The Effect of Non-uniformity in ANLAB Colour Space Interpretation of Visual Colour Differences on the

RODERICK McDONALD

Research Laboratory J. & P. Coats Ltd Anchor Mills Paisley

Several investigations have been carried out in recent years into variables affecting the accuracy of instrumental colour passing. lo the U.K. there have been notable investigations by McLaren [ I ] , Jaeckel [2], sand Coates and Rigg [3]. As a result, the Adams---Nickerson colour-difference formula with a scale factor of 40 (originally 42) has now been adopted by the Society of Dyers and Colourists for use with textiles in the U.K. under the name of ANLAB(40) colour space and by IS0 as a Tentative Test for colour-difference work in textiles. It has also been adopted as a British Standard for plastics and is under consideration by IS0 for this purpose.

There are, however, even in this recommended space, highly significant variations in the visual equivalence of numerical colour differences from different areas of colour space. A numerical colour difference of 1 .O AN unit in a grey is easily seen, whereas with a yellow a colo.ur difference of 2.0 AN units is hardly detectable, Considerable caution must therefore be exercised in the interpretation of numerical colour-difference values from different areas of colour space.

A practical solution to this variation is to adjust individual numerical tolerances as necessary to agree with visual observa- tion.

McLaren has reported attempts to improve the correlation of the formula with visual assessments, using multiple-regres- sion techniques [4]. The Davidson and Friede (51 visual samples chosen for his investigation consisted of a large number of colour pairs which were assessed for match acceptability for dyeing carpet yarns [4]. McLaren has shown that the matching panel tolerance in the Davidson and Friede investigation (5% acceptable level) is about 1.5 AN(42) units. The investigation therefore relates to the application of a fairly tight matching tolerance and not to the larger tolerances which can also be applied in the textile industry. (For example, in the sewing-thread industry tolerances of around 3.0 AN(42) units are acceptable for certain articles.)

The purpose of the current investigation was to investigate, by means of a colour-matching grey scale, how numerical colour values vary for different grades of match throughout ANLAB colour space, to determine whether the irregularity could be specified in the form of an equation, and to try to reduce the 'non-uniformi ty' to less significant proportions.

Experim ntal The investigations relate to ANLAB space with a scale factor of SO [ANLAB(SO)], in which L=50(0.23 V y ) , a=50(Vx -

Z/ZMgo = f(V,) and f(V) = 1.22191" - 0.23111p t

Over the years each skein dyed in our normal laboratory

vv), b=50[0.4(vy - VZ)] , x / X ~ g o = f(vx), Y = f(vy>,

0.23951 V3 0 . 0 2 1 0 0 9 ~ t 0 .0008404~ .

work has been wound into a 6 cm X 6 cm card and each card has been measured and filed under its colour co-ordinates. From this file of some 60,000 cards a minimum of five cards was selected from each of 16 colour centres and 11 grey centres* The selected centres corresponded to the following visual description:

Bright colours:

Dull colours:

Greys:

Red, Orange, Yellow, Yellow Green, Green, Turquoise, Blue, Violet Red, Orange, Yellow, Yellow Green, Green, Turquoise, Blue, Violet A series ranging from dark to pale L 1 6 4 8 0

The colours selected were all of approximately the same lightness value L56-L80. The mean L a b values for each colour centre are given in Table 1 .

TABLE 1

Mean L a b Values for Colour Centres

L

62.78 82.92 65.02 62.20 65.36 59.94 58.28 61.50 60.86 79.36 77.64 80.26 65.20 50.02 17.52 34.78 52.38 79.48 57.36 36.78 69.76 29.50 36.44 59.50 64.46 6 1.48 60.54

a

-1.66 8.68

--43.56 -9.76 43.36 22.50 -2.34

-17.98 13.54 27.32 8.90

- 10.32 -24.96

1.26 0.64

-1.06 0.18 0.38 0.52 1.42

-0.06 0.82

-0.52 -6.02 18.06

-1 5.78 6.34

A colour-matching

b

2.34 89.22 4.26

-29.34 0.44

-0.06 -1 0.22

3.16 -17.22

30.12 37.78 37.20

-12.70 0.86

-0.36 0.78 0.44 I .66 0.82 0.66 1.64

-3.94 -2.08 21.00 12.98

-4.56 -6.18

grey scale had been used in the - - _ company for many years as a guide to the tolerances

*In a few greys 6, 7 or 8 cards were selected

JSDC June1974 189

applicable to the various articles manufactured. This was made from soft cotton thread dyed with various concentrations of Sirius Supra Grey GG (C.I. Direct Black 77). The scale consisted of four 5 cm X 5 cm thread cards, each card having as a reference a 2.5 cin X 5 cm strip ofwound thread dyed at 1% concentration adjaccnt to a similar strip dyed at a slightly heavier dcpth. The dye concentration and measured ilE values for each pair are given in Table 2.

TABLE 2

Colour-matching Grey Scale

Matching grade Reference 1 2 3 4

%I Sirius Supra Grey GG 1 .O 1.04 1.09 1.16 1.25

Ah’ AN(50) from reference 0.66 0.92 2.6 3.14

For the initial visual appraisals, a highly experienced colourist (AP) was chosen.

The observer was asked to assess each possible pair of samples at each colour centre and to classify these according to the grey scale into grade 1, 2, 3 or 4 classes. The samples considered to have greater colour differences than the grey scale grade 4 were assessed as 5 (reject) and excluded from the subsequent numerical analysis. For a colour centre with five cards, 10 possible combinations of pairs, and therefore 10 visual gradings, are obtained.

The cards were measured on a Spectromat FS3A, and L a b co-ordinates and colour differences for each pair were computed under llluminant D 10” field conditions. Repeat measurements of colour differences indicated a variation in reproducibility of less than 0.35 AN(50) units in the neutral grcy region

The colour differences for each pair were recorded as a colour difference occurring at a position in colour space, taken as the mean of the co-ordinates of the two samples.

To assess the reproducibility of the observer, he was asked to repeat the visual gradings two weeks later.

Results and Discussion

CORRELATION BETWEEN AE AND VISUAL GRADING To assess the significance of the relationship between the numerical colour differences and the visual grading, the colour difference AE was plotted against the first visual grading of observer AP. The results are shown in Figure 1 for some of the colours. I t can be seen that there is good correlatiotl between the measured AE and the visual grading within each colour centre. I t is evident, however, that the magnitude of the numerical colour differcnce is different for the different colour centres.

VARIATION OF AE WITH POSITION IN COLOUK SPACE I t is known from practical experience with instrumental colour matching that the non-uniformity in ANLAB colour space IS

clearly dependent on saturation, and this has also been denionstrated by McLaren [4]. In ANLAB space, the distance from the neutral axis (a = 0, b=O) was taken as a measure of the saturation.

The numerical colour differences from the above data wctc split into groups corresponding to visual grades 1, 2, 3 and 4, and the A,? value between each pair of samples was plotted against the mean distance ( r ) of the pair from tlic ncutral axis. i.e.

The results shown in Figures 2-5 indicate that there is I significant relationship between AE and Y values.

The neutral grey samples, which have all approximately the same (small) radius, were similarly split into groups and Ah; was plotted against the lightness L value. These results indicated a less cvident but still significant relationship between AE and the L value of the samples.

McLaren [4] investigatcd the Davidson and Friede data using multiple-regression analysis. He found indications of a significant correlation of colour difference with L,r, and also the hue angle [e = arctan (b/a)l

Multiple-regression analysis was therefore carried out on the initial grading of observer AP to find the relationship between AE and the following variables for the individual grades of match:

r L e r2 e 2 If the relationship between the visual gradings and the

colour-difference formula were perfect, it would be expected that all samples, for example, in grade 2 would have the same numeric AE value of, say, 2.4, which is the mean of this grade. If there is a considerable range of numeric values within each grade group, then the variance about this mean value will be large. The object of the regression analysis is to fit an equation to the data, so that, when each individual colour difference is transformed by the equation, the variance is reduced to a minimu in.

One measure of the efficiency of such equation is the ‘A goodness of fit, which measures the proportion of the variance which has been explained by the fitted equation (1OffX1 fit means a perfect equation). The regression analysis showed that the most significant relationship was that between AE and r as follows :

A E = m r + k (1)

There was a significant improvement in the f i t when a lightness tcrm (L) was addcd to give:

but there was no significant improvement by including the hue angle 6 or 0’ or rz into the equation (as found by McLaren)

The equations derived, details of the soodness of fit, and other statistical details are given in Table 3.

Fairly good equation fit (SO -6Wh) was obtained for grade 2, 3 and 4 groups, but a very poor fit was obtained for grade 1. This may be due to the insufficient number of samples falling into this group.

Most of the fit is accounted for by the variable r in Eqn I , with the L variable making orily a sinall though significant contribution in Eqn 2. For practical purposes, the variable Z, could be omitted without any great loss of fit.

141.

190 JSDC June 1974

I Bright Red

81 6

8-

6-

Bright Red

Grade

6

4r Q I t

Bright Yellow 8

2 1. 8-

6- 4r Q

4-

2-

Bright Yellow 8

*

4 1

Grade

Bright Green

Lu Q

2i 4-

2-

8

I I ; i 4 Grade

Figure I Visual grading versus colour difference AE

KEPKODUC‘IIJI LITY OF OBSERVER AP GRADlNGS To assess thc rcproducibility of the observer (AP) the first visual gradings were compared with the second visual gradings within each group. Nearly half of the samples in each group were classed a visual grade higher or lower on the second appraisal. I t was considered that those samples that had been graded diffeieiitly on the two appraisals were more likely to be borderline gradiiigs than those samples that were graded the same on both appraisals.

The samples were therefore re-grouped as follows:

Grade Description 2 2.5

3.0 3.5

4.0 4.5

Graded 2 on both appraisals Gradcd 2 on one appraisal and 3 on the other appraisal Graded 3 on both appraisals Graded 3 on onc appraisal and 4 on the othcr appraisal Graded 4 on both appraisals Graded 4 on one appraisal and 5 on the other appraisal

Multiple-regression analysis was again applied to the re-grouped data and a considerable improvement in the goodness of fit (ca 70%) was obtained with Eqn 1 for grades 2 and 3 . Surprisingly, an equally good fit was also obtained for the new intermediate gradings.

No improvement (5%) was found on grade 4, and grade 4.5 gave a poor fit (18%). This result is not surprising since grade 5 is an ‘open-ended’ grade, i.e. there is no grey scale grade 5 to constrain the colourist when he is making visual assessments. Thus anomalous visual gradings could occur more easily.

The Eqn 1 constants for each matching grade, together with other relevant statistical details, are given in Table 4. Again for practical purposes the contribution of L is insignifi- cant and can be omitted. From Table 4 it can be seen that Eqn 1 accounts for approximately 70% of the variation of AE across colour space for observer AP.

ANALYSIS OF KESULTS One of the most interesting results of this investigation was thc increase in the value of the r coefficient as the visual

JSDC June1974 191

10

8

6 4 Q

4

Figure 2 Grade 1

8

6 iil Q

Figure 3 ~ Grade 2

I 06

8

6 '4 Q

I

a

0

2 P"

I Figure 5 ~~- Grade 4

* *

a

8 . 0 .

a 8 S

a

4 I

24 40 80 80 20 60 I 40 r

Figures 2--5 - Relationship betweeiz AE arid r for visual grades 1 4

~olerarice is increased (higher grade number). I he r coefficients for observer AP are plotted against grade

in Figure 6 . I t can he seen that the increase is remarkably iinif'urni. I t is therefore not likely to be due to randorti effects. The incrcasc in value of the r coefficient can also be seen in thc differing slopes of the first visual gradings in Figures 2 - 5 .

observer AP are of the forin: _ 1

Ah' = rily + k

For a colour at the neutral point (a = 0, b = O), r = 0 iiiicl

therefore Af f = k . I t can be seen, therefore, that the k constant The individual linear matching-grade equations for for each matching grade in Table 4 represents the ineaii

192 JSDC J u n e 1 9 7 4

TABLE 3

Matching Equations of Observer AP Derived by Multiple Regression Analysis: Derived from Initial Visual Gradings

No. of samples

Grade I Ah7=0.00171rt 1.0184 15 AE = 0.001 36r + 0.00909L t 0.4822

Grade 2 Ah' = 0.0349 Ir + 1.6408 AE= 0.02763 t 0.01 553L t 0.8962

Grade 3

at:'= 0.04364r t 2.7094 68 AE = 0.03735r t 0.01 3851, + 2.0036

Grade 4 LW = 0.05822r t 4.2734 LIE = 0.05070r t 0.01 720L + 3.070

53

91

*AE = colour difference in AN(50)units Tits. = not significant

Mean M* % F i t

1.063 8.75 10.6

2.348 64 68

3.432 51 53

4.996 53 54

Significance-/- level (%)

N.S. N .S.

0.1 1 .o

0.1 5 .0

0.1 N.S.

r alone L after r

r alone L after r

r alone L after r

r alone L after r

TABLE 4

Matching Equations of Observer AP Derived by Multiple Regression Analysis: Derived from Average of Two Visual Gradings

No. of samples

Grade 2 Mi = 0.03943 t 1.438 Ah7 = 0.021179 t 0.02735L t 0.0624

Grade 2.5 Ah,> = 0.04058r + 1 A492 AE = 0.0365% t 0.007401, t 1.4890

Grade 3

Ah'= 0.05670r t 2.6106 37 = 0.04865r t 0.225201, t 1.3544

Grade 3 . 5

b? = 0.06297r t 2.921 8 Ah' = 0.05575r + 0.01 590L t 2.2022

Grade 4 AE = 0.07825r t 3.66820 AE = 0.06989r + 0.023861, t 2.354

Grade 4.5

&?'= 0.13760r t 4.00600 27 AE = 0.09324r + 0.045721, t 1.9342

37

25

38

51

Mean AL' %Fit

2.390 72 77

2.618 71 72

3.682 72 76

4.272 73 74

5.164 50 52

4.520 18 39

Significance level (%)

0.1 1 .o

0. I N.S.

0.1 5 .O

0.1 N.S.

0.1 N.S.

5 .0 N.S.

r alone L after r

r alone L after r

r alone I, after r

r alone L after r

r alone 1, after r

r alone L after r

JSDC J u n e 1974 193

.02

1 2 3 4 Grade

Figure 6 - Variation of regression coefficient with grade of match

tolerance for thc gradc at the neutral ‘achromatic’ point. For cotivcnicnce these can be called AE, wherc Ah’, = ‘achromatic colour difference’. If the m values for each matching grade are plotted against the AE, values for each grade, a linear ielationhip is obtained (Figure 7). By regression analysis from Figure 7 it can be shown that:

rn = 0.022AEa

Substitution of this expression for rn in the individual Eqn I culour-matching correction equations of Table 4 gives:

AR = I)lr t at:,

A l Y = I 0.022Ma]r t Ma

LIE = [ I t 0.022rj AEa ( 3 )

Thus the individual regression equations derived for the different grades of match are in fact a fanlily of equations of the general form Eqii 3.

The equation can be reariariged to give:

AE

I t 0.022r AE, = (4)

k q n 3 gives the numerical colour tolerance for any given colour equivalent to that of the tolerance specified at the ncutral ‘achromatic’ position in colour space.

Eqn 4 gives the cquivalent numerical colour difference a t the achromatic position in colour space to any given colour difference at any other position in colour space.

*b Figure 7 - Relationship between observer AP matching equations and AE,

OTllLR OBSERVERS ‘I’he above equations arc howcvel based on the results of one obscrver only aiid it was considered desirable to tcst the

validity of the equation when applied to other observers. Visual colour gradings, duplicating the work reported

above, were therefore collected from a further 10 industrial colourists as follows:

(a) T w o observers from Patons & Baldwin’s Dyehouse at

(b) Eight observers from the wet-processing staff a t Alost, Darlington

Belgium

Each observer was asked to grade the colour diffcrcnce between the colour pairs, with reference t o the colour-match- ing grey scale, as grade 1, 2, 3, 4 or 5 (reject). The visual gradings were repeated and thc average of the two gradings was calculatcd for each colour pair. This resulted in a scries of nine possible groups of grade 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5 and 5. Gradings greater than 4.5 were omitted from sub- sequent analysis (as were gradings in which the repeat differed by inore than 1 grade from the original).

The visual gradings for each observer were analysed separately in a similar manner t o that for the original observer AP.

I t was again found that only equations in terms of r gave significant correlation with the variation of AE across colour space. In a few cases the introduction of an L term into the individual grade matching equation (Eqn 2 above) will produce a significant improvement in fit to the data. However, the improvement is inconsistent, even for one obscrver. i t is not considered advisable therefore t o include the L term in thc colour-matching improvement equation. The rcsults of each Eqn 1 regression analysis are given in Tablc 5.

Comparison of the % goodness of fit of Eqn I for each observer shows that the fit for observcr AP (approx. 7WX) is much better than that for these other observers (approx. 30%). In many cases the linear matching Eqn 1 was not significant at the 5% lcvcl and these have not been tabulated in Table 5.

The linear relationships were relatively poor for the data from this investigation and in some cases n o significant Eqn 1 relationship was found between Lv:’ and r for a given matching grade. However, by using the Eqri 1 data that were significant in grades 1 t o 4 for each observer, a test was made to determine whethcr a similar relationship to that found for obscrver AP could be found between the constant (m) for each matching grade and the observers average achromatic tolerance AE, for that gradc, i.e. m =par:’,.

The optiniiim valuc of p for each observer was determined by regression analysis through the origin using rn and AE,

This again enabled the individual match equations of each observer t o be combined into a general equation of the form of Eqn 3 and 4, i.e.

or

AE

1 + p r AE, = __

Thc p values derived for each obscrver are given in Table 6. I n computing the p constant, only those individual graclc matching equations which gave 2 5% significance lcvcl were included in the computation. (If the original individual grade

194 JSDC lunc1974

TABLE 5

Grade Matching Equations Derived for Ten Industrial Colourists: Derived from Average of Two Visual Grading (Ah; = mr + Ah',)

Observe1

HB

TT

ODS

AD

WP

YVDB

LG

RB

CM

TL

Grade

3 .O 3.5 4 .O 4.5

3.5 4.5

2.0 2.5 3 .O 3.5 4 .O

3 .O 4.0 4.5

2.0 2.5 3 .O 3.5 4 .O 4.5

1.5 2.0 2.5 3 .O 3.5 4 .O 4.5

2.5 3.5 4.0 4.5

4.0 4.5

2.5 3 .5 4.0 4.5

1.5 2.5 3 .O 3.5 4.0

ni Ull

0.05545 2.4918 0.03544 3.4085 0.05635 3.6240 0.04272 4.1320

0.06090 2.3300 0.03836 3.7140

0.03 140 2.2963 0.0400 3.2958 0.05670 3.21 76 0.07300 3.9486 0.13850 4.2741

0.4497 3.5390 0.1 1920 3.2800 0.1081 4.780

0.05555 2.0650 0.35 12 3.3340 0.05010 3.4490 0.07740 3.7170 0.05570 3.5570 0.10170 3.7050

0.02929 2.0533 0.04432 2.9647 0.06070 3.2097 0.04267 3.9870 0.0597 3.2270 0.1571 3.6237 0.1 89 1 3.4370

0.0542 2.329 0.0612 3.188 0.0909 3.659 0.1403 3.444

0.0560 3.0628 0.0579 3.4399

0.06265 1.2599 0.04954 3.0400 0.03272 4.0380 0.09610 4.5180

0.03290 I .040 0.05490 2.282 0.05 1 10 2.929 0.04977 3.923 0.0689 4.495

No. of samples

26 33 29 39

35 50

13 56 51 68 80

99 17 18

23 38 39 42 26 29

30 31 40 58 37 33 25

51 33 24 33

33 32

6 72 74

100

6 51 41 59

106

Mean AE 3.39 4.15 4.72 4.84

3.48 4.5 1

3.22 4.20 4.16 5.10 5.13

4.39 5.05 6.54

3.24 4.10 4.52 5.13 4.72 5.77

2.90 3.84 4.36 4.71 4.40 5.36 4.56

3.34 4.54 5.20 4.65

4.47 4.70

3.28 3.86 4.71 5.66

2.02 3.58 4.05 4.74 5.14

72 Fil

22.4 15.4 16.1 18.9

33.7 13.1

37.0 16.3 18.8 32.7 28.3

17.4 60.7 43.3

24.1 11.4 18.7 31.3 29.9 53.5

13.2 15.2 28.3 9.8

49.7 36.5 52.1

25 .o 53.2 39.5 49.7

44.1 33.8

71.7 18.5 16.8 28.9

19.4 24.8 31.1 17.4 21.7

Significance level (%)

I .o 5 .O 5 .o 1 .o 0.1 1 .o 5 .o 1 .o I .o 0.1 0.1

0. I 0.1 1 .o 5 .O 5 .O 1 .o 0.1 1 .o 0.1

5 .o 5 .O 1 .o 5 .o 0.1 0.1 0.1

0.1 0.1 1 .o 0.1

0.1 0.1

5 .o 0.1 0.1 0.1

5 .o 0.1 0.1 1 .o 0.1

matching equation did not give a significant fit to the data it is obviously useless to include it in any subsequent numerical treatment.)

I t can be seen from Table 6 that the coefficients of the final matchirig equations derived for each observer are all of the same order and similar to those derived for observer AP. It

can therefore be argued that the data examined in this investigation substantiate the validity of the AE conversion relationship found from observer AP in the first investigation. The poorer % fits of the relationships could be due to the grcater irregularity in the matching data of the observers in relation to that of observer AP.

JSDC June 1974 195

TABLE 6

General AE Correction Equations for Various Observers (AE, = aE'measured/l + pr)

Computed mean Mu for each grade* Observer p 1.0 1.5 2.0 2.5 3.0 3.5 4.0

A I' 1iB TT ODs AD WP YVDB LG KB CM TL

0.022 0.01 5 0.026 0.02 1 0.012 0.017 0.021 0.023 0.0 18 0.01 4 0.016

1.4 1.8 2.6 2.9 3.7 2.5 3.4 3.6

2.3 2.3 3.3 3.2 3.9 4.3

3.5 3.3 2.1 3.3 3.4 3.7 3.6

2.1 3.0 3.2 4.0 3.2 3.6 2.3 3.2 3.7

3.1 I .3 3.0 4.0

1 .o 2.3 2.9 3.9 4.5

*Values are quoted only when the individual grade matching equations in 'Table 5 are statistically significant (,F > 5%)

The achroma tic (Mu) niean tolerance for each grade of match is also listed in Table 6 for those individual grade ni:i tching equations that give significant (2 5%) correlation. It can bc seen that the individuals vary in their mean achromatic matching tolerancc for each gradc, although thc similarity in p value indicates a similarity in the variation of AE across colour spacc found from each set of data,

The m and AE, values for each individual observer niatching equation in Table 5 which were significant at the 1% level are shown in Figure 8, together with the values of observer AP.* Regression through the origin gives a line of slope 0.02 I , i.e. from these 40 highly significant equations we obtain :

??I = 0.02 1 AE,

T h i 5 IS exceptionally close to the value of 0.022 found oiipinally Tor observer AP.

AEa

Figure 8 - Statistically significarit individual matching coejficients for 1 I observers

A Mean value for each grade

*bar grade 2 the three equations significant at 5% level were also in cluiled.

EVALUATION O F EQUATIONS McLaren 11, 41 and Jaeckel [2] have assessed the usefulncss of colour-difference formulae by comparing the AE values from a large number of sample pairs with the 2, acceptability of the pairs when assessed by a panel of' observers. For a large number of sample pairs, regression analysis of acceptability versus aE: yields a correlation coefficient that can be used as ;I

measure of the uscfulness of the formula. The colour-matching data of all thc 11 observers were

therefore treatcd t o derive ($1 acceptability ratings f o r each grade of match for each saniplc pair, as follows. 1P the criterion of match is grade 3, then each sample pair assessed by ail

observer as grade 3, grade 2 or gradc 1 is also acceptable foi the grade 3 match. A similar approach was applied to each grade o f match. The number of acceptances in all 22 observations (1 1 observers each with two observations) is thcn expressed as a percentage. Sample pairs with zero % acccpt- ability were not included in the 7;) acceptability iwsus AL regression analysis.

Correlation coefficients obtaincd are shown in Table 7 for each grade of match. I t can be seen that there is a significuni improvement in the correlation coefficients when the Mu Lqn 4 modification is incorporated in the ANLAB forrnula.

TABLE 7

J . & P. Coats Data: Correlation with Numerical Colour Differences

No. of samples Matching (with % acceptability Correlation coeff grade greater than zero) AE Ah;

1 72 2 194 3 267 4 309

-0.36 -0.48 -0.42 -0.53 -0.44 -0.58 -0.41 -0.6 1

A second criterion, utilised by McLaren [4] and Jaeckel [ 2 ] , is the number of wrong decisions reached by use of the formula in relation to those expected from a single visual observer, when compared with the average acceptability decision of the matching panel (samples with greater than 50% acceptability are deemed acceptable). Table 8 lists the number of wrong decisions obtained using the modified and unmodi- fied ANLAB formulae, together with those calculated as shown by McLaren 141- for the individual visual observer. It can be seen that the modification to the ANLAB formula results in a worthwhile reduction in the number of wrong decisions.

APPLICATION TO DAVIDSON AND FRIEDE DATA I t is obviously desirable t o check whether the above equation will be equally successful when applied t o other independently collected data.

Much of the international colour-difference work in recent years has revolved around the Davidson and Friede colour- matching data [ 5 ] , and it was therefore decided to check the usefulness of the modified ANLAB equation by applying i t tc, these data.

To assess t l r e degree of correlation between '%, acceptability given by the Davidson and Friede matching panel and colour

196 JSDC J u n e 1 9 7 4

TABLE 8 matchng data than many other colour-difference formulae in general use at present.

J . & P. Coats Data: Table of Wrong Decisions

Errors in 309 sample pair comparisons

accepts rejects decisions Grade Criterion Wrong Wrong Wrong

1 Vlsllal 10 1 11 AL 0 4 4 ulz 0 4 4

2 Visual 28 14 42 A& 5 28 33 M’lI 8 23 31

3 Visual 29 43 72 A/: 35 58 93

31 49 80

4 Visual 49 19 68 M 42 30 72 uu 29 22 51

difference, linear regression was carried out on the data to relate %A to Af; and %,A to AEa respectively. Correlation coefficients for the two regression lines are given in Table 9, together with values quoted by McLaren [ I ] for the same data, using alternative colour-different formulae. The correla- tion coefficient for Ah> ( r = -0.68) is seen to be significantly better (5%. level) than that found for the standard AE ANLAB colour-diffcrcnce forniula ( r = -0.57). As can be seen (Table 9), by this criterion the AEu formula is significantly better than any of the other standard colour-difference formulae currently in use.

McL,aren 1 1 1 has given details of the number of wrong decisions obtained using other colour-difference formulae and these are given in Table 10 together with those from the modified ANLAB formula (AEa).

From examination of Table 10 it can be seen that by this criterion the modified ANLAB (A&) formula is again much better than the other formulae tested by McLaren. The number of wrong decisions resulting from the modified ANLAB formula is similar to those from a single observer, whereas all the other standard formulae are worse. The number of wrong rejections is slightly greater than to be expected from a single visual observer, but the number of wrong acceptances ~~ more important in the industrial situ- ation as already pointed out by McLaren - - is in fact less than to be expected from a single visual observer. On this criterion the modified ANLAB formula is much closer in performance to the individual visual observer than other formulae.

It is encouraging that the modified ANLAB formula, derived from visual-matching experiments described in this paper, should perform so satisfactorily in comparison with other standard formulae on the Davidson and Friede data.

Conclusions The modification to the ANLAB(5O) colour-difference formula defined in this paper results in a significant improve- ment in the agreement between measured colour differences and visual assessment by a matching panel. It has also given a significantly better fit to the Davidson and Friede visual

TABLE 9

Davidson and Friede Data: Correlation Coefficient for Various Colour-difference Formulae

Formula

1 ANLAB(5O)

3 CIE64 4 ANLAB(42) 5 Cube Root 6 Munsell Renotation 7 Simon Goodwin 8 Friele-MacAdam -

9 Friele-MacAdam-

2 A&

Chickering 1 (FMC 1)

Chickering 2 (FMC 2 )

Correlation coefficient

-0.57 Present -0.68 investigation -0.54 -0.58 -0.58 -0.55 -0.5 8 McLaren [ 11

-0.46

--0.62

TABLE 10

Davidson and Friede Data: Table of Wrong Decisions

aE,, Wrong Wrong Wrong decisions rejections acceptances

Visual 49 M U 1.03 45 CIE 64 1.2 60 ANLAB(42) 1.3 59 Cube Root 1.2 58 Munsell

Renotation 0.7 58 Simon

Goodwin 2.3 70 FMC 1 1.5 96 FMC 2 2.5 56

24 25 43 44 42

52

43 94 45

25 20 17 15 16

18

18 2

11

RESIDUAL DISTORTION OF ANLAB(5O) SPACE Figure 9 illustrates from calculations based on Eqn 3 the variation in size of computed numerical colour differences that are visually equivalent to 1 ANLAB(5O) unit at the neutral grey point (a = 0, b = 0).

APPLICATION OF EQUATIONS The matching equation derived in this paper can be used as follows:

1. Inspection of a colour-matching grey scale could be carried out to assess the Grey Scale tolerance whch would be acceptable for a given article.

2. The AE colour difference between the selected pair of grey-scale standards would be measured.

3. The AE tolerance for any other colour could be deter- mined by inserting the radius, i.e. r = (a2 + b2)” of the colour into Eqn 3.

4. Alternatively the equivalent numerical grey-scale colour

JSDC June1974 197

-80 -60 -40 -20 0 20 40 60 80

a

dpprox. boundary of vdt dye gnmut

I$?gure Y colour s p a w using Eqri -3

Variation of' visual tolerance AE with posit ion iii

tlilli.ieiice ( A L L ) between the given colour staiid;ird aiid a i ~ y comparison sample could be deterinined by inserting the measured AL' and the radius, i.e. r = (a2 + h 2 ) " , i n t o t:clll 4.

USE WITH OTiiEII ANLAB SCALING FACTORS The ANLAB modification t'oriiiula was derived i i i this paper. lor ANLAB spacc with a scaling [actor o l SO. To coiivett f'o~ use with co lour differences measured in ANLAB( 40) spxc ' thc Eqii 4 constant of 0.022 should be iiiultiplietl b y 50/40 to givc thc constant 0.0275, i.c. ~ b r ANLAE(40) space:

AlY AB = ~ _ _ _ -

I + 0 . 0 2 7 9

References

1. McLareii, J.S.D.C., 86 ( 1970) 354; 389. 3,. Jacckcl, Helinholtc. Memoi-ial Syiiiposiuin on Colotir

Metrics, Driebergen. Holland (Sept 1071). 3. 4. McLarcn, I telmholtz Memorial Syniposiuiii o i l ('OI[JU~

Meti-ics, Driebergcn, Holland (Scpt 107 1 ) 5. Davidsori aiid Friede, J . Opt. Soc. Anlei-.. ( 1053) 58 I .

Coates, Day, I'rovost !.S.D.C., 88 (1973) 60,