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  1. Italic numbers in parentheses refer to literature cited at end of this paper.
  2. For a discussion of color concepts refer to “The concept of color,” O.S.A. Colorimetry Committee Report, J. Opt. Soc. Am.33, 552 (1943), Fig. 3.
  3. The MacAdam report based on the Nutting observations can be made the basis for setting tolerances, but not so directly and conveniently unless an approximate representation of the MacAdam data in 3-dimensional space is employed.
  4. The square of rho (P2), though lower than P, is used hereafter in this paper for it seems a more useful number than P to use to represent the degree of correlation. P (rho) represents multiple linear correlation, R represents simple linear correlation.
  5. Suggestions regarding differences in relations of value to hue and chroma, depending upon conditions of observation, are discussed in a recent paper (36), with illustrations of two such solids, and any final tolerance formula based on this concept should include a term that will provide adjustment in accord with conditions of observation.
  6. The figures are usually read to the nearest 0.5 step of hue and nearest 0.1 step of chroma, with value read to the second decimal place as given in Table II of the O.S.A. report. When adjustments are made for hue and chroma for interpolation between two value charts the results are carried to one decimal place for hue and two places for chroma in order to avoid rejection errors. It is not implied that color differences as small as 0.1 hue step or 0.01 chroma step can be recognized.
  7. Development of this formula is given in detail by Hunter in (18), pp. 519–521.
  8. See Table II of reference (32).
  9. Judd comments on this breakdown in the Inter-Society Color Council’s Discussion Session on Small Color Differences, published in the Am. Dyestuff Rept. 33, 231 ff. (1944).

1944 (1)

Judd comments on this breakdown in the Inter-Society Color Council’s Discussion Session on Small Color Differences, published in the Am. Dyestuff Rept. 33, 231 ff. (1944).

Hunter,

Development of this formula is given in detail by Hunter in (18), pp. 519–521.

Judd,

Judd comments on this breakdown in the Inter-Society Color Council’s Discussion Session on Small Color Differences, published in the Am. Dyestuff Rept. 33, 231 ff. (1944).

Am. Dyestuff Rept. (1)

Judd comments on this breakdown in the Inter-Society Color Council’s Discussion Session on Small Color Differences, published in the Am. Dyestuff Rept. 33, 231 ff. (1944).

Other (8)

Italic numbers in parentheses refer to literature cited at end of this paper.

For a discussion of color concepts refer to “The concept of color,” O.S.A. Colorimetry Committee Report, J. Opt. Soc. Am.33, 552 (1943), Fig. 3.

The MacAdam report based on the Nutting observations can be made the basis for setting tolerances, but not so directly and conveniently unless an approximate representation of the MacAdam data in 3-dimensional space is employed.

The square of rho (P2), though lower than P, is used hereafter in this paper for it seems a more useful number than P to use to represent the degree of correlation. P (rho) represents multiple linear correlation, R represents simple linear correlation.

Suggestions regarding differences in relations of value to hue and chroma, depending upon conditions of observation, are discussed in a recent paper (36), with illustrations of two such solids, and any final tolerance formula based on this concept should include a term that will provide adjustment in accord with conditions of observation.

The figures are usually read to the nearest 0.5 step of hue and nearest 0.1 step of chroma, with value read to the second decimal place as given in Table II of the O.S.A. report. When adjustments are made for hue and chroma for interpolation between two value charts the results are carried to one decimal place for hue and two places for chroma in order to avoid rejection errors. It is not implied that color differences as small as 0.1 hue step or 0.01 chroma step can be recognized.

Development of this formula is given in detail by Hunter in (18), pp. 519–521.

See Table II of reference (32).

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Figures (3)

Fig. 1
Fig. 1

Scatter diagram of colors in 9 groups of samples plotted for Munsell value and chroma (hue indicated by numbers attached to each sample position). The standard, samples accepted, and samples rejected are indicated.

Fig. 2
Fig. 2

Munsell 5/ value color samples plotted on Judd’s uniform chromaticity scale diagram. In a true uniform chromaticity scale diagram these samples would plot more nearly in concentric circles.

Fig. 3
Fig. 3

Munsell 5/ value color samples plotted on Adams’ chromatic value diagram. In a true uniform chromaticity scale diagram these samples would plot more nearly in concentric circles.

Tables (8)

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Table I Color specifications (I.C.I. and Munsell) for 11 series containing 200 samples included in this test.

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Table II Extent of agreement of 10 observers on 11 series of samples classified on a scale of 6, from 1, a “very good match,” to 6, a “very poor match.” Percentages are shown of samples classed in more than 1 out of 6 groups on this scale.

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Table III Bias in individual judgments shown by degree to which each individual’s scores depart from the average of the first ten observers. Scoring is on scale of 6, from 1, very good, to 6, very poor.

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Table IV Correlation results of visual observations by 12 individuals against hue, value, and chroma for 9 series of chromatic colors. Rho square (P2) is a measure of the multiple correlation.

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Table V Correlation (R2) of 14 observers results against average placement by the first 10 of these observers.

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Table VI Small-difference specifications on 9 chromatic and 2 neutral series of colors according to several formulas, each adjusted by a factor so that 1 equals a difference slightly larger than I (the Nickerson index of fading, intended to be about 1 3 of a Munsell chroma step) and slightly smaller than ΔE (the Judd NBS unit, a difference “of some commercial importance”).

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Table VII Tolerance indices adjusted so that they may be compared with each other.

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Table VIII Correlation (R2) of tolerance indices by 7 formulas (1) to (7) against average visual placement of samples by 10 observers.

Equations (41)

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T i = C / 3 0.5 Δ H + 2 Δ V + 2 Δ C .
2.5 Y 5.97 / 3.30
3.0 Y 6.06 / 3.14
1.4 Y 6.31 / 4.32.
T i = C / 3 ( 0.5 Δ H ) + 2 Δ V + 2 Δ C .
T i 2 = 1.05 ( 0.5 ) ( 0.5 ) + 2 ( .09 ) + 2 ( .16 ) = 0.76 , T i 23 = 1.44 ( 0.5 ) ( 1.1 ) + 2 ( .34 ) + 2 ( 1.02 ) = 3.51.
I = C / 5 ( 2 Δ H ) + 6 Δ V + 3 Δ C .
I 2 = 0.63 ( 2 ) ( 0.5 ) + 6 ( .09 ) + 3 ( .16 ) = 1.65 , I 23 = 0.86 ( 2 ) ( 1.1 ) + 6 ( .34 ) + 3 ( 1.02 ) = 6.99.
I = [ ( C / 5 2 Δ H ) 2 + ( 6 Δ V ) 2 + ( 20 / π Δ C ) 2 ] 1 2 .
I 2 = [ [ 0.63 ( 2 ) ( 0.5 ) ] 2 + ( 6 × .09 ) 2 + ( 6.4 × .16 ) 2 ] 1 2 = 1.32 , I 23 = [ [ 0.86 ( 2 ) ( 1.1 ) ] 2 + ( 6 × .34 ) 2 + ( 6.4 × 1.02 ) 2 ] 1 2 = 7.09.
Y = 0.2973 ;             x = 0.3698 ;             y = 0.3741.
Y = 0.3081 ;             x = 0.3658 ;             y = 0.3722.
Y = 0.3377 ;             x = 0.3876 ;             y = 0.3849.
Δ E J = f g { [ 7 Y 1 4 [ ( Δ α ) 2 + ( Δ β ) 2 ] 1 2 · 10 2 ] 2 + [ k 1 Δ ( Y 1 2 ) ] 2 } 1 2 ,
α = 2.4266 x - 1.3631 y - 0.3214 1.0000 x + 2.2633 y + 1.1054 , β = 0.5710 x + 1.2447 y - 0.5708 1.0000 x + 2.2633 y + 1.1054 , f g = 1.0 ,             and             k 1 = 100.
α Std . = 0.0285 ; β Std . = 0.0457. α No . 2 = 0.0255 ; β No . 2 = 0.0438. α No . 23 = 0.0400 ; β No . 23 = 0.0548.             Δ E No . 2 = f g { [ 7 ( .3081 ) 1 4 ( .0030 2 + .0019 2 ) 1 2 ( 100 ) ] 2 + [ 0.98 ] 2 } 1 2 = 2.10 , Δ E No . 23 = f g { [ 7 ( .3377 ) 1 4 ( .0115 2 + .0091 2 ) 1 2 ( 100 ) ] 2 + [ 3.58 ] 2 } 1 2 = 8.60.
α = A - G A + 2 G + B ,             and             β = 0.4 ( G - B ) A + 2 G + B ,
Δ E H - S = [ ( L 1 - L 0 ) 2 + ( a 1 - a 0 ) 2 + ( b 1 - b 0 ) 2 ] 1 2 ,
L = 54.53             a = 10.88             b = 17.44.
L = 55.51             a = 9.91             b = 17.02.
L = 58.11             a = 16.27             b = 22.29.         Δ E H - S No . 2 = [ ( 55.51 - 54.53 ) 2 + ( 9.91 - 10.88 ) 2 + ( 17.02 - 17.44 ) 2 ] 1 2 = 1.44 ,         Δ E H - S No . 23 = [ ( 58.11 - 54.53 ) 2 + ( 16.27 - 10.88 ) 2 + ( 22.29 - 17.44 ) 2 ] 1 2 = 8.09.
Δ E A = [ Δ V Y 2 + [ 7.5 Δ ( V X - V Y ) ] 2 + [ 3.0 Δ ( V Z - V Y ) ] 2 ] 1 2
Δ E A = [ ( k Δ V ) 2 + [ Δ ( V X - V Y ) ] 2 + [ 0.4 Δ ( V Z - V Y ) ] 2 ] 1 2 .
X = 0.2940 ;             Y = 0.2973 ;             Z = 0.2035.
X = 0.3028 ;             Y = 0.3081 ;             Z = 0.2170.
X = 0.3400 ;             Y = 0.3377 ;             Z = 0.1996.
V X = 5.99 ;             V Y = 5.97 ;             V Z = 4.71.
V X = 6.07 ;             V Y = 6.06 ;             V Z = 4.84.
V X = 6.38 ;             V Y = 6.31 ;             V Z = 4.67.
( V X - V Y ) = + 0.02 ;             ( V Z - V Y ) = - 1.26.
( V X - V Y ) = + 0.01 ;             ( V Z - V Y ) = - 1.22.
( V X - V Y ) = + 0.07 ;             ( V Z - V Y ) = - 1.64.             Δ E A NO . 2 = [ [ 0.23 ( .09 ) ] 2 + ( .01 ) 2 + [ 0.4 ( .04 ) ] 2 ] 1 2 = 0.028 , Δ E A No . 23 = [ [ 0.23 ( .34 ) ] 2 + ( .05 ) 2 + [ 0.4 ( .38 ) ] 2 ] 1 2 = 0.178.
Δ E A = [ ( k Δ V ) 2 + ( Δ W X ) 2 + ( 0.4 Δ W Z ) 2 ] 1 2 ,
W X = [ ( X c / Y ) - 1 ] V ;             and             W Z = [ ( Z c / Y ) - 1 ] V .
X c = 0.2998 ;             Y = 0.2973 ;             Z c = 0.1723 ;             V = 5.97.
X c = 0.3089 ;             Y = 0.3081 ;             Z c = 0.1837 ;             V = 6.06.
X c = 0.3468 ;             Y = 0.3377 ;             Z c = 0.1690 ;             V = 6.31 ,
W X = + 0.05 ;             W Z = - 2.51.
W X = + 0.02 ;             W Z = - 2.45.
W X = + 0.17 ;             W Z = - 3.15.
E A No . 2 = [ ( 0.5 × .09 ) 2 + ( .03 ) 2 + ( 0.4 × .06 ) 2 ] 1 2 = 0.06 E A No . 23 = [ ( 0.5 × .34 ) 2 + ( .12 ) 2 + ( 0.4 × .64 ) 2 ] 1 2 = 0.33.