Abstract

The effect of dividing-strip width (sample proximity) upon sensitivity to suprathreshold and threshold color differences is explored by three methods that involve ratio comparisons, liminal determinations, and repeated color matchings. The results suggest, in general, that sample separation impairs lightness discrimination more than chromaticness discrimination and that it may be necessary to introduce a proximity factor into color-difference formulas when evaluating threshold or small-size color differences.

© 1976 Optical Society of America

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References

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  1. G. Wyszecki, J. Opt. Soc. Am. 55, 896 (1974).
  2. D. B. Judd, J. Res. Nat. Bur. Stand. 5, 1161 (1930).
  3. D. B. Judd, Textile Res. X,  253, 292 (1939).
    [CrossRef]
  4. D. B. Judd, Am. J. Psych. 52, 418 (1939).
    [CrossRef]
  5. R. S. Hunter, J. Opt. Soc. Am. 32, 509 (1942).
    [CrossRef]
  6. A. C. Traub, The proximity factor in Judd’s color difference formula (Ph. D. thesis, University of Cincinnati, 1952).
  7. A. C. Traub and I. Balinkin, J. Opt. Soc. Am. 51, 755 (1961).
    [CrossRef] [PubMed]
  8. A. R. Robertson, Proceedings of 18th Session of CIE, London, 1975 (Bureau Central, Commission Internationale de l’Eclairage, 4 Av. du Recteur Poincaré, 75–Paris 16e, France, 1976), Paper No. 10.
  9. J. P. Guilford, Psychometric Methods, 2nd ed. (McGraw-Hill, New York, 1954), p. 125.
  10. G. Wyszecki and G. H. Fielder, J. Opt. Soc. Am. 61, 1135 (1971).
    [CrossRef] [PubMed]
  11. G. Wyszecki, J. Opt. Soc. Am. 55, 1319 (1965).
    [CrossRef] [PubMed]
  12. G. Wyszecki and W. S. Stiles, Color Science (Wiley, New York, 1967), p. 1152.
  13. B. R. Bellamy and S. M. Newhall, J. Opt. Soc. Am. 32, 465 (1942).
    [CrossRef]
  14. It is difficult to draw any finer comparisons between the two studies, because the same Munsell colors were not employed as stimuli. There are two exceptions, however; two color centers, 5Y 8/8 and N 6, were used in both studies. For the former, Bellamy and Newhall obtained a hue limen of 0.67, a chroma limen of 0.31, and a value limen of 0.04. We obtained a hue limen of 0.30 a chroma limen of 0.16, and a value limen of 0.05. The agreement therefore in this case is poor. For the achromatic sample, Bellamy and Newhall obtained a value limen of 0.023 and we obtained 0.024. The agreement therefore in this case is very good.
  15. H. R. Davidson, J. Opt. Soc. Am. 41, 104 (1951).
    [CrossRef]
  16. A. R. Robertson (personal communication).
  17. The size of elliptical cross sections of ellipsoids probably changes with test-field-luminance level. For instance, the observations of W. R. J. Brown [, J. Opt. Soc. Am. 41, 684 (1951)] suggest that ellipses increase in size as test-field luminance decreases.
    [CrossRef] [PubMed]
  18. See, however, Ref. 10, footnote 14, p. 1152.
  19. These values actually correspond to the average proportional increase of the square root of the ellipse area. The square root of the ellipse area was taken so that the increase could be compared with the luminance increase (a linear change).
  20. Only a small increase of ellipse area and ΔY/Y size was found for the N 6/ color center. This may be due to a crispening effect, because its tristimulus values were almost identical to those of the surround color. Or, perhaps the surround counteracted the effect of the dividing-strip width by appearing as an extension of the test color.
  21. D. L. MacAdam, Rev. Opt. 28, 172 (1949); Doc. Ophthalmol. 3, 231 (1949); in Color Metrics, (AIC/Holland, c/o Institute for Perception TNO, Soesterberg, 1972), p. 160.
  22. D. L. MacAdam, in American Institute of Physics Handbook, 2nd ed. (McGraw-Hill, New York, 1963), p. 6–149.
  23. G. Wyszecki, Farbe 14, 67 (1965).

1974 (1)

1971 (1)

1965 (2)

1961 (1)

1951 (2)

1949 (1)

D. L. MacAdam, Rev. Opt. 28, 172 (1949); Doc. Ophthalmol. 3, 231 (1949); in Color Metrics, (AIC/Holland, c/o Institute for Perception TNO, Soesterberg, 1972), p. 160.

1942 (2)

1939 (2)

D. B. Judd, Textile Res. X,  253, 292 (1939).
[CrossRef]

D. B. Judd, Am. J. Psych. 52, 418 (1939).
[CrossRef]

1930 (1)

D. B. Judd, J. Res. Nat. Bur. Stand. 5, 1161 (1930).

Balinkin, I.

Bellamy, B. R.

Brown, W. R. J.

Davidson, H. R.

Fielder, G. H.

Guilford, J. P.

J. P. Guilford, Psychometric Methods, 2nd ed. (McGraw-Hill, New York, 1954), p. 125.

Hunter, R. S.

Judd, D. B.

D. B. Judd, Textile Res. X,  253, 292 (1939).
[CrossRef]

D. B. Judd, Am. J. Psych. 52, 418 (1939).
[CrossRef]

D. B. Judd, J. Res. Nat. Bur. Stand. 5, 1161 (1930).

MacAdam, D. L.

D. L. MacAdam, Rev. Opt. 28, 172 (1949); Doc. Ophthalmol. 3, 231 (1949); in Color Metrics, (AIC/Holland, c/o Institute for Perception TNO, Soesterberg, 1972), p. 160.

D. L. MacAdam, in American Institute of Physics Handbook, 2nd ed. (McGraw-Hill, New York, 1963), p. 6–149.

Newhall, S. M.

Robertson, A. R.

A. R. Robertson, Proceedings of 18th Session of CIE, London, 1975 (Bureau Central, Commission Internationale de l’Eclairage, 4 Av. du Recteur Poincaré, 75–Paris 16e, France, 1976), Paper No. 10.

A. R. Robertson (personal communication).

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science (Wiley, New York, 1967), p. 1152.

Traub, A. C.

A. C. Traub and I. Balinkin, J. Opt. Soc. Am. 51, 755 (1961).
[CrossRef] [PubMed]

A. C. Traub, The proximity factor in Judd’s color difference formula (Ph. D. thesis, University of Cincinnati, 1952).

Wyszecki, G.

Am. J. Psych. (1)

D. B. Judd, Am. J. Psych. 52, 418 (1939).
[CrossRef]

Farbe (1)

G. Wyszecki, Farbe 14, 67 (1965).

J. Opt. Soc. Am. (8)

J. Res. Nat. Bur. Stand. (1)

D. B. Judd, J. Res. Nat. Bur. Stand. 5, 1161 (1930).

Rev. Opt. (1)

D. L. MacAdam, Rev. Opt. 28, 172 (1949); Doc. Ophthalmol. 3, 231 (1949); in Color Metrics, (AIC/Holland, c/o Institute for Perception TNO, Soesterberg, 1972), p. 160.

Textile Res. X (1)

D. B. Judd, Textile Res. X,  253, 292 (1939).
[CrossRef]

Other (10)

A. C. Traub, The proximity factor in Judd’s color difference formula (Ph. D. thesis, University of Cincinnati, 1952).

G. Wyszecki and W. S. Stiles, Color Science (Wiley, New York, 1967), p. 1152.

A. R. Robertson, Proceedings of 18th Session of CIE, London, 1975 (Bureau Central, Commission Internationale de l’Eclairage, 4 Av. du Recteur Poincaré, 75–Paris 16e, France, 1976), Paper No. 10.

J. P. Guilford, Psychometric Methods, 2nd ed. (McGraw-Hill, New York, 1954), p. 125.

See, however, Ref. 10, footnote 14, p. 1152.

These values actually correspond to the average proportional increase of the square root of the ellipse area. The square root of the ellipse area was taken so that the increase could be compared with the luminance increase (a linear change).

Only a small increase of ellipse area and ΔY/Y size was found for the N 6/ color center. This may be due to a crispening effect, because its tristimulus values were almost identical to those of the surround color. Or, perhaps the surround counteracted the effect of the dividing-strip width by appearing as an extension of the test color.

A. R. Robertson (personal communication).

It is difficult to draw any finer comparisons between the two studies, because the same Munsell colors were not employed as stimuli. There are two exceptions, however; two color centers, 5Y 8/8 and N 6, were used in both studies. For the former, Bellamy and Newhall obtained a hue limen of 0.67, a chroma limen of 0.31, and a value limen of 0.04. We obtained a hue limen of 0.30 a chroma limen of 0.16, and a value limen of 0.05. The agreement therefore in this case is poor. For the achromatic sample, Bellamy and Newhall obtained a value limen of 0.023 and we obtained 0.024. The agreement therefore in this case is very good.

D. L. MacAdam, in American Institute of Physics Handbook, 2nd ed. (McGraw-Hill, New York, 1963), p. 6–149.

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Figures (8)

FIG. 1
FIG. 1

Array of the seven visual fields provided by the NRC calorimeter.

FIG. 2
FIG. 2

Configuration of the visual field used in the first method. Hatched area is the grey surround, cross-hatched is the white surround (not to scale).

FIG. 3
FIG. 3

CIE 1931 chromaticity diagram showing chromaticity points of test stimuli used throughout this experiment. The numbers correspond to the Munsell notations (1) 5R 8.25/3, (2) 7.5R 6/6, (3) 5Y 8/8, (4) 7.5G 6/6, (5) 5B 4/4, (6) N6. Points R, G, B represent the chromaticities of the instrument primaries, SG the grey surround, and SW the white surround. The broken line represents the gamut of the NRC seven-field colorimeter.

FIG. 4
FIG. 4

Section of CIE 1931 chromaticity diagram showing cross sections (2.5 times enlarged) of color-matching ellipsoids obtained in (x, y, l) space. Solid-line ellipses represent mean results obtained by Wyszecki and Fielder’s10 three observers (after Robertson16). Broken-line ellipses represent results obtained by observer L. S. for 0 cm field separation. The numbers correspond to the Munsell notations given in Fig. 3. Points R, G, B represent the chromaticities of the instrument primaries.

FIG. 5
FIG. 5

Portion of the CIE chromaticity diagram showing cross sections of color-matching ellipsoids obtained in (x, y, l) space for observer L. S. Solid-line ellipses are for the 0 cm separation and broken-line ellipses are for the 8.2 cm separation. The numbers correspond to the Munsell notations given in Fig. 3. Points R, G, B represent the chromaticities of the instrument primaries. The axes of the ellipses are five times actual size.

FIG. 6
FIG. 6

Portion of the CIE 1931 chromaticity diagram showing cross sections of color-matching ellipsoids obtained in (x, y, l) space for observer L. S., who produced sets of color matches on three different occasions, with identical observing conditions. The numbers correspond to the Munsell notations given in Fig. 3. The axes of the ellipses are 2.5 times actual size.

FIG. 7
FIG. 7

Portion of the CIE 1931 chromaticity diagram, showing cross sections of color-matching ellipsoids obtained in (x, y, l) space for the same color center 5R 8.25/3 at three conditions of field separation. The numbers indicate width of dividing strip in centimeters.

FIG. 8
FIG. 8

Portion of the CIE 1931 chromaticity diagram showing cross sections of color-matching ellipsoids obtained in (x, y, l) space for the same color center N6. Solid-line ellipses represent color matches made with 4° field and light dividing strip and surround. Broken-line ellipses represent color matches made with 2° field and dark dividing strip and surround. The separation for each ellipse is given in centimeters.

Tables (4)

Tables Icon

TABLE I Values of k1 the proximity factor, suggested by Judd (taken from Hunter5).

Tables Icon

TABLE II Equal value differences.

Tables Icon

TABLE III Attribute difference limens for two conditions of field separation.

Tables Icon

TABLE IV Color-matching ellipsoids and their cross sections for observer L. S. for 0, 3.2, and 8.2 cm field separations.

Equations (2)

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k 1 ( Θ ) = 30 + [ 18 / ( 0.2 + Θ 1 / 2 ) ] ,
( d s ) 2 = g 11 ( x - x 0 ) 2 + g 22 ( y - y 0 ) 2 + g 33 ( l - l 0 ) 2 + 2 g 12 ( x - x 0 ) ( y - y 0 ) + 2 g 13 ( x - x 0 ) ( l - l 0 ) + 2 g 23 ( y - y 0 ) ( l - l 0 ) = 7.81 ,