Abstract

Five observers made color-difference judgments by the method of triads. A triad (S: A,B) consisted of a standard stimulus S and two comparison stimuli, A and B. The observer reported which color difference appeared smaller, that between A and S or that between B and S. Triads were composed of monochromatic stimuli, adjusted to constant brightness for each observer. They contained both small color differences and ones that are markedly supraliminal. For any triad (S: A,B) it was assumed that the choice probability is an index of the relative sizes of the subjective differences (A,S) and (B,S). Estimated choice probabilities were converted to estimated distance measures by means of a scaling model based on assumptions about the observers’ judgmental task.

The obtained distance estimates were compared with standard wavelength-discrimination data, with Wright’s data on slightly supraliminal color differences, and with the large-difference predictions of the Hurvich–Jameson HBS color specification system. While the present data cannot be regarded as providing definitive color-difference measures (even for the limited range of conditions employed) they nevertheless contribute to the development of a metric space representation combining discriminability and supraliminal similarity.

© 1967 Optical Society of America

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References

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  1. W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 46, 459 (1934).
    [Crossref]
  2. R. A. Weale, J. Physiol. (London) 113, 115 (1951).
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    [Crossref] [PubMed]
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    [Crossref]
  7. T. Indow and T. Uchizono, J. Exper. Psychol. 59, 321 (1960).
    [Crossref]
  8. W. D. Wright, Proc. Phys. Soc. (London) 53, 93 (1941).
    [Crossref]
  9. G. Ekman, J. Psychol. 38, 467 (1954).
    [Crossref]
  10. C. E. Helm, J. Opt. Soc. Am. 54, 256 (1964).
    [Crossref] [PubMed]
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    [Crossref]
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  13. L. M. Hurvich and D. Jameson, J. Opt. Soc. Am. 46, 416 (1956).
    [Crossref] [PubMed]
  14. The spectra] sensitivity curve of the photomultiplier tube was supplied by L. M. Hurvich and D. Jameson.
  15. I particularly wish to thank Dr. Robert M. Steinman (RMS) for advice regarding apparatus construction, as well as for unfailing care and patience during more than 150 hours of observing. This research was greatly aided by his interest.
  16. Munsell Book of Color (Munsell Color Co., Baltimore, 1929).
  17. W. D. Wright, Researches on Normal and Defective Colour Vision (C. V. Mosby Co., St. Louis, 1947).
  18. L. C. Thomson, J. Physiol. (London) 112, 114 (1951).
  19. Y. Hsia and C. H. Graham, Proc. Natl. Acad. Sci. (U. S.) 38, 80 (1952).
    [Crossref]
  20. L. M. Hurvich and D. Jameson, J. Opt. Soc. Am. 43, 485 (1953).
    [Crossref] [PubMed]
  21. R. A. Weale, J. Physiol. (London) 114, 435 (1951).
  22. L. C. Thomson, Nature 157, 805 (1946).
    [Crossref]
  23. L. C. Thomson and P. W. Trezona, J. Physiol. (London) 114, 98 (1951).
  24. H. v. Helmholtz, Ilandb. d. Physiologischen Optik, 2nd ed. (Voss, Hamburg, 1896).
  25. R. H. Sinden, J. Opt. Soc. Am. 28, 339 (1938).
    [Crossref]
  26. W. S. Stiles, Proc. Phys. Soc. (London) 58, 41 (1946).
    [Crossref]
  27. L. Silberstein, Phil. Mag. VII:  37, 126 (1946).
  28. W. S. Torgerson, Theory and Methods of Scaling (John Wiley & Sons, Inc., New York, 1958).
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    [Crossref] [PubMed]
  30. R. N. Shepard, Psychometrika 27, 125 (1962).
    [Crossref]
  31. R. D. Luce, Psychometrika 26, 151 (1961).
    [Crossref]
  32. If some probabilities are zero in the formal model underlying the data, Eq. (1) is assumed to hold only where probabilities are nonzero. A formal treatment of the model, incorporating zero probabilities, is found in Ref. 12.
  33. R. D. Luce, Individual Choice Behavior (John Wiley & Sons, Inc., New York, 1959).

1967 (1)

D. H. Krantz, J. Math. Psychol. 4, 226 (1967).
[Crossref]

1965 (1)

1964 (1)

1962 (1)

R. N. Shepard, Psychometrika 27, 125 (1962).
[Crossref]

1961 (1)

R. D. Luce, Psychometrika 26, 151 (1961).
[Crossref]

1960 (1)

T. Indow and T. Uchizono, J. Exper. Psychol. 59, 321 (1960).
[Crossref]

1958 (1)

R. N. Shepard, Psychol. Rev. 65, 242 (1958).
[Crossref] [PubMed]

1956 (1)

1954 (1)

G. Ekman, J. Psychol. 38, 467 (1954).
[Crossref]

1953 (1)

1952 (1)

Y. Hsia and C. H. Graham, Proc. Natl. Acad. Sci. (U. S.) 38, 80 (1952).
[Crossref]

1951 (4)

R. A. Weale, J. Physiol. (London) 114, 435 (1951).

L. C. Thomson, J. Physiol. (London) 112, 114 (1951).

R. A. Weale, J. Physiol. (London) 113, 115 (1951).

L. C. Thomson and P. W. Trezona, J. Physiol. (London) 114, 98 (1951).

1949 (1)

1946 (3)

W. S. Stiles, Proc. Phys. Soc. (London) 58, 41 (1946).
[Crossref]

L. Silberstein, Phil. Mag. VII:  37, 126 (1946).

L. C. Thomson, Nature 157, 805 (1946).
[Crossref]

1943 (1)

1942 (1)

1941 (1)

W. D. Wright, Proc. Phys. Soc. (London) 53, 93 (1941).
[Crossref]

1938 (1)

1934 (1)

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 46, 459 (1934).
[Crossref]

1926 (1)

Brown, W. R. J.

Ekman, G.

G. Ekman, J. Psychol. 38, 467 (1954).
[Crossref]

Graham, C. H.

Y. Hsia and C. H. Graham, Proc. Natl. Acad. Sci. (U. S.) 38, 80 (1952).
[Crossref]

Helm, C. E.

Helmholtz, H. v.

H. v. Helmholtz, Ilandb. d. Physiologischen Optik, 2nd ed. (Voss, Hamburg, 1896).

Hsia, Y.

Y. Hsia and C. H. Graham, Proc. Natl. Acad. Sci. (U. S.) 38, 80 (1952).
[Crossref]

Hurvich, L. M.

Indow, T.

T. Indow and T. Uchizono, J. Exper. Psychol. 59, 321 (1960).
[Crossref]

Jameson, D.

Jones, L. A.

Judd, D. B.

Krantz, D. H.

D. H. Krantz, J. Math. Psychol. 4, 226 (1967).
[Crossref]

Lowry, E. M.

Luce, R. D.

R. D. Luce, Psychometrika 26, 151 (1961).
[Crossref]

R. D. Luce, Individual Choice Behavior (John Wiley & Sons, Inc., New York, 1959).

MacAdam, D. L.

Newhall, S. M.

Nickerson, D.

Pitt, F. H. G.

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 46, 459 (1934).
[Crossref]

Shepard, R. N.

R. N. Shepard, Psychometrika 27, 125 (1962).
[Crossref]

R. N. Shepard, Psychol. Rev. 65, 242 (1958).
[Crossref] [PubMed]

Silberstein, L.

L. Silberstein, Phil. Mag. VII:  37, 126 (1946).

Sinden, R. H.

Stiles, W. S.

W. S. Stiles, Proc. Phys. Soc. (London) 58, 41 (1946).
[Crossref]

Thomson, L. C.

L. C. Thomson and P. W. Trezona, J. Physiol. (London) 114, 98 (1951).

L. C. Thomson, J. Physiol. (London) 112, 114 (1951).

L. C. Thomson, Nature 157, 805 (1946).
[Crossref]

Torgerson, W. S.

W. S. Torgerson, Theory and Methods of Scaling (John Wiley & Sons, Inc., New York, 1958).

Trezona, P. W.

L. C. Thomson and P. W. Trezona, J. Physiol. (London) 114, 98 (1951).

Uchizono, T.

T. Indow and T. Uchizono, J. Exper. Psychol. 59, 321 (1960).
[Crossref]

Weale, R. A.

R. A. Weale, J. Physiol. (London) 113, 115 (1951).

R. A. Weale, J. Physiol. (London) 114, 435 (1951).

Wright, H.

Wright, W. D.

W. D. Wright, Proc. Phys. Soc. (London) 53, 93 (1941).
[Crossref]

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 46, 459 (1934).
[Crossref]

W. D. Wright, Researches on Normal and Defective Colour Vision (C. V. Mosby Co., St. Louis, 1947).

J. Exper. Psychol. (1)

T. Indow and T. Uchizono, J. Exper. Psychol. 59, 321 (1960).
[Crossref]

J. Math. Psychol. (1)

D. H. Krantz, J. Math. Psychol. 4, 226 (1967).
[Crossref]

J. Opt. Soc. Am. (9)

J. Physiol. (London) (4)

R. A. Weale, J. Physiol. (London) 114, 435 (1951).

L. C. Thomson and P. W. Trezona, J. Physiol. (London) 114, 98 (1951).

R. A. Weale, J. Physiol. (London) 113, 115 (1951).

L. C. Thomson, J. Physiol. (London) 112, 114 (1951).

J. Psychol. (1)

G. Ekman, J. Psychol. 38, 467 (1954).
[Crossref]

Nature (1)

L. C. Thomson, Nature 157, 805 (1946).
[Crossref]

Phil. Mag. VII (1)

L. Silberstein, Phil. Mag. VII:  37, 126 (1946).

Proc. Natl. Acad. Sci. (U. S.) (1)

Y. Hsia and C. H. Graham, Proc. Natl. Acad. Sci. (U. S.) 38, 80 (1952).
[Crossref]

Proc. Phys. Soc. (London) (3)

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 46, 459 (1934).
[Crossref]

W. D. Wright, Proc. Phys. Soc. (London) 53, 93 (1941).
[Crossref]

W. S. Stiles, Proc. Phys. Soc. (London) 58, 41 (1946).
[Crossref]

Psychol. Rev. (1)

R. N. Shepard, Psychol. Rev. 65, 242 (1958).
[Crossref] [PubMed]

Psychometrika (2)

R. N. Shepard, Psychometrika 27, 125 (1962).
[Crossref]

R. D. Luce, Psychometrika 26, 151 (1961).
[Crossref]

Other (8)

If some probabilities are zero in the formal model underlying the data, Eq. (1) is assumed to hold only where probabilities are nonzero. A formal treatment of the model, incorporating zero probabilities, is found in Ref. 12.

R. D. Luce, Individual Choice Behavior (John Wiley & Sons, Inc., New York, 1959).

W. S. Torgerson, Theory and Methods of Scaling (John Wiley & Sons, Inc., New York, 1958).

H. v. Helmholtz, Ilandb. d. Physiologischen Optik, 2nd ed. (Voss, Hamburg, 1896).

The spectra] sensitivity curve of the photomultiplier tube was supplied by L. M. Hurvich and D. Jameson.

I particularly wish to thank Dr. Robert M. Steinman (RMS) for advice regarding apparatus construction, as well as for unfailing care and patience during more than 150 hours of observing. This research was greatly aided by his interest.

Munsell Book of Color (Munsell Color Co., Baltimore, 1929).

W. D. Wright, Researches on Normal and Defective Colour Vision (C. V. Mosby Co., St. Louis, 1947).

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Figures (9)

Fig. 1
Fig. 1

Linking of large and small differences. Euclidean distance in the figure is used to represent size of color differences. (S,S) is a zero difference, (A,S) a small difference, and (B,S), (C,S) are large differences. Triads presented are (S: A,S) [to evaluate (4,S)], (S: B,A) [to evaluate (B,S) in terms of (A,S)] and (S: C,B).

Fig. 2
Fig. 2

Schematic drawing of the apparatus and the stimulus display. M1, M2, M3 are identical monochromators. The three light paths have the same length and contain the same optical elements: m, a front-surface plane mirror; L and L, achromatic lenses. D is a ground-glass diffuser. The stimulus display consists of three circular test fields near the center of a circular surround field.

Fig. 3
Fig. 3

Experimental design for small differences within one wavelength region. (A,B), (B,C), (C,D) are three adjacent small differences, with A, B,C, D ordered from shorter to longer wavelengths. Eight triads are formed from these three differences and the four zero differences at their endpoints: ( A : A , B ) ( B : B , C ) ( C : C , D ) ( B : A , C ) ( B : A , B ) ( C : B , C ) ( D : C , D ) ( C : B , D ) .

Fig. 4
Fig. 4

Series I, II, and III of large differences. Points represent stimuli, with wavelength in nm indicated. Series I : ( 460 , 468 ) , ( 468 , 475 ) , Series II : ( 460 , 475 ) , ( 475 , 490 ) , Series III : ( 460 , 490 ) , ( 490 , 540 ) , .

Fig. 5
Fig. 5

Luminosity functions for individual observers based on heterochromatic brightness matches. ●—RMS, +—JPE, ○—KR, □—SI, ×—HC. The four functions for RMS, JPE, KR, SI are equated arbitrarily at 580 nm; the one for HC is equated with that for RMS at 540 nm. The standard error of the estimate of log relative luminosity, for individual observers, for pairs of wavelengths 20 nm apart, is about 0.03 log units.

Fig. 6
Fig. 6

Comparison of average wavelength-discrimination curves. ●—Wright & Pitt,1 ordinate is Δλ (right-hand scale); ×—Weale,2 ordinate is Δλ (right-hand scale); ○—present study, ordinate is Δλ/[(1/υ − 1)1/5] (left-hand scale). The unit size on the left-hand scale was adjusted for clarity of the graph, since there is no rational basis for comparison of absolute sensitivities between the present method and previous ones. The estimate of Δλ/[(1/υ − 1)1/5] at 650 nm averages 14.0 for two observers, and is infinite for two others.

Fig. 7
Fig. 7

Comparison of the smallest large differences in the present study with constant subjective steps of Wright.8 The abscissa for each point is the midpoint of the wavelength interval measured. ●—Δλ for Wright, averaged over observers, ○—Δλ/[(1/υ − 1)1/5] for the present study, averaged over observers.

Fig. 8
Fig. 8

HBS configuration for an equal-brightness spectrum for the CIE standard observer with neutral adaptation.13 The polar coordinates are θarctangent of HBS hue index (ratio of the red-green response to the yellow-blue response), and r—value of the HBS saturation index (ratio of summed absolute chromatic responses to summed absolute chromatic and achromatic responses).

Fig. 9
Fig. 9

Comparison of the averaged large-difference measures for Series I (Fig. 4) with the predictions of the HBS system. Each point has as its abscissa the midpoint of the wavelength interval measured. ●—Δλ/HBS distance, where the values of HBS distance are proportional to the distances between successive points in Fig. 8. ○—Δλ/[(1/υ − 1)1/5] measured in the present study.

Tables (6)

Tables Icon

Table I Small-difference triads. The first column under “triads” specifies the standard; the second and third columns specify the comparison stimuli. All stimuli are understood to be specified in nm, with bandwidth and luminance as described in the text. For each subject, the numerals to the left of the diagonal slash refer to the number of choices of the comparison stimulus in the second column as closer to the standard. The numerals to the right of the slash refer to the total number of trials on which the triad was presented.

Tables Icon

Table II Triads comparing small and large differences. Notation as in Table I.

Tables Icon

Table III Large-difference triads. Notation as in Table I.

Tables Icon

Table IV Discriminability of small wavelength differences. Differences are specified by a pair of numbers giving wavelengths in nm. Each entry is 1 minus the υ-scale value for Eq. (8).

Tables Icon

Table V Wavelength directional bias estimates from small-difference triads. Values shown are α(S) from Eq. (8) for each region. Values close to 1.0 represent extreme short-wavelength bias; values close to 0.0 represent extreme long-wavelength bias.

Tables Icon

Table VI Goodness-of-fit of Eq. (8) for small differences. Table entries are minimum chi-square values (approximate) with appropriate degrees of freedom in parentheses. Boldfaced values are statistically significant at the 0.01 level. The starred values are significant at the 0.05 level, but not at the 0.01 level. The entries labeled “total nonsignificant chi-square” exclude the boldfaced values but not the starred ones.

Equations (15)

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( 591 : 585 , 600 ) ( 591 : 585 , 628 ) ( 591 : 585 , 608 ) ( 591 : 572 , 608 ) ( 591 : 581 , 600 ) ( 591 : 572 , 628 ) . ( 591 : 581 , 608 )
p ( S : A , B ) = υ ( A , S ) / [ υ ( A , S ) + υ ( B , S ) ] .
υ ( A , B ) = p ( B : A , B ) / p ( B : B , A ) .
υ ( B , S ) / υ ( A , S ) = p ( S : B , A ) / p ( S : A , B ) .
d ( A , B ) = log [ 1 / υ ( A , B ) ] .
p ( B : A , B ) 1 2 ( positivity )
p ( B : A , B ) = p ( A : B , A ) ( symmetry )
p ( B : A , B ) p ( C : A , B ) ( triangle inequality ) .
d ( A , B ) + d ( B , C ) ( A , C ) ,
p ( S : A , B ) = F S [ υ ( A , S ) , υ ( B , S ) ] ,
p ( S : A , B ) = α ( S ) υ ( A , S ) α ( S ) υ ( A , S ) + [ 1 α ( S ) ] υ ( B , S )
p ( S : A , B ) p ( S : B , A ) = α ( S ) 1 α ( S ) υ ( A , S ) υ ( B , S ) ,
d ( A , B ) = { [ 1 / υ ( A , B ) ] 1 } 1 / 5 .
( A : A , B ) ( B : B , C ) ( C : C , D ) ( B : A , C ) ( B : A , B ) ( C : B , C ) ( D : C , D ) ( C : B , D ) .
Series I : ( 460 , 468 ) , ( 468 , 475 ) , Series II : ( 460 , 475 ) , ( 475 , 490 ) , Series III : ( 460 , 490 ) , ( 490 , 540 ) , .