JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Evaluation of Single-Number Expressions of Color Difference*

ANGELA C. LITTLE

University of California, Berkeley, California(Received 2 July 1962)

Single-number expressions of color differences among three pairs of samples of vegetable purees werecalculated by eleven methods of computing AE. The samples differed mainly in chromaticity, and showedcolor differences more complex than simple nonmetameric ones. Experimental conditions were controlled bylimiting the study to an analysis of the relative ability with which the eleven methods were able to rankthe three pairs of samples. Serious discrepancies in magnitude and order were found.

INTRODUCTION

MOST federal and state specifications include colorM requirements in their definitions of standards forboth raw and processed foods. Color may be a limitingfactor in determining the grade that can be assigned.

In many specifications (U. S. Department of Agri-culture, Agricultural Marketing Service) "good color"is defined as "uniform, bright, characteristic of thevariety," and score points are based on personaljudgment.

Color is an indicator of quality in evaluating pro-cessing and subsequent packaging and storage and indetermining the shelf life of the product under differingstorage conditions.

The problems confronting the food technologist re-quire that color measurements be made and colorsspecified in psychophysical terms and that color differ-ences be evaluated. Problems involving color matchesare seldom, if ever, encountered. Instead, interest isfocused on the specification of allowable differences ortolerance limits to be set for grading purposes and onthe magnitude of the color changes during processingand in storage.

Since 1936, when Nickerson' formulated her Indexof Fading equation to express small color differences inthe MWunsell system, a number of investigators haveproposed methods of calculating color differences interms of a single number. These methods are all basedon some perceptibility limen, and measure the distancein perceptibility steps between two colors plotted in auniform color space. Modifications of the originalIndex of Fading equation have been proposed byBalinkin 2 and Godlove.3 Some of the equations arebased on nonlinear projections of the nonuniform CIEchromaticity diagram in order to conform to Munsellrenotation spacing. Such diagrams are the Adamschromatic valence and chromatic value diagrams,4 andthe Saundersom-Milner "zeta" space.5

Another approach has been the formulation of color-difference equations based on projective transforma-

* This work was supported by a grant from the NationalInstitutes of Health, Bethesda, Maryland.

'D. Nickerson, Textile Research 6, 509 (1936).2 I. A. Balinkin, Am. Ceram. Soc. Bull. 20, 392 (1941).I. H. Godlove, J. Opt. Soc. Am. 41, 760 (1951).

4 E. Q. Adams, J. Opt. Soc. Am. 32, 168 (1942).5 J. L. Saunderson and B. I. Milner, J. Opt. Soc. Am. 36, 36

(1946).

tions of the CIE diagram by Judd,6 Hunter,7 andScofield.'

In contrast to attempts to measure color differencesin a so-called uniform-color space, use has been madeof the known irregularities of the CIE system as de-fined by the MacAdam ellipsoids.9 Transformationequations, which define a uniform color space for arestricted portion of the diagram, are established. Tosimplify the evaluation of color differences, chroma-ticity difference and lightness difference charts havebeen developed by Davidson and Hanlon"° and bySimon and Goodwin."1

The most recent proposal of a color-difference equa-tion was based on a cube-root coordinate system for-mulated by Glasser et al.12 They reported good correla-tion with subjective appraisals when color differenceswere calculated by their equation, but there is nopublished information on the performance of thismethod relative to other methods.

A number of studies, in which comparisons havebeen made of some of the methods of evaluation ofcolor differences with each other and with visualappraisals,'3 - 5 mostly on dyed textile samples, havebeen reported. According to the evidence presented,there is no one method which offers a clear-cut advant-age over the others.

In studies comparing visual appraisals with color-difference equations applied to objective color meas-urements, uncontrolled variables such as errors of in-strumentation, sample variation, distribution of samplesin color space, observer variations, and inaccuracies inthe color-difference equations, may serve to becloudthe issue. Thus, Nickerson and Stultz state: ". . .

I D. B. Judd, J. Research Natl. Bur. Standards 14, 41 (1935);J. Opt. Soc. Am. 25, 24 (1935).

7 R. S. Hunter, National Bureau of Standards Circ. C429(1942); J. Opt. Soc. Am. 32, 518 (1942).

8 F. Scofield, National Paint, Varnish, and Lacquer AssociationScientific Circ. 664 (1943).

9 D. A. MacAdam, J. Opt. Soc. Am. 32, 247 (1942).10 H. R. Davidson and J. J. Hanlon, J. Opt. Soc. Am. 45, 617

(1955).11 F. T. Simon and W. J. Goodwin, J. Opt. Soc. Am. 47, 1050

(1957).'2 L. G. Glasser, A. H. McKinney, C. D. Reilly, and P. D.

Schnelle, J. Opt. Soc. Am. 48, 736 (1958).13 D. Nickerson and K. F. Stultz, J. Opt. Soc. Am. 34, 550

(1944).4 H. R. Davidson, J. Opt. Soc. Am. 41, 1052 (1951).

15 H. R. Davidson and E. Friede, J. Opt. Soc. Am. 43, 581(1953).

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ANGELA C. LITTLE

particular series of samples may seem to give resultsthat prove the formulas not adequate, when the faultmay be with the sample distribution or the accuracyof the measurement rather than with the formula."

Furthermore, the experimental bases for formulatingcolor-difference equations differ for the various methods.Thus the application of an equation derived from color-matching data of self-luminous areas may differ fromthat of an equation derived from data pertaining tosurface color differences in the 2\1unsell system. Al-though different experimental situations require differ-ent color-difference formulas, the formulas are toooften used heedlessly, and experimental results areinterpreted, according to the magnitude of the cal-culated color differences, without question. The in-struction books supplied with photoelectric tristimuluscolorimeters often include methods of calculating colordifferences. The suggested method is chosen for con-venience of calculation and will differ for the variousinstruments. For the Gardner and Hunter instruments,which give results in terms of L or RD, a and b coordi-nates, the obvious choice is the Hunter-Scofieldequation:

BE= [(AL)2+ (Aa)2+ (Ab)2]f.

A Color-Eye Delta E color tolerance computer hasbeen developed for use in conjunction with the Color-Eye. Color differences are evaluated by the Adams'chromatic-value equation adjusted to the NBS unit.

Along with the increasing use of electronic computersin reducing spectrophotometric data to CIE tristimulusvalues, there is a trend to incorporate the calculationof color differences in the programming. For example,Opler e al.'6 reported on the use of the punched-cardoperated IBTNl 602A computer in translating the CIEspace to Adams space, and color differences are calcu-lated in terms of Adams' equation adjusted to Judd'sNBS unit. Recently Faulhaber and Schnelle'7 describedan electromechanical cube-root-coordinate color-differ-ence analog computer which converts tristimulus valuesdirectly to AL, a, Ab, and LAE in the cube-root co-ordinate system.'2

With such aids, it is only natural that advantage betaken of the ease and convenience of calculation.

Successful application of color-difference equationsto color differences or color changes in foods wouldoffer several obvious advantages. Single-number speci-fications are highly acceptable to the industry forgrading and quality-control purposes. The magnitudeof color changes on processing and storage could bereadily appreciated by applying a metric, and the re-porting of data would be simplified.

In the study reported here, we have examined therelative performances of eleven methods of evaluating

"6 A. Opler, R. W. Merkle, and M. J. Charlesworth, J. Opt.Soc. Am. 43, 550 (1953).

17 M. E. Faulhaber and P. D. Schnelle, J. Opt. Soc. Am. 52,604 (1962).

color differences for three pairs of samples of vegetablepurees to test the feasibility of applying color-differenceequations to tolerance specifications and the evaluationof color changes in foods.

By avoiding visual comparisons, restricting thesamples to a small area of color space, and using onlyone set of physically obtained data for each example,uncontrolled variables should be eliminated and theresults should then give an unbiased appraisal of thedegree of consistency shown by the various methodsin separating the pairs of samples.

PROCEDURE

Reflectance measurements were made on three sam-ples of vegetable pur6e which were prepared by mixingdifferent amounts of a carrot pure with a pea pur6e. Amodel DU Beckman spectrophotometer with a reflect-ance attachment was used, and readings were maderelative to MXlgO. The spectrophotometric data werereduced to CIE specifications by the weighted-ordinatemethod.'

Munsell renotation specifications were obtained fromconversion charts'9 available from the Munsell ColorCompany, Baltimore, -\'Iaryland.

Color difference evaluations among the three com-binations of pairs (samples 1 and 2, samples 1 and 3,samples 2 and 3), were made as follows:

Based on MXunsell space:

1-Nickerson Index of Fading

I= (C/5) (2H)+6AV+3XC.

2-Nickerson-Balinkin Index of Fading

I'-(5CAH)2 (6A\)2 (20AC/7r)']l

3-Godlove Index of Fading

I4= [2CCOH+ (AC)2 + (4AV)2]-

where11= 1-cos3.6°AH.

Based on Adams' spaces:

4-Adams' chromatic valence

AE=,(0.5,A V,) 2+ (AW.) 2+ (O.4AW )2],

where V, is the M1'unsell value function,

W2= V1(Zc/Y) -1].

5-Adams' chromatic value

A\E = [(O.23A V,)2+ A ( V- V)2+0.OA ( - V,)2]1.

18 A. C. Hardy, andbook of Colorimetry (Technology Press,Cambridge, Massachusetts, 1936), pp. 32 ff.

19 S. M. Newlhall, D. Nickerson, and D. B. Judd, J. Opt. Soc.Am. 33, 385 (1943).

294 Vol. 53

February1963 SINGLE-NUMBER EXPRESSIONS OF COLOR DIFFERENCE

6-Saunderson-Milner "zeta" space

where,AE= (N')+ (2)2+ (3)2],

l i= (9.37+0.79 cos) (V- V,),

t 2 = kV,(k= 2),3- (3.33+0.87 sin) (V -V V),

tan = 0.4 (V, - V,) /(Ve - ,).

TABLE II. Specification differences between pairs of samples.

Sample CIE Munsell renotationpairs AY Ax Ay AHl AV AC

1-2 -0.70 +0.0143 +0.0009 -2.1 -0.07 +0.51-3 -1.86 +0.0169 +0.0180 -0.4 -0.20 +0.92-3 -1.16 +0.0026 +0.0171 +1.7 -0.13 +0.4

Based on projective transformations of thediagram:

CIE

7-Judd-Hunter "alpha-beta" chromaticity diagram(redefined NBS unit)

zAE= {[700Yi(A a + z 12) 1]2 ±+[100z\((Y)]2 } ,

where2 .4266x- 1.363ly- 0.3214

1.OOOOx+ 2.2633y+ 1.1054

0.5710x± 1.2 447 y-0.5708

1.0000x+ 2 .2 6 3 3y+ 1.1054

8-Hunter-Scofield a, b coordinate system:

AE= [(zXL) 2 + (Aa) 2 + (zAb)2 `,

(a) where L=100YI, a=7La, b=7LF; (b) whereL= IOOY1, a=175(1.02X-Y)/YI,b=70(Y-0.847Z)/Y.

Graphical methods:

9-Davidson-Hanlon

10-Simon-Goodwin

Other methods:

11-Cube-root coordinate system

AE= [(AL) 2 + (za) 2+ (Ab)2] 1,

where L=25.29 G 1 -18.38, a= 106.0 (R111 -G"3),b=42.34 (G111-B"11), R= 1.25 (X-0.18Z/1.18), G= Y,B=Z/1.18.

RESULTS AND DISCUSSION

The CIE and Afunsell renotation specifications forthe three samples of puree are shown in Table I.

The differences in CIE Y, x, and y and AMunsell hue,value, and chroma for the three combinations of pairsare shown in Table II.

TABLE I. CIE and Munsell specifications forthe three vegetable purees.

CIE Munsell renotationSample X Y Z x y Hue Value Chroma

1 18.85 20.80 7.29 0.4016 0.4431 8.8Y 5.11 5.22 18.83 20.10 6.34 0.4159 0.4440 6.71Y 5.04 5.73 17.19 18.94 4.95 0.4185 0.4611 8.41Y 4.91 6.1

Because of the manipulation of the relative distribu-tion of chlorophyll and carotenoid pigments by varyingthe ratio of carrot puree to pea puree, chromaticitydifferences are important in these examples, as shownin Table II. This is of particular interest to foodtechnologists because changes in pigment compositionof fruits and vegetables are a common occurrence inripening. Because the addition of carrot to the peapure resulted in a decrease in reflectance below, andan increase above, 590 mp, these examples also repre-sent a more complex situation than is found in thecase of simple nonmetameric differences. There thecolor difference is manifested by an over-all increaseor decrease in total reflectance with no crossovers inthe spectral reflectance curves.

The calculated color differences between the samplepairs by the eleven methods listed above are tabulatedin Table III.

The divergent results listed in Table III are in partdue to the different scale factors used in defining colordifferences according to various formulas. The degreeto which relative differences are maintained can beshown better by adjusting the results to unity for onepair of samples and the corresponding values calculatedfor the other two pairs. These results are shown inTable IV.

It is immediately apparent from Table IV that thedifferent methods rank the sample pairs differently.Closer examination discloses that the color differencesbetween samples 1 and 2 and samples 1 and 3 haveequal chance of being evaluated the largest, while thecolor difference between samples 2 and 3 are almostequally distributed between first and second place. If

TABLE III. Calculated color differences between thethree pairs of samples of vegetable puree.

Sample pairEquation 1-2 1-3 2-3

1 6.49 4.80 5.992 5.59 6.10 4.813 0.91 1.21 0.914 0.17 0.14 0.165 0.09 0.14 0.116 0.75 0.92 0.837 6.35 6.06 4.988a 4.11 3.88 3.168b 2.72 2.47 2.639 9.7 9.6 5.9

10 10.0 10.9 6.811 4.62 6.31 4.56

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ANGELA C. LITTLE

TABLE IV. Color difference evaluations with AE forsample 1-2 adjusted to unity.

Equation 1-2 1-3 2-3

1 1 0.74 0.922 1 1.09 0.863 1 1.33 1.004 1 0.81 0.955 1 1.55 1.216 1 1.23 1.117 1 0.95 0.788a 1 0.80 0.778b 1 0.91 0.979 1 0.99 0.67

10 1 1.07 0.6811 1 1.36 0.99

we consider the color difference between samples 1 and2 to be the maximum permissible, then the acceptanceor rejection of sample 3 also becomes a matter ofchance.

We have used two methods of calculating the a andb coordinates for the Hunter-Scofield equation [Eqs.(8a) and (8b)] to illustrate the discrepancies that mayarise depending on how the coordinates are obtained.If a and b are calculated directly from CIE tristimulusvalues, according to method (8b) above, the contribu-tion of the Z value is not included in computing a,nor is the contribution of the X value included in b.In contrast, when a and b are calculated from thechromaticity coordinates x and y by way of the a, system [Eq. (8a)], the contribution of all three tri-stimulus values is included. In the first pair of samples

of vegetable purees particularly, differences in X and Ytristimulus values were small, with the major differencelying in Z, and the chromaticity difference was mani-fested mainly in the x coordinates. Calculation of thea coordinates by method (8b) therefore failed toseparate the samples adequately, and the correspond-ing color difference evaluation was consequently lowerthan that obtained by method (8a). The remaining twosample pairs showed similar but less marked trends,because in these examples the differences in X and Yvalues were not insignificant.

Method (8b) is of particular interest because the rela-tionships defined by this method are incorporated inthe circuiting of the Gardner and Hunter color-differ-ence meters. While these instruments may be entirelysuccessful in separating samples showing simple non-metameric differences, they may fail to separate ade-quately such samples as the vegetable purees wherechromaticity differences play an important role.

The results from this study corroborate those ofprevious studies20 by suggesting that color-differenceequations should be restricted to situations where ahigh correlation is established between a given methodand visual evaluation. Thus, each new problem mustnow be studied separately. As time progresses and in-formation becomes available, the applicability of spe-cific color-difference methods to specific grading prob-lems will become clearer and the use of color-differencemethods will be better standardized than it is now.

20 D. Nickerson, Paper Trade J. 125, 6, 153 (1947).

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