Abstract

Two psychophysical responses to surface or self-luminous stimuli are hypothesized. A response to the luminance of the stimulus (α) and a response to the luminance difference between the stimulus and its surround (β) are both considered to be power functions. Lightness or brightness is taken to be an additive or subtractive combination of these two responses (α±) depending on whether the surround is darker or brighter than the stimulus, respectively. This model is shown to produce a quantitatively adequate explanation of Takasaki’s data on crispening. An attempt is made to use this formulation to fit scaling data from previous magnitude-estimation and partitioning studies of lightness and brightness in which different results have been obtained from different backgrounds. Data from matching experiments that involve different backgrounds for the comparison and standard stimuli are also analyzed by means of the same formulation. The model is compared with the Adams–Cobb–Judd formulation of background effect on lightness, the Takasaki empirical formula for crispening, and Stevens’s power-law formulation for brightness and lightness.

© 1970 Optical Society of America

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References

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  1. E. Q. Adams and P. W. Cobb, J. Exptl. Psychol. 5, 39 (1922).
    [Crossref]
  2. D. B. Judd, J. Res. Natl. Bur. Std. (U.S.) 24, 293 (1940).
    [Crossref]
  3. T. Kaneko, Acta Chromatica 1, 103 (1963).
  4. S. S. Stevens, in Psychological Scaling; Theory and Applications, edited by H. Gulliksen and S. Messick (Wiley, New York, 1960), p. 49.
  5. W. S. Torgerson, in Ref. 4, p. 21.
  6. D. B. Judd, Color Eng. 8, 36 (1970).
  7. S. S. Stevens, Psychol. Rev. 64, 153 (1957).
    [Crossref] [PubMed]
  8. S. S. Stevens, in Sensory Communication, edited by W. A. Rosenblith (M.I.T. Press, Cambridge, Mass., 1961), p. 1.
  9. S. S. Stevens, Science 133, 80 (1961).
    [Crossref] [PubMed]
  10. D. Jameson and L. Hurvich, Vision Res. 4, 133 (1964).
    [Crossref]
  11. H. Takasaki, J. Opt. Soc. Am. 56, 504 (1966).
    [Crossref] [PubMed]
  12. J. C. Stevens and S. S. Stevens, J. Opt. Soc. Am. 53, 375 (1963).
    [Crossref] [PubMed]
  13. D. B. Judd and G. Wyszecki, Color in Business, Science and Industry (Wiley, New York, 1963).
  14. S. M. Newhall, D. Nickerson, and D. B. Judd, J. Opt. Soc. Am. 33, 385 (1943).
    [Crossref]
  15. S. M. Newhall, J. Opt. Soc. Am. 30, 617 (1940).
    [Crossref]
  16. The actual illuminances used in the study are unavailable. However, G. Howett made available to the author the illuminances that were used in a recent (as yet unpublished) study of the OSA Committee on Uniform Color Scales, which also instructed its observers to use north-sky light or its equivalent. The mean illuminance reported was approximately 1500 lx.
  17. J. J. Glenn and J. T. Killian, J. Opt. Soc. Am. 30, 609 (1940).
    [Crossref]
  18. H. Helson, Adaptation-Level Theory (Harper and Row, New York, 1964).
  19. H. Helson, J. Opt. Soc. Am. 33, 555 (1943).
    [Crossref]

1970 (1)

D. B. Judd, Color Eng. 8, 36 (1970).

1966 (1)

1964 (1)

D. Jameson and L. Hurvich, Vision Res. 4, 133 (1964).
[Crossref]

1963 (2)

1961 (1)

S. S. Stevens, Science 133, 80 (1961).
[Crossref] [PubMed]

1957 (1)

S. S. Stevens, Psychol. Rev. 64, 153 (1957).
[Crossref] [PubMed]

1943 (2)

1940 (3)

1922 (1)

E. Q. Adams and P. W. Cobb, J. Exptl. Psychol. 5, 39 (1922).
[Crossref]

Adams, E. Q.

E. Q. Adams and P. W. Cobb, J. Exptl. Psychol. 5, 39 (1922).
[Crossref]

Cobb, P. W.

E. Q. Adams and P. W. Cobb, J. Exptl. Psychol. 5, 39 (1922).
[Crossref]

Glenn, J. J.

Helson, H.

H. Helson, J. Opt. Soc. Am. 33, 555 (1943).
[Crossref]

H. Helson, Adaptation-Level Theory (Harper and Row, New York, 1964).

Hurvich, L.

D. Jameson and L. Hurvich, Vision Res. 4, 133 (1964).
[Crossref]

Jameson, D.

D. Jameson and L. Hurvich, Vision Res. 4, 133 (1964).
[Crossref]

Judd, D. B.

D. B. Judd, Color Eng. 8, 36 (1970).

S. M. Newhall, D. Nickerson, and D. B. Judd, J. Opt. Soc. Am. 33, 385 (1943).
[Crossref]

D. B. Judd, J. Res. Natl. Bur. Std. (U.S.) 24, 293 (1940).
[Crossref]

D. B. Judd and G. Wyszecki, Color in Business, Science and Industry (Wiley, New York, 1963).

Kaneko, T.

T. Kaneko, Acta Chromatica 1, 103 (1963).

Killian, J. T.

Newhall, S. M.

Nickerson, D.

Stevens, J. C.

Stevens, S. S.

J. C. Stevens and S. S. Stevens, J. Opt. Soc. Am. 53, 375 (1963).
[Crossref] [PubMed]

S. S. Stevens, Science 133, 80 (1961).
[Crossref] [PubMed]

S. S. Stevens, Psychol. Rev. 64, 153 (1957).
[Crossref] [PubMed]

S. S. Stevens, in Sensory Communication, edited by W. A. Rosenblith (M.I.T. Press, Cambridge, Mass., 1961), p. 1.

S. S. Stevens, in Psychological Scaling; Theory and Applications, edited by H. Gulliksen and S. Messick (Wiley, New York, 1960), p. 49.

Takasaki, H.

Torgerson, W. S.

W. S. Torgerson, in Ref. 4, p. 21.

Wyszecki, G.

D. B. Judd and G. Wyszecki, Color in Business, Science and Industry (Wiley, New York, 1963).

Acta Chromatica (1)

T. Kaneko, Acta Chromatica 1, 103 (1963).

Color Eng. (1)

D. B. Judd, Color Eng. 8, 36 (1970).

J. Exptl. Psychol. (1)

E. Q. Adams and P. W. Cobb, J. Exptl. Psychol. 5, 39 (1922).
[Crossref]

J. Opt. Soc. Am. (6)

J. Res. Natl. Bur. Std. (U.S.) (1)

D. B. Judd, J. Res. Natl. Bur. Std. (U.S.) 24, 293 (1940).
[Crossref]

Psychol. Rev. (1)

S. S. Stevens, Psychol. Rev. 64, 153 (1957).
[Crossref] [PubMed]

Science (1)

S. S. Stevens, Science 133, 80 (1961).
[Crossref] [PubMed]

Vision Res. (1)

D. Jameson and L. Hurvich, Vision Res. 4, 133 (1964).
[Crossref]

Other (6)

S. S. Stevens, in Sensory Communication, edited by W. A. Rosenblith (M.I.T. Press, Cambridge, Mass., 1961), p. 1.

S. S. Stevens, in Psychological Scaling; Theory and Applications, edited by H. Gulliksen and S. Messick (Wiley, New York, 1960), p. 49.

W. S. Torgerson, in Ref. 4, p. 21.

H. Helson, Adaptation-Level Theory (Harper and Row, New York, 1964).

The actual illuminances used in the study are unavailable. However, G. Howett made available to the author the illuminances that were used in a recent (as yet unpublished) study of the OSA Committee on Uniform Color Scales, which also instructed its observers to use north-sky light or its equivalent. The mean illuminance reported was approximately 1500 lx.

D. B. Judd and G. Wyszecki, Color in Business, Science and Industry (Wiley, New York, 1963).

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Figures (7)

Fig. 1
Fig. 1

Application of the Adams–Cobb formula [B = L/(L+Lb)] to Helson’s data obtained from observers who matched brightly illuminated stimuli for lightness with stimuli under three levels of depth of shadow. Solid dots, ×, and ⊗ represent data produced by matching standard stimuli illuminated by 9.46, 4.17, and 0.10 lx, respectively, with comparison stimuli illuminated by 173.77 lx. The half-filled circles represent data for which the standard and comparison illuminances were 9.46 and 173.77 lx, respectively, and the standard appeared on a white background with the comparison on a black background (left half filled) and vice versa (right half filled). In these calculations Lb, the adaptation luminance, was taken equal to the arithmetic mean of the stimulus and background luminances.

Fig. 2
Fig. 2

Data from Takasaki’s Figs. 9 and 10 with fitted curves generated by Eq. (3), m = n = K = 0.2. The data were obtained by observers matching lightness of two stimuli that were displayed on backgrounds of different reflectance. Notations beside each set of data indicate the Munsell values of the background pair used in each case.

Fig. 3
Fig. 3

Lightness generated by Eq. (3) given five different background values (Munsell values 1, 3, 5, 7, 9 from top to bottom). These curves were used to generate those in Fig. 2.

Fig. 4
Fig. 4

Lightness according to Eq. (3), m = 0.4, n = 0.2, K = 0.65, for backgrounds of 4.3% reflectance (points), 1.21% reflectance (×), and zero background (dashed line) on log–log coordinates. Approximate slopes of visually fitted solid lines through points and ×’s are 1.05 and 0.52, respectively. The dashed line has a slope of 0.34.

Fig. 5
Fig. 5

Data from Munsell renotation study15 for backgrounds of 85.2% reflectance (circled points) and backgrounds of 4% reflectance (uncircled points). Two lightness formulas are represented: Adams–Cobb–Judd with anchoring at 2% and 74% (dashed lines), and Eq. (3) modified with anchoring at 2% and 74% (solid lines).

Fig. 6
Fig. 6

Data from Munsell renotation study15 for background of 25.3% reflectance (dots), Adams–Cobb–Judd formula anchored at 2% and 74% (dashed line), and Eq. (3) (solid line).

Fig. 7
Fig. 7

Application of Eq. (4) (m = 0.4, n = 0.2, K = 0.3) to data of Helson (same data used in Fig. 1). See Fig. 1 for legend.

Equations (4)

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B = L / ( L + L b ) ,
L = V - C 1 V b + C 2 V ¯ b [ ( V - V b ) / C 3 ] e - V - V b / C 3 ,
L = S m + K S - B n ,             S B L = S m - K S - B n ,             S B ,
L = ( 10 S L ) m + K 10 S L - 10 B L n ,             S L B L L = ( 10 S L ) m - K 10 S L - 10 B L n ,             S L B L ,