Abstract

All color difference equations are based, either explicitly or implicitly, on the measurement of the distance between the two colors when plotted in a visually uniform color space. The accuracy of these equations depends upon the approximations assumed in their derivation and the uniformity of the color space chosen. Judd’s Uniform Chromaticity space, Adam’s Chromatic Value space, the Munsell space, and others have been used as the basis of color difference equations.

Instead of explicitly transforming the ICI space into a visually uniform space, its known distortions can be compensated by means of the MacAdam ellipsoids. Color differences may be calculated very simply by a graphical method, assuming any point on the ellipsoid to represent a unit color difference from the center of the ellipsoid. Calculations of this sort have been applied to the Balinkin data on tiles and to data more recently obtained on textile dyeings.

Color differences calculated by this method correlate with visually estimated color differences as closely as do differences calculated by the best of the equations based upon uniform color spaces. This appears to be further confirmation of the validity of the MacAdam ellipsoids and of their usefulness in specification of color tolerances.

© 1951 Optical Society of America

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References

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  1. R. S. Hunter, J. Opt. Soc. Am. 32, 518–519 (1942).
  2. D. Nickerson, Textile Research 6, 505–514 (1936).
    [Crossref]
  3. I. A. Balinkin, Bull. Am. Ceram. Soc. 20, 392–402 (1941).
  4. E. Q. Adams, J. Opt. Soc. Am. 32, 168–173 (1942).
    [Crossref]
  5. I. H. Godlove, J. Opt. Soc. Am. 41, 760 (1951).
    [Crossref]
  6. D. Nickerson, Am. Dyestuff Rept. 39, 541 (1950).
  7. D. B. Judd, Textile Research 9, 253–308 (1939).
    [Crossref]
  8. D. Nickerson and K. F. Stultz, J. Opt. Soc. Am. 34, 550–570 (1944).
    [Crossref]
  9. D. L. MacAdam, J. Opt. Soc. Am. 33, 18 (1943).
    [Crossref]
  10. For a more complete description of visual sensitivity ellipses, see D. L. MacAdam, J. Opt. Soc. Am. 32, 247–274 (1942); W. J. R. Brown and D. L. MacAdam, J. Opt. Soc. Am. 39, 808–834 (1949); H.R. Davidson, J. Opt. Soc. Am. 41, 104–111 (1951). Ellipses, or ellipsoids, given in these papers are derived for a stated probability of visually detecting a color difference.
    [Crossref] [PubMed]
  11. H. R. Davidson, Am. Dyestuff Rept. 40, 247 (1951).
  12. H. R. Davidson, J. Opt. Soc. Am. 41, 104–111 (1951).
    [Crossref]
  13. Reference 12, Figs. 1, 2, and 3.

1951 (3)

1950 (1)

D. Nickerson, Am. Dyestuff Rept. 39, 541 (1950).

1944 (1)

1943 (1)

1942 (3)

1941 (1)

I. A. Balinkin, Bull. Am. Ceram. Soc. 20, 392–402 (1941).

1939 (1)

D. B. Judd, Textile Research 9, 253–308 (1939).
[Crossref]

1936 (1)

D. Nickerson, Textile Research 6, 505–514 (1936).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

I.C.I. color coordinates.

Fig. 2
Fig. 2

Color differences in I.C.I. color space.

Fig. 3
Fig. 3

Calculation of color differences from visual sensitivity ellipsoids.

Fig. 4
Fig. 4

Visual and calculated sizes of color differences—red samples.

Fig. 5
Fig. 5

Visual and calculated sizes of color differences—blue samples.

Fig. 6
Fig. 6

Visual and calculated sizes of color differences—green samples.

Fig. 7
Fig. 7

Visual and calculated sizes of color differences—Balinkin’s samples.

Tables (4)

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Table I Visual judgments of red series.

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Table II Visual judgments of blue series.

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Table III Visual judgments of green series.

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Table IV Summary of correlation data.

Equations (5)

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( Judd ) Δ E = { [ 7 Y 1 4 [ ( Δ α ) 2 + ( Δ β ) 2 ] 1 2 · 10 2 ] 2 + [ 10 2 Δ ( Y 1 2 ) ] 2 } 1 2 ,
α = - 2.4266 x - 1.3631 y - 0.3214 1.000 x + 2.2633 y + 1.1054 , β = 0.5710 x + 1.2447 y - 0.5708 1.0000 x + 2.2633 y + 1.1054 . ( Nickerson ) I = 1 5 C ( 2 Δ H ) + 6 Δ V + 3 Δ C ,
( Balinkin ) I = { ( 1 5 C · 2 Δ H ) 2 + ( 6 Δ V ) 2 + [ ( 20 / π ) · Δ C ] 2 } 1 2 ,
( Adams ) Δ E = { ( 0.23 Δ V y ) 2 + [ Δ ( V x - V y ) ] 2 + [ 0.4 Δ ( V z - V y ) ] 2 } 1 2 ,
( Godlove ) I = { 2 C 1 C 2 [ 1 - cos ( 3.6 Δ H ) ] + ( Δ C ) 2 + ( 4 Δ V ) 2 } 1 2 .