ratios produced by light (under simulated natural daylight at 6500 K) from two surfaces viewed directly e and through a transparent filter e. Based on 1000 iterations.

Tables (6)

Tables Icon

Table 6 Spectral Reflectance Factors for Surfaces Used to Generate Data Shown in Table 1

Tables Icon

Table 1 Gradient of Least-Squares Linear Fit for Plots of Ratios for Surfaces Viewed through a Filter versus the Same Surfaces Viewed Directly for Three N.D. Filters and Four Color Filters

Tables Icon

Table 2 Gradient of Least-Squares Linear Fit for Plots of Ratios for Surfaces Viewed through a Filter (with r=0 and A0=1) versus the Same Surfaces Viewed Directly for Achromatic and Chromatic Filtersa

Tables Icon

Table 3 Gradient of Least-Squares Linear Fit for Plots of Ratios for Surfaces Viewed through a Chromatic Filter (σ=50 nm and A0=1) versus the Same Surfaces Viewed Directly for Different Values of ra

Tables Icon

Table 4 Gradient of Least-Squares Linear Fit for Plots of Ratios for Surfaces Viewed through a Chromatic Filter (σ=50 nm) versus the Same Surfaces Viewed Directly for Different Values of A0a

Tables Icon

Table 5 Gradient of Least-Squares Linear Fit for Plots of Ratios for Surfaces Viewed through a Chromatic Filter (σ=50 nm) versus the Same Surfaces Viewed Directly with Increased Number n of Absorption Peaks in the Filtera

Equations (4)

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

ei,E·R1/ei,E·R2=ei,E·R1/ei,E·R2.
R1(λ)E(λ)ϕi(λ)δλR2(λ)E(λ)ϕi(λ)δλ=R1(λ)T2(λ)E(λ)ϕi(λ)δλR2(λ)T2(λ)E(λ)ϕi(λ)δλ.
R(λ)=R(λ)T2(λ).
R(λ)=R(λ)[T(λ)(1-r)2]2.

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