Abstract

We describe the results of an experiment designed to test the accuracy of the Helson–Judd formulation in predicting the perceived color of objects in two-primary projections. Five trained subjects gave color-naming responses for hue, lightness, and saturation of perceived color in computer-generated artificial images viewed in red and white projection. The averaged results indicate predictions that are 90% correct for hue, 81% for lightness and 61% for saturation at mesopic luminance levels, and 83% correct for hue, 67% for lightness, and 78% for saturation at photopic luminance levels.

© 1969 Optical Society of America

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References

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  1. D. B. Judd, J. Opt. Soc. Am. 30, 2 (1940).
    [Crossref]
  2. D. B. Judd, J. Opt. Soc. Am. 50, 254 (1960).
    [Crossref] [PubMed]
  3. E. H. Land, Proc. Natl. Acad. Sci. (U. S.) 45, 115 (1959).
    [Crossref]
  4. L. Wheeler, J. Opt. Soc. Am. 52, 1058 (1962).
    [Crossref] [PubMed]
  5. L. Wheeler, J. Opt. Soc. Am. 53, 978 (1963).
    [Crossref] [PubMed]
  6. With the luminance contributions so adjusted, Eqs. (11), (15), and (16) take the simple form given at a later point in the text.
  7. E. H. Land, Amer. Sci. 52, 247 (1964).
  8. H. Helson, D. B. Judd, and M. H. Warren, Illum. Eng. 51, 329 (1956).
  9. A. H. Munsell, A Color Notation (Munsell Color Co., Baltimore, 1941).
  10. Munsell Book of Color, Cabinet Edition (Munsell Color Co., Baltimore, 1966).
  11. D. B. Judd, J. Opt. Soc. Am. 25, 24 (1935).
    [Crossref]
  12. The UCS diagram hereafter referred to in this paper is that just cited.
  13. E. Q. Adams and P. W. Cobb, J. Exptl. Psychol. 5, 39 (1922).
    [Crossref]
  14. W. T. Wintringham of these laboratories has called our attention to the fact that the measured densities might not be accurate for the projection system used in the experiment. Our measurement yielded diffuse density whereas the more appropriate parameter might be specular density. The ratio of the specular to diffuse density is known as the Callier-Q factor and is a function of photographic gamma and density. The effect of this factor is not a simple one to evaluate in terms of our experiment, but we are currently pursuing this aspect.
  15. E. H. Land, Proc. Natl. Acad. Sci. (U. S.) 45, 636 (1959).
    [Crossref]
  16. R. M. Evans, J. Opt. Soc. Am. 33, 579 (1943).
    [Crossref]
  17. D. B. Judd, private communication.
  18. J. Mandelbaum and E. Nelson, Arch. Ophthalmol. (Chicago) 93, 402 (1960).
    [Crossref]

1964 (1)

E. H. Land, Amer. Sci. 52, 247 (1964).

1963 (1)

1962 (1)

1960 (2)

J. Mandelbaum and E. Nelson, Arch. Ophthalmol. (Chicago) 93, 402 (1960).
[Crossref]

D. B. Judd, J. Opt. Soc. Am. 50, 254 (1960).
[Crossref] [PubMed]

1959 (2)

E. H. Land, Proc. Natl. Acad. Sci. (U. S.) 45, 115 (1959).
[Crossref]

E. H. Land, Proc. Natl. Acad. Sci. (U. S.) 45, 636 (1959).
[Crossref]

1956 (1)

H. Helson, D. B. Judd, and M. H. Warren, Illum. Eng. 51, 329 (1956).

1943 (1)

1940 (1)

1935 (1)

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]

Evans, R. M.

Helson, H.

H. Helson, D. B. Judd, and M. H. Warren, Illum. Eng. 51, 329 (1956).

Judd, D. B.

Land, E. H.

E. H. Land, Amer. Sci. 52, 247 (1964).

E. H. Land, Proc. Natl. Acad. Sci. (U. S.) 45, 115 (1959).
[Crossref]

E. H. Land, Proc. Natl. Acad. Sci. (U. S.) 45, 636 (1959).
[Crossref]

Mandelbaum, J.

J. Mandelbaum and E. Nelson, Arch. Ophthalmol. (Chicago) 93, 402 (1960).
[Crossref]

Munsell, A. H.

A. H. Munsell, A Color Notation (Munsell Color Co., Baltimore, 1941).

Nelson, E.

J. Mandelbaum and E. Nelson, Arch. Ophthalmol. (Chicago) 93, 402 (1960).
[Crossref]

Warren, M. H.

H. Helson, D. B. Judd, and M. H. Warren, Illum. Eng. 51, 329 (1956).

Wheeler, L.

Amer. Sci. (1)

E. H. Land, Amer. Sci. 52, 247 (1964).

Arch. Ophthalmol. (Chicago) (1)

J. Mandelbaum and E. Nelson, Arch. Ophthalmol. (Chicago) 93, 402 (1960).
[Crossref]

Illum. Eng. (1)

H. Helson, D. B. Judd, and M. H. Warren, Illum. Eng. 51, 329 (1956).

J. Exptl. Psychol. (1)

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

J. Opt. Soc. Am. (6)

Proc. Natl. Acad. Sci. (U. S.) (2)

E. H. Land, Proc. Natl. Acad. Sci. (U. S.) 45, 115 (1959).
[Crossref]

E. H. Land, Proc. Natl. Acad. Sci. (U. S.) 45, 636 (1959).
[Crossref]

Other (6)

D. B. Judd, private communication.

The UCS diagram hereafter referred to in this paper is that just cited.

W. T. Wintringham of these laboratories has called our attention to the fact that the measured densities might not be accurate for the projection system used in the experiment. Our measurement yielded diffuse density whereas the more appropriate parameter might be specular density. The ratio of the specular to diffuse density is known as the Callier-Q factor and is a function of photographic gamma and density. The effect of this factor is not a simple one to evaluate in terms of our experiment, but we are currently pursuing this aspect.

With the luminance contributions so adjusted, Eqs. (11), (15), and (16) take the simple form given at a later point in the text.

A. H. Munsell, A Color Notation (Munsell Color Co., Baltimore, 1941).

Munsell Book of Color, Cabinet Edition (Munsell Color Co., Baltimore, 1966).

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Figures (2)

Fig. 1
Fig. 1

Schematic of experimental conditions.

Fig. 2
Fig. 2

Computer-generated quilts. Quilt (a) was projected in red light and quilt (b) was projected in incandescent-tungsten light. These quilts are designated as quilt pair A in this paper.

Tables (14)

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Table I Measured density values for quilt pair A. Upper number in each cell refers to red-projected quilt; lower numbers refer to white-projected quilt.

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Table II Apparent density values for quilt pair A. Upper number in each cell refers to red-projected quilt; lower numbers refer to white-projected quilt.

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Table III Measured density values for quilt-pair B. Upper number in each cell refers to red-projected quilt; lower numbers refer to white-projected quilt.

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Table IV Apparent density values for quilt pair B. Upper number in each cell refers to red-projected quilt; lower numbers refer to white-projected quilt.

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Table V Test scores for the five subjects, taken at the conclusion of the training period.

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Table VI Responses of all five subjects for each cell in the quilt pair A at photopic levels. Responses are given in terms of hue, lightness and saturation.

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Table VII Responses of all five subjects for each cell in the quilt pair A at mesopic levels. Responses are given in terms of hue, lightness and saturation.

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Table VIII Responses of all five subjects for each cell in the quilt pair B at photopic levels. Responses are given in terms of hue, lightness and saturation.

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Table IX Responses of all five subjects for each cell in the quilt pair B at mesopic levels. Responses are given in terms of hue, lightness and saturation.

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Table X Determination of hue (reprinted from Ref. 1).

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Table XI Input parameters for Helson–Judd formulas based on measured densities.

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Table XII Predictions of hue, lightness, and saturation for quilt pair A at both photopic and mesopic levels. Upper symbols in each cell refer to predictions based on the measured densities; lower symbols are predictions based on the apparent densities.

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Table XIII Predictions of hue, lightness, and saturation for quilt pair B at both photopic and mesopic levels. Upper symbols in each cell refer to predictions based on the measured densities; lower symbols are predictions based on the apparent densities.

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Table XIV Percent-correct scores of predictions.

Equations (19)

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H = f [ ( r - r n ) / ( g - g n ) , sign ( r - r n ) ] ,
L = 10 ( β - 0.03 ) ( β f + 1.00 ) ( 1.00 - 0.03 ) ( β f + β ) ,
S = 50 D = 50 [ ( r - r n ) 2 + ( g - g n ) 2 + ( b - b n ) 2 ] 1 2 .
r n = r f - D f [ 0.1 L ( r f - 0.360 ) - 0.009 b f ( β 0 + β ¯ ) ( L ) 2 log 2000 I ] ,
g n = g f - D f [ 0.1 L ( g f - 0.300 ) - 0.030 ] .
D f = [ ( r f - 0.44 ) 2 + ( g f - 0.47 ) 2 + ( b f - 0.09 ) 2 ] 1 2 ,
L = 10 β / ( β + β f ) - 3.0.
β f = ( β 0 + β ¯ ) / 2.
T L i j = 10 - D L i j ,
T S i j = 10 - D S i j ,
r i j = ( r L T L i j + r S T S i j ) / ( T L i j + T S i j ) g i j = ( g L T L i j + g S T S i j ) / ( T L i j + T S i j )
b i j = 1 - r i j - g i j .
T ¯ = ( i , j T L i j + T S i j ) / 200.
T f = ( B T 0 + S T ¯ ) / ( B + S ) .
T ¯ L = i , j T L i j / 100 , T ¯ S = i , j T S i j / 100 ,
r ¯ = ( T ¯ L r L + T ¯ S r S ) / ( T ¯ L + T ¯ S ) , g ¯ = ( T ¯ L g L + T ¯ S g S ) / ( T ¯ L + T ¯ S ) , b ¯ = 1 - r ¯ - g ¯ ,
r 0 = ( T L 0 r L + T S 0 r S ) / ( T S 0 + T L 0 ) , g 0 = ( T L 0 g L + T S 0 G S ) / ( T S 0 + T L 0 ) , b 0 = 1 - r 0 - g 0 ,
r f = ( B r 0 + S r ¯ ) / ( B + S ) , g f = ( B g 0 + S g ¯ ) / ( B + S ) , b f = 1 - r f - g f .
L i j = 10 ( T max + T f ) ( T i j - T min ) / ( T i j + T f ) × ( T max - T min ) .