colour reproduction. For example, the CIEDE2000 colour difference formula (Luo and Rigg. 2001) recommended by the CIE in 2000 stated that it should be used ...
AIC 2004 Color and Paints, Interim Meeting of the International Color Association, Proceedings
Assessing colour differences with different magnitudes K. M. Raymond HO, Guihua CUI, Ming Ronnier LUO, and B. RIGG Department of Colour and Polymer Chemistry, University of Leeds
ABSTRACT The CIEDE2000 colour difference formula recommended by the CIE in 2000 is mainly used for evaluating small size colour-differences (less than 5 ∆Eab* units). This study is intended to investigate the performances of this formula together with the others in predicting a newly accumulated experimental data set having a wide range of colour differences. The data included 4 subsets: surface textile samples, and CRT colours with small, medium and large magnitudes. Each subset had 62 pairs surrounding 5 colour centers. 1. INTRODUCTION Colour-difference formulae have been widely used in the surface colour industries such as textiles, coatings, plastics. They have been devised mainly based upon the colour differences of small magnitudes because the majority of the colour differences concern with accurate colour reproduction. For example, the CIEDE2000 colour difference formula (Luo and Rigg 2001) recommended by the CIE in 2000 stated that it should be used for evaluating colour differences less than 5 ∆Eab* units. However, in many applications such as product design and graphic arts, the colour differences concerned cover a large range. In this study, new experiments were carried out to accumulate data covering a wide range of colour-differences. The data were used to investigate the performance of various colour difference formulae. 2. EXPERIMENTAL Experiments were conducted using two different media: physical textile samples and colour stimuli presented on a CRT display. Sixty-two pairs with an average of 5.4 ∆Eab* units of textile samples were first assessed against a grey background having L* = 50 by a panel of 8 observers and each repeated the same experiment twice using grey scale method. All pairs were mainly exhibited chromatic differences, i.e. ∆L* values were relatively small. All observers had normal vision according the Ishihara test. Each sample had about 10o viewing field subtended to observers’ eyes and the experiment was conducted under a D65 simulator. Each observer was asked to provide the visual results in terms of grade value of the reference grey scale. Finally, the grade values were transformed to a linear scale in terms of visual colour difference (∆V). The average ∆V for each pair was used for subsequent data analysis. The details of the grey scale method can be found in the article by Luo and Rigg (1986). The physical samples were originally prepared by Xin, Lam and Luo (2001) to surround four chromatic colour centres and a grey centre (see Table 1). The selection of colour centers was based upon the study of Hegie, Wardman and Luo (1996), which investigated the largest disagreement between three advanced colour-difference formulae CMC (Clarke, McDonald and Rigg 1984), CIE94 (CIE 1995) and BFD (Luo and Rigg 1987). The experiment was then repeated by reproducing these colour stimuli on a Barco monitor. All simulated pairs were 117
AIC 2004 Color and Paints, Interim Meeting of the International Color Association, Proceedings
assessed by the same group of observers. Two additional sets of CRT stimuli were also generated with 150% and 200% colour difference enlargements of the original pairs. This was achieved by adjusting the colour co-ordinates of the “batch” of a pair with no change of the “standard”. The ∆L*, ∆C* and ∆H* in the original pair were multiplied by a factor of 1.5 or 2.0 in order to obtain the colour co-ordinates of the “batch” sample. The average ∆Eab* values of three subsets of CRT stimuli are 5.4, 8.0 and 10.7 units. Table 1. CIELAB values of five colour centres. Colour centre Orange Yellow Green Blue Grey
L*
a*
b*
C*
h°
48.9 76.3 29.6 26.7 48.8
10.3 -1.8 -13.4 8.4 -1.7
16.9 19.3 -0.1 -20.1 -0.3
20.0 19.6 13.6 22.1 3.8
59.6 95.3 180.6 292.8 177.3
3. DATA ANALYSIS The PF/3 measure (Luo and Rigg 1987) was used here to indicate the degree of disagreement between two sets of data in terms of percentage errors. It is a statistical measure including three different measures of fit, γ ,VAB and CV. For the prefect agreement, PF/3 should be 0. A PF/3 value of 20 means a 20% disagreement between the two data sets compared. Observer uncertainty was investigated in terms of observer accuracy and repeatability. It was found the PF/3 values of 42 and 38 for accuracy (individual against mean) and repeatability (individual’s two repeated assessments) respectively. For revealing the media effect, the ∆V values of physical pairs were plotted against those of CRT stimuli. It was found a good agreement between them, i.e. a small scatter with strong positive correlation. However, there is a systematic trend that the perceived colour differences of physical samples are 20% larger than those of CRT. In studying the magnitude effect, all sample pairs were divided into three categories according to the magnitudes of CIELAB ∆Eab* values. They are named CRT-small ( ∆Eab* 8). These were used to test the six chosen formulae: CIELAB, CMC, BFD, CIE94, CIEDE2000, and Attridge and Pointer (AP) (2000). Table 2 summaries their performances using the three subsets and the combined set designated as “All”. Note that Attridge and Pointer derived a power function based upon each formula to fit their own experimental data, which also included a large range of colour differences. The best performed formula is 1.7256∆E940.6471. When comparing between a formula’s predictions and visual results, a slope was calculated to adjust the former to have the same scale as the latter. It was found that all equations had the highest and the lowest slope for the CRT-large and CRT-small subsets, respectively. The mean ratios from all formulae are about 1.00:1.10:1.20 corresponding to small:medium:large colour differences. This indicates that all formulae over-predicted medium and large colour differences by about 10% and 20% respectively. Comparing the performances between different formulae, all formulae had the lightness parametric factor of one. As mentioned earlier, all pairs had mainly chromatic difference so that there is no need to test formulae by varying lightness parametric factor. The results for the combined set (“All”) showed that CIEDE2000, BFD, CIE94 and AP gave similar performance and outperformed CMC and CIELAB. CIEDE2000 gave the most accurate prediction to the 118
AIC 2004 Color and Paints, Interim Meeting of the International Color Association, Proceedings
small and medium magnitude subsets. Comparing the performance of a particular colour-difference formula in different magnitudes, CMC performs better in the small colour-difference; in contrast, CIELAB, CIE94 and BFD are more accurate in predicting the large subset than the small subset. The AP formula performed quite well, which indicates that a great similarity between the presented data and Attridge and Pointer data. Overall, all formulae performed quite accurate, i.e. their prediction errors ranged from 20 to 25 PF/3 units are much less than observer uncertainty (about 40 PF/3 units). Finally, a 2nd order polynomial equation, ∆EN, was fitted to the “all” data set for each colour difference formula, i.e. ∆EN = c1∆E2 + c2∆E. The results are also given in Table 2. In addition, the visual results (∆V) are plotted against colour differences calculated from six colour difference formulae and given in Table 2. As shown in Figure 1, the ∆EN equation for each of the six colour difference formulae forcing the curve to go through the origin was used to fit the whole data set. These plots confirm with those found by Attridge and Pointer that a power function should fit the data well and more scatter in large colour-difference region. Table 2. Colour difference formulae performance in terms of PF/3.
CRT-small CRT-medium CRT-large
∆EN
* ∆Eab 8
All All
CIELAB 31 26 22 25 25
CIE94 19 18 18 20 19
CMC 22 22 24 24 20
BFD 23 19 18 20 19
CIEDE2000 18 16 19 20 18
AP 23 19 19 20 20
The results in Table 2 clearly showed that comparing the performances of different formulae to fit the whole data set using the best fitted line and the curve line (∆EN), the improvement is quite limited, i.e. within 2 PF/3 units except for CMC (4 units). This implies that although each formula was designed for estimating small magnitude colour differences, they are capable of predicting large magnitude colour differences with reasonably accuracy. 4. CONCLUSION A new set of experimental data was accumulated including 4 subsets based upon textile samples and CRT colours having different colour difference magnitudes. The results are summarised below:• Regarding to media difference, the results showed that physical samples appear to have a 20% larger colour difference than CRT colours. • All colour difference formulae over-predict larger colour differences. • All formulae predicted the current data set more accurate than the observer uncertainty. • CIEDE2000, BFD and CIE94 performed slightly better than CIELAB and CMC. • The current data agreed well with the Attridge and Pointer data. • To apply a 2nd order polynomial function has little improvement for each formula to predict the current data set. This implies that all formulae are capable of predicting a wide range of colour differences.
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AIC 2004 Color and Paints, Interim Meeting of the International Color Association, Proceedings
∆ E * ab vs ∆ V
∆ E 94 vs ∆ V
25
25
∆ E C MC vs ∆ V 25
(b)
(a) y = -0.0031x 2 + 0.7721x
20
(c ) y = -0.024x 2 + 1.1311x
20
20
15
15
∆V
∆V
∆V
15
10
10
10
5
5
5
0
0
0 0
5
10
*
∆ E ab
15
20
0
25
5
∆ E BF D vs ∆ V
10
∆ E94
15
20
0
25
(d)
y = -0.0267x 2 + 1.0853x
20
15 ∆V
∆V
V
10
10
5
5
5
∆ EB FD
15
20
25
25
0
0 10
20
15
10
5
15
y = -0.034x 2 + 1.2766x
20
15
0
∆ EC M C
(f )
(e) y = -0.0087x 2 + 0.6703x
10
∆ E A P vs ∆ V
25
25
20
5
∆ E 00 vs ∆ V
25
0
y = -0.0231x 2 + 0.9651x
0
5
10
∆ E00
15
20
25
0
5
10 ∆ EAP 15
20
25
Figure 1. Visual results against colour difference calculated from 5 colour difference formulae. REFERENCES Attridge, G. G., and M. R. Pointer. 2000. Some aspects of the visual scaling of large colour differences – II. Color Research and Application 25: 116-122. CIE. 1995. Technical report: Industrial colour-difference evaluation, CIE Pub. 116. Vienna: Central Bureau of the CIE. Clarke, F. J. J., R. McDonald, and B. Rigg. 1984. Modification to the JPC79 colour-difference formula. Journal of the Society of Dyers and Colourists 100: 128-132. Hegie, D., R. H. Wardman, and M. R. Luo. 1996. A comparison of the colour differences computed using the CIE94, CMC(l:c) and BFD(l:c) formulae. Journal of the Society of Dyers and Colourists 112: 264-269. Luo, M. R., and B. Rigg. 1986. Chromaticity-discrimination ellipses for surface colours. Color Research and Application 11: 25-42. ——. 1987. BFD(l:c) colour-difference formula. Part I. Development of the formula. Journal of the Society of Dyers and Colourists 103: 86-94. Luo, M. R., G. Cui, and B. Rigg. 2001. The development of the CIE 2000 colour-difference formula: CIEDE2000. Color Research and Application 26: 340-350. Xin, H. J, C. C. Lam, and M. R. Luo. 2001. Investigation of parametric effects using medium colour-difference pairs. Color Research and Application 26: 376-383. Address: K. M. Raymond Ho, Department of Colour and Polymer Chemistry University of Leeds, LS2 9JT, United Kingdom E-mails:
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