Abstract

The level of reflectance of pigmented surfaces observed in daylight affects saturation growth in different ways, depending on the wavelength of the samples. Numerical and matching judgments collected in previous experiments were replotted in families of monochromatic (constant hue) saturation power functions for blue, green, yellow, and red. For each hue the set of functions intersected at a point at which the colorimetric purity and saturation were invariant with reflectance. The points of intersection were: blues, 0.081 colorimetric purity (Pc) and 2.7 cromes; greens, 0.257 Pc and 4.6 cromes; yellows, 0.694 Pc and 8.3 cromes; and reds, 0.144 Pc and 3.6 cromes. A straight line fitted to these four intersecting points makes it possible to interpolate other intersecting points for other hues. Two additional experiments were designed to compare a function of saturation with a function of lightness for a set of different hues (heterochromatic functions). Observers judged saturation in one experiment and lightness in the other. Lightness grows linearly with reflectance, and saturation increases as the 0.5 power of Pc, suggesting a different perceptual discrimination for the two dimensions. The relation between changes in quantity and percentage of color perceived was tested in an additional experiment. Observers assigned the following saturation values to the samples with Pc close to the converging points: 13% of color for blues, 20% for reds, 25% for greens, and 40% for yellows.

© 1981 Optical Society of America

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References

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  1. M. Guirao and M. L. F. de Mattiello, “Saturation of colored samples at various levels of reflectance,” J. Opt. Soc. Am. 67, 647–651 (1977).
    [Crossref] [PubMed]
  2. T. Indow and S. S. Stevens, “Scaling of saturation and hue,” Percept. Psychophys. 1, 253–271 (1966).
    [Crossref]
  3. M. Guirao and M. L. F. de Mattiello, “Equal saturation contours for surface colors,” in AIC Color 77, F. W. Billmayer and G. Wyszecki, eds. (Hilger, Bristol, 1978), pp. 348–350.
  4. M. L. F. de Mattiello and R. A. Arizaga, “Delimitation of saturation in CIE systems,” J. Opt. Soc. Am. 68, 1400–1401(A) (1978).
  5. M. L. F. de Mattiello, “On the estimation of saturation in pigmented surfaces and the DIN and Munsell colour order systems,” Die Farbe 29, 3–6 (1980).
  6. J. W. Onley and et al., “Quantitative estimates of saturation,” J. Opt. Soc. Am. 53, 487–493 (1963).
    [Crossref] [PubMed]
  7. D. W. Panek and S. S. Stevens, “Saturation of red: a prothetic continuum,” Percept. Psychophys. 2, 59–66 (1966).
    [Crossref]
  8. J. C. Stevens and S. S. Stevens, “Brightness function: effects of adaptation,” J. Opt. Soc. Am. 53, 375–385 (1963).
    [Crossref] [PubMed]
  9. M. L. F. de Mattiello and M. Guirao, “Direct estimation of lightness of surface colors,” J. Opt. Soc. Am. 64, 206–209 (1974).
    [Crossref] [PubMed]
  10. S. S. Stevens, “On the psychophysical law,” Psychol. Rev. 64, 153–181 (1957).
    [Crossref] [PubMed]
  11. L. C. Martin, F. L. Warburton, and W. J. Morgan, “The determination of the sensitiveness of the eye to differences in the saturation of colours,” G. B. Med. Res. Counc., Spec. Rep. Ser. 188, 5–42 (1933).
  12. J. H. Nelson, “The colour-vision characteristics of a trichromat,” Proc. Phys. Soc. London 49, 332–337 (1937).
    [Crossref]
  13. W. D. Wright and F. G. H. Pitt, “The saturation discrimination of two trichromats,” Proc. Phys. Soc. London 49, 329–331 (1937).
    [Crossref]
  14. M. Guirao and M. L. F. de Mattiello, “Saturation scales for surface colors,” Vision Res. 14, 487–493 (1974).
    [Crossref] [PubMed]
  15. J. C. Stevens and L. L. Rubin, “Psychophysical scales of apparent heaviness and the size-weight illusion,” Percept Psychophys. 8, 225–230 (1970).
    [Crossref]
  16. S. S. Stevens, “Power-group transformation under glare, masking, and recruitment,” J. Acoust. Soc. Am. 39, 725–735 (1966).
    [Crossref]
  17. S. S. Stevens and M. Guirao, “Loudness functions under inhibition,” Percept Psychophys. 2, 459–465 (1967).
    [Crossref]
  18. S. S. Stevens and A. L. Diamond, “Effect of glare angle on the brightness function for a small target,” Vision Res. 5, 649–659 (1965).
    [Crossref] [PubMed]
  19. J. C. Stevens, “Families of converging power functions in psychophysics,” in Sensation and Measurement, H. Moskowitz, B. Sharf, and J. C. Stevens, eds. (Reidel, Dordrecht, The Netherlands, 1974), pp. 157–165.
    [Crossref]
  20. R. M. Evans and B. K. Swenholt, “Chromatic strength of colors. I. Dominant wavelength and purity,” J. Opt. Soc. Am. 57, 1319–1324 (1967).
    [Crossref] [PubMed]
  21. L. T. Troland, “Apparent brightness; its conditions and properties,” Trans. Illum. Eng. Soc. 11, 947–966 (1916).
  22. R. H. Sinden, “Studies based on the spectral complementaries,” J. Opt. Soc. Am. 7, 1123–1153 (1923).
    [Crossref]
  23. D. L. MacAdam, “Photometric relations between complementary colors,” J. Opt. Soc. Am. 28, 103–111 (1938).
    [Crossref]
  24. D. Jameson and L. Hurvich, “Some quantitative aspects of an opponent colors theory. I. Chromatic responses and spectral saturation,” J. Opt. Soc. Am. 45, 546–552 (1955).
    [Crossref]
  25. W. D. Wright, Researches on Normal and Defective Colour Vision (Henry Kimpton, London, 1946).

1980 (1)

M. L. F. de Mattiello, “On the estimation of saturation in pigmented surfaces and the DIN and Munsell colour order systems,” Die Farbe 29, 3–6 (1980).

1978 (1)

M. L. F. de Mattiello and R. A. Arizaga, “Delimitation of saturation in CIE systems,” J. Opt. Soc. Am. 68, 1400–1401(A) (1978).

1977 (1)

1974 (2)

M. L. F. de Mattiello and M. Guirao, “Direct estimation of lightness of surface colors,” J. Opt. Soc. Am. 64, 206–209 (1974).
[Crossref] [PubMed]

M. Guirao and M. L. F. de Mattiello, “Saturation scales for surface colors,” Vision Res. 14, 487–493 (1974).
[Crossref] [PubMed]

1970 (1)

J. C. Stevens and L. L. Rubin, “Psychophysical scales of apparent heaviness and the size-weight illusion,” Percept Psychophys. 8, 225–230 (1970).
[Crossref]

1967 (2)

1966 (3)

S. S. Stevens, “Power-group transformation under glare, masking, and recruitment,” J. Acoust. Soc. Am. 39, 725–735 (1966).
[Crossref]

D. W. Panek and S. S. Stevens, “Saturation of red: a prothetic continuum,” Percept. Psychophys. 2, 59–66 (1966).
[Crossref]

T. Indow and S. S. Stevens, “Scaling of saturation and hue,” Percept. Psychophys. 1, 253–271 (1966).
[Crossref]

1965 (1)

S. S. Stevens and A. L. Diamond, “Effect of glare angle on the brightness function for a small target,” Vision Res. 5, 649–659 (1965).
[Crossref] [PubMed]

1963 (2)

1957 (1)

S. S. Stevens, “On the psychophysical law,” Psychol. Rev. 64, 153–181 (1957).
[Crossref] [PubMed]

1955 (1)

1938 (1)

1937 (2)

J. H. Nelson, “The colour-vision characteristics of a trichromat,” Proc. Phys. Soc. London 49, 332–337 (1937).
[Crossref]

W. D. Wright and F. G. H. Pitt, “The saturation discrimination of two trichromats,” Proc. Phys. Soc. London 49, 329–331 (1937).
[Crossref]

1933 (1)

L. C. Martin, F. L. Warburton, and W. J. Morgan, “The determination of the sensitiveness of the eye to differences in the saturation of colours,” G. B. Med. Res. Counc., Spec. Rep. Ser. 188, 5–42 (1933).

1923 (1)

1916 (1)

L. T. Troland, “Apparent brightness; its conditions and properties,” Trans. Illum. Eng. Soc. 11, 947–966 (1916).

Arizaga, R. A.

M. L. F. de Mattiello and R. A. Arizaga, “Delimitation of saturation in CIE systems,” J. Opt. Soc. Am. 68, 1400–1401(A) (1978).

de Mattiello, M. L. F.

M. L. F. de Mattiello, “On the estimation of saturation in pigmented surfaces and the DIN and Munsell colour order systems,” Die Farbe 29, 3–6 (1980).

M. L. F. de Mattiello and R. A. Arizaga, “Delimitation of saturation in CIE systems,” J. Opt. Soc. Am. 68, 1400–1401(A) (1978).

M. Guirao and M. L. F. de Mattiello, “Saturation of colored samples at various levels of reflectance,” J. Opt. Soc. Am. 67, 647–651 (1977).
[Crossref] [PubMed]

M. Guirao and M. L. F. de Mattiello, “Saturation scales for surface colors,” Vision Res. 14, 487–493 (1974).
[Crossref] [PubMed]

M. L. F. de Mattiello and M. Guirao, “Direct estimation of lightness of surface colors,” J. Opt. Soc. Am. 64, 206–209 (1974).
[Crossref] [PubMed]

M. Guirao and M. L. F. de Mattiello, “Equal saturation contours for surface colors,” in AIC Color 77, F. W. Billmayer and G. Wyszecki, eds. (Hilger, Bristol, 1978), pp. 348–350.

Diamond, A. L.

S. S. Stevens and A. L. Diamond, “Effect of glare angle on the brightness function for a small target,” Vision Res. 5, 649–659 (1965).
[Crossref] [PubMed]

Evans, R. M.

Guirao, M.

M. Guirao and M. L. F. de Mattiello, “Saturation of colored samples at various levels of reflectance,” J. Opt. Soc. Am. 67, 647–651 (1977).
[Crossref] [PubMed]

M. Guirao and M. L. F. de Mattiello, “Saturation scales for surface colors,” Vision Res. 14, 487–493 (1974).
[Crossref] [PubMed]

M. L. F. de Mattiello and M. Guirao, “Direct estimation of lightness of surface colors,” J. Opt. Soc. Am. 64, 206–209 (1974).
[Crossref] [PubMed]

S. S. Stevens and M. Guirao, “Loudness functions under inhibition,” Percept Psychophys. 2, 459–465 (1967).
[Crossref]

M. Guirao and M. L. F. de Mattiello, “Equal saturation contours for surface colors,” in AIC Color 77, F. W. Billmayer and G. Wyszecki, eds. (Hilger, Bristol, 1978), pp. 348–350.

Hurvich, L.

Indow, T.

T. Indow and S. S. Stevens, “Scaling of saturation and hue,” Percept. Psychophys. 1, 253–271 (1966).
[Crossref]

Jameson, D.

MacAdam, D. L.

Martin, L. C.

L. C. Martin, F. L. Warburton, and W. J. Morgan, “The determination of the sensitiveness of the eye to differences in the saturation of colours,” G. B. Med. Res. Counc., Spec. Rep. Ser. 188, 5–42 (1933).

Morgan, W. J.

L. C. Martin, F. L. Warburton, and W. J. Morgan, “The determination of the sensitiveness of the eye to differences in the saturation of colours,” G. B. Med. Res. Counc., Spec. Rep. Ser. 188, 5–42 (1933).

Nelson, J. H.

J. H. Nelson, “The colour-vision characteristics of a trichromat,” Proc. Phys. Soc. London 49, 332–337 (1937).
[Crossref]

Onley, J. W.

Panek, D. W.

D. W. Panek and S. S. Stevens, “Saturation of red: a prothetic continuum,” Percept. Psychophys. 2, 59–66 (1966).
[Crossref]

Pitt, F. G. H.

W. D. Wright and F. G. H. Pitt, “The saturation discrimination of two trichromats,” Proc. Phys. Soc. London 49, 329–331 (1937).
[Crossref]

Rubin, L. L.

J. C. Stevens and L. L. Rubin, “Psychophysical scales of apparent heaviness and the size-weight illusion,” Percept Psychophys. 8, 225–230 (1970).
[Crossref]

Sinden, R. H.

Stevens, J. C.

J. C. Stevens and L. L. Rubin, “Psychophysical scales of apparent heaviness and the size-weight illusion,” Percept Psychophys. 8, 225–230 (1970).
[Crossref]

J. C. Stevens and S. S. Stevens, “Brightness function: effects of adaptation,” J. Opt. Soc. Am. 53, 375–385 (1963).
[Crossref] [PubMed]

J. C. Stevens, “Families of converging power functions in psychophysics,” in Sensation and Measurement, H. Moskowitz, B. Sharf, and J. C. Stevens, eds. (Reidel, Dordrecht, The Netherlands, 1974), pp. 157–165.
[Crossref]

Stevens, S. S.

S. S. Stevens and M. Guirao, “Loudness functions under inhibition,” Percept Psychophys. 2, 459–465 (1967).
[Crossref]

S. S. Stevens, “Power-group transformation under glare, masking, and recruitment,” J. Acoust. Soc. Am. 39, 725–735 (1966).
[Crossref]

D. W. Panek and S. S. Stevens, “Saturation of red: a prothetic continuum,” Percept. Psychophys. 2, 59–66 (1966).
[Crossref]

T. Indow and S. S. Stevens, “Scaling of saturation and hue,” Percept. Psychophys. 1, 253–271 (1966).
[Crossref]

S. S. Stevens and A. L. Diamond, “Effect of glare angle on the brightness function for a small target,” Vision Res. 5, 649–659 (1965).
[Crossref] [PubMed]

J. C. Stevens and S. S. Stevens, “Brightness function: effects of adaptation,” J. Opt. Soc. Am. 53, 375–385 (1963).
[Crossref] [PubMed]

S. S. Stevens, “On the psychophysical law,” Psychol. Rev. 64, 153–181 (1957).
[Crossref] [PubMed]

Swenholt, B. K.

Troland, L. T.

L. T. Troland, “Apparent brightness; its conditions and properties,” Trans. Illum. Eng. Soc. 11, 947–966 (1916).

Warburton, F. L.

L. C. Martin, F. L. Warburton, and W. J. Morgan, “The determination of the sensitiveness of the eye to differences in the saturation of colours,” G. B. Med. Res. Counc., Spec. Rep. Ser. 188, 5–42 (1933).

Wright, W. D.

W. D. Wright and F. G. H. Pitt, “The saturation discrimination of two trichromats,” Proc. Phys. Soc. London 49, 329–331 (1937).
[Crossref]

W. D. Wright, Researches on Normal and Defective Colour Vision (Henry Kimpton, London, 1946).

Die Farbe (1)

M. L. F. de Mattiello, “On the estimation of saturation in pigmented surfaces and the DIN and Munsell colour order systems,” Die Farbe 29, 3–6 (1980).

G. B. Med. Res. Counc., Spec. Rep. Ser. (1)

L. C. Martin, F. L. Warburton, and W. J. Morgan, “The determination of the sensitiveness of the eye to differences in the saturation of colours,” G. B. Med. Res. Counc., Spec. Rep. Ser. 188, 5–42 (1933).

J. Acoust. Soc. Am. (1)

S. S. Stevens, “Power-group transformation under glare, masking, and recruitment,” J. Acoust. Soc. Am. 39, 725–735 (1966).
[Crossref]

J. Opt. Soc. Am. (9)

Percept Psychophys. (2)

J. C. Stevens and L. L. Rubin, “Psychophysical scales of apparent heaviness and the size-weight illusion,” Percept Psychophys. 8, 225–230 (1970).
[Crossref]

S. S. Stevens and M. Guirao, “Loudness functions under inhibition,” Percept Psychophys. 2, 459–465 (1967).
[Crossref]

Percept. Psychophys. (2)

T. Indow and S. S. Stevens, “Scaling of saturation and hue,” Percept. Psychophys. 1, 253–271 (1966).
[Crossref]

D. W. Panek and S. S. Stevens, “Saturation of red: a prothetic continuum,” Percept. Psychophys. 2, 59–66 (1966).
[Crossref]

Proc. Phys. Soc. London (2)

J. H. Nelson, “The colour-vision characteristics of a trichromat,” Proc. Phys. Soc. London 49, 332–337 (1937).
[Crossref]

W. D. Wright and F. G. H. Pitt, “The saturation discrimination of two trichromats,” Proc. Phys. Soc. London 49, 329–331 (1937).
[Crossref]

Psychol. Rev. (1)

S. S. Stevens, “On the psychophysical law,” Psychol. Rev. 64, 153–181 (1957).
[Crossref] [PubMed]

Trans. Illum. Eng. Soc. (1)

L. T. Troland, “Apparent brightness; its conditions and properties,” Trans. Illum. Eng. Soc. 11, 947–966 (1916).

Vision Res. (2)

S. S. Stevens and A. L. Diamond, “Effect of glare angle on the brightness function for a small target,” Vision Res. 5, 649–659 (1965).
[Crossref] [PubMed]

M. Guirao and M. L. F. de Mattiello, “Saturation scales for surface colors,” Vision Res. 14, 487–493 (1974).
[Crossref] [PubMed]

Other (3)

M. Guirao and M. L. F. de Mattiello, “Equal saturation contours for surface colors,” in AIC Color 77, F. W. Billmayer and G. Wyszecki, eds. (Hilger, Bristol, 1978), pp. 348–350.

J. C. Stevens, “Families of converging power functions in psychophysics,” in Sensation and Measurement, H. Moskowitz, B. Sharf, and J. C. Stevens, eds. (Reidel, Dordrecht, The Netherlands, 1974), pp. 157–165.
[Crossref]

W. D. Wright, Researches on Normal and Defective Colour Vision (Henry Kimpton, London, 1946).

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Figures (7)

Fig. 1
Fig. 1

Saturation of pigmented surfaces of four different groups of hues at different levels of reflectance. Functions were obtained by methods of numerical estimation. The straight lines (power functions) are spread apart to facilitate inspection of the data. Percent reflectance can be read at the top of each function (after Guirao and Mattiello1).

Fig. 2
Fig. 2

Convergence of saturation functions (replotted data from Fig. 1). The family of straight lines in each hue converges at a point represented by a filled circle: blue 0.081 Pc at 2.7 cromes, green 0.257 Pc at 4.6 cromes, red 0.144 Pc at 3.6 cromes, and yellow 0.694 Pc at 8.3 cromes. The dash–dot line corresponds to the heterochromatic functions (squares) in Fig. 3.

Fig. 3
Fig. 3

(a) Saturation convergence points for the four hues from Fig. 2 drawn along a single line give a function in which a crome of 10 at a value of 1.0 Pc intersects log k at 1.0. (b) Sixteen just-perceptible steps for ten different wavelengths taken from the data provided by Martin (small symbols) and Warburton (big symbols).11 The wavelengths are: 460, open triangles; 496, open circles; 530 asterisks; 546, open squares; 578, crosses; 582, inverted triangles; 600, diamonds; 623, closed triangles; 650, closed circles; and 680, closed squares.

Fig. 4
Fig. 4

The relation between the exponent values of saturation functions and k intersections. The values for log k were read from the dashed vertical lines in Fig. 2, and the values of the exponents were taken from Fig. 1 (see Table 1). The intersection point of log k 1.0 was read from Fig. 3.

Fig. 5
Fig. 5

Numerical estimation of saturation and lightness of the same heterochromatic set of eight stimuli. All the samples were selected to fall at the intersecting points of Fig. 2. Squares represent blue, crosses green, triangles red, and circles yellow. The function for saturation verifies the one locating the intersecting points in Fig. 3 (squares). Lightness is a linear function.

Fig. 6
Fig. 6

Relation between two scales: cromes and percent quantity of color. Open circles were read from function Fig. 3(a). Triangles represent the average estimation in the amount of color perceived at the intersecting points. Filled circles correspond to the calculated values of G0 (from Evans20) at a value of 5 for hues 470, 620, and 510 nm.

Fig. 7
Fig. 7

Abbreviations stand for saturation thresholds from Martin,11 Wright,13 Nelson,12 Pitt,13 and Warburton.11 Predicted intersecting-points function. The four points were obtained experimentally (dashed line and circles). The 100% color curve corresponds to data read from right ordinate in Fig. 6 (solid line and squares). The curve at the low end represents the G0 data provided by Evans.20

Tables (1)

Tables Icon

Table 1 Exponents and Logarithms of the Constant Proportionality (k) for Saturation Function under Different Levels of Reflectance

Equations (6)

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

ψ = k ϕ β ,
log ψ = log k + β log ϕ ,
log ψ 0 = log k ( r ) + β ( r ) log ϕ 0 .
β ( r ) = log ψ 0 log ϕ 0 - 1 log ϕ 0 log k ( r ) .
n = - 1 log ϕ 0 ,
log ψ 0 ( λ ) = 0.5 log ϕ 0 ( λ ) + 1.