Testing uniform colour spaces and colour‐difference formulae using printed samples

A grey‐scale psychophysical experiment was carried out for evaluating colour differences using printed colour patches. In total, 446 pairs of printed samples were prepared surrounding 17 colour centers recommended by the CIE with an average δE of 3 units. Each pair was assessed 27 times by nine observers. The visual results were used to test some selected more advanced colour‐difference formulae and uniform colour spaces. The results showed that CIELAB and OSA performed the worst, and the advanced formulae and spaces gave quite satisfactory performance such as CIEDE2000, CIE94, DIN99d, CAM02‐UCS, and OSA‐GP‐Eu. The colour discrimination ellipses were used to compare with those of the earlier studies. The results showed that they agreed well with each other. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2012     

Comparing large colour‐difference data sets

This study investigated the differences between different large colour‐difference (LCD) data sets (with a mean ΔE value about 10). Six data sets were studied. For each data set, various CIELAB based colour difference models were derived to fit the data. These models were compared to shed light on the difference between the different data sets. It was found that all data sets have very similar characteristics except for the Munsell data. Detailed investigation showed that the discrepancy is mainly due to the balance between the lightness and chromatic differences used previously for the Munsell data set. It was found that one unit of Munsell Value appears to be three times as large colour difference as one unit of Munsell Chroma at least under the experimental conditions for the data sets studied here. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2011     

Uniform colour spaces based on the DIN99 colour‐difference formula

Several colour‐difference formulas such as CMC, CIE94, and CIEDE2000 have been developed by modifying CIELAB. These formulas give much better fits for experimental data based on small colour differences than does CIELAB. None of these has an associated uniform colour space (UCS). The need for a UCS is demonstrated by the widespread use of the a*b* diagram despite the lack of uniformity. This article describes the development of formulas, with the same basic structure as the DIN99 formula, that predict the experimental data sets better than do the CMC and CIE94 colour‐difference formulas and only slightly worse than CIEDE2000 (which was optimized on the experimental data). However, these formulas all have an associated UCS. The spaces are similar in form to L*a*b*. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 282–290, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10066     

Some aspects of the visual scaling of large colour differences—II

In an earlier article the authors related visually‐ scaled large colour differences to ΔE* values calculated using four colour‐difference formulae. All four metrics yielded linear regressions from plots of visual colour difference against ΔE*, and ΔE gave the best linear fit, but the correlations were rather low. In an effort to clarify matters, the previous investigation is expanded to include data not hitherto examined. The link between visual colour difference and ΔE* colour metrics is further explored in terms of a power law relationship over a wide range of lightness, hue, and chroma variations within CIELAB colour space. It is shown that power‐law fits are superior to linear regressions in all cases, although correlations over large regions of the colour space are not very high. Partitioning of the experimental results to give reduced data sets in smaller regions is shown to improve correlations markedly, using power‐law fits. Conclusions are drawn concerning the uniformity of CIELAB space in the context of both linear and power‐law behavior. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 116–122, 2000     

The ULAB colour space

A new colour space, named ULAB, is developed. It is derived from the CIELAB colour space and can be converted to and from CIELAB. Unlike modified CIELAB colour‐difference formulae, ULAB incorporates corrections for lightness, chroma, and hue differences into its colour coordinates. For the small magnitude colour difference data, it shows the performance as good as more complicated formulae such as CIEDE2000. ULAB shows another chance of developing a colour space approximately more uniform than CIELAB. © 2013 Wiley Periodicals, Inc. Col Res Appl, 40, 17–29, 2015     

Estimation of hue discrimination thresholds using a computer interactive method

An experimental approach is described for measuring colour discrimination thresholds of human observers. Special software was developed for the accurate display of colour pairs on a high resolution CRT, using serial feedback from a spectroradiometer. Discrimination thresholds between a test and a target colour are determined by repeatedly showing an observer a circle composed of four separate quadrants, one of which has a different colour from the other three. Three quadrants are of the test colour and one of the target colour, or vice versa. Observers are asked to select the quadrant that differs from the others. An experiment is described where hue‐dependent effects affecting hue discrimination are investigated. Eighteen hue threshold values around the hue circle, at constant L = 51 and C = 25, were measured for three observers. Hue thresholds were found to vary around the hue circle, exhibiting an abrupt change in the blue to purple region (240° ≤ h_ab,10 = 300°) This change is not fully accounted for by any CIELAB‐based colour difference formula, including the most recent CIEDE2000 formula. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 410–415, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20153     

Riemannian formulation and comparison of color difference formulas

Study of various color difference formulas by the Riemannian approach is useful. By this approach, it is possible to evaluate the performance of various color difference formulas having different color spaces for measuring visual color difference. In this article, the authors present mathematical formulations of CIELAB (ΔE), CIELUV (ΔE), OSA‐UCS (ΔE_E) and infinitesimal approximation of CIEDE2000 (ΔE₀₀) as Riemannian metric tensors in a color space. It is shown how such metrics are transformed in other color spaces by means of Jacobian matrices. The coefficients of such metrics give equi‐distance ellipsoids in three dimensions and ellipses in two dimensions. A method is also proposed for comparing the similarity between a pair of ellipses. The technique works by calculating the ratio of the area of intersection and the area of union of a pair of ellipses. The performance of these four color difference formulas is evaluated by comparing computed ellipses with experimentally observed ellipses in the xy chromaticity diagram. The result shows that there is no significant difference between the Riemannized ΔE₀₀ and the ΔE_E at small color difference, but they are both notably better than ΔE and ΔE. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2011;     

Evaluation of performance of various color‐difference formulae using an experimental black dataset

The objective of this study was to develop a specific visual dataset comprising black‐appearing samples with low lightness (L* ranging from approximately 10.4 to 19.5), varying in hue and chroma, evaluating their visual differences against a reference sample, and testing the performance of major color difference formulas currently in use as well as OSA‐UCS‐based models and more recent CAM02 color difference formulas including CAM02‐SCD and CAM02‐UCS models. The dataset comprised 50 dyed black fabric samples of similar structure, and a standard (L*= 15.33, a* = 0.14, b* = ?0.82), with a distribution of small color differences, in ΔE^*_ab, from 0 to approximately 5. The visual color difference between each sample and the standard was assessed by 19 observers in three separate sittings with an interval of at least 24 hours between trials using an AATCC standard gray scale for color change, and a total of 2850 assessments were obtained. A third‐degree polynomial equation was used to convert gray scale ratings to visual differences. The Standard Residual Sum of Squares index (STRESS) and Pearson's correlation coefficient (r), were used to evaluate the performance of various color difference formulae based on visual results. According to the analysis of STRESS index and correlation coefficient results CAM02 color difference equations exhibited the best agreement against visual data with statistically significant improvement over other models tested. The CIEDE2000 (1:1:1) equation also showed good performance in this region of the color space. © 2013 Wiley Periodicals, Inc. Col Res Appl, 39, 589–598, 2014     

A top down description of S‐CIELAB and CIEDE2000

Recent work in color difference has led to the recommendation of CIEDE2000 for use as an industrial color difference equation. While CIEDE2000 was designed for predicting the visual difference for large isolated patches, it is often desired to determine the perceived difference of color images. The CIE TC8‐02 has been formed to examine these differences. This paper presents an overview of spatial filtering combined with CIEDE2000, to assist TC8‐02 in the evaluation and implementation of an image color difference metric. Based on the S‐CIELAB spatial extension, the objective is to provide a single reference for researchers desiring to utilize this technique. A general overview of how S‐CIELAB functions, as well as a comparison between spatial domain and frequency domain filtering is provided. A reference comparison between three CIE recommended color difference formulae is also provided. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 425–435, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10195     

Evaluation of the crispening effect using CRT‐displayed colour samples

In this study, the crispening effect was clearly observed when 38 neutral‐coloured sample pairs with only lightness differences were assessed under 5 neutral backgrounds of different lightness values. The sample pairs are CRT‐based colours, and they are selected along the CIELAB L* axis from 0 to 100. The magnitude of colour difference of each pair is 5.0 CIELAB units. The visual assessment results showed that there is a very large crispening effect. The colour differences of the same pair assessed under different backgrounds could differ by a factor of up to 8 for a sample pair with low lightness. The perceived colour difference was enlarged when the lightness of a sample pair was similar to that of the background. The extent of crispening effect and its quantification are discussed in this investigation. The performances of five colour‐difference equations were also tested, including the newly developed CIEDE2000. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 374–380, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20045     

The use of sensory difference tests to investigate perceptible colour‐difference in a cosmetic product

Two sensory difference tests have been used to assess the ability of an untrained population to perceive colour difference in a cosmetic product. The two tests used were the triangle test and the “two‐out‐of‐five” test. Participants were presented with groups of samples with varying colour differences and asked to identify the odd sample in the triangle test and the pair in the two‐out‐of‐five test. From these data, the number of correct responses was correlated with the calculated colour difference using three colour‐difference equations (CMC, CIE94, and CIEDE2000). These correlations were optimized by varying the parameters in the colour‐difference equations. With the parameters optimized, each of the three colour‐difference equations gave a correlation coefficient of ～0.97 with the two‐out‐of‐five test and a correlation coefficient of ～0.79 with the triangle test. These correlation coefficients suggest that sensory difference testing can be used to investigate perception of colour difference. However, for the triangle test the correlation between the sensory data and the calculated colour difference is weak and the two‐out‐of‐five test should be preferred. The minimum perceptible colour difference was estimated from the regression plots between the optimised colour‐difference equations and the sensory data. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 299–304, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20025     

A cross‐cultural colour‐naming study. Part III—A colour‐naming model

A colour‐naming model was developed to categorize volumes for each of the 11 basic names in CIELAB colour space. This was tested with three different sets of data for two languages (English and Mandarin), derived from extensive colour categorization experiments. The performance of the model in predicting colour names was satisfactory, with an average prediction error of 8.3%. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 270–277, 2001     

Performance of advanced color difference and CAM02‐based formulas in prediction of the Crispening effect for reflective samples

The Crispening effect is defined as an increase in the perceived color difference of the two stimuli, when their color (chromaticity or luminance) is close to the background on which the two stimuli are compared. In this study, the amount of the Crispening effect for three achromatic backgrounds and also the performance of six different color difference formulas (CDFs) for prediction of this effect have been investigated, by preparing 85 sample pairs in 9 CIE's recommended color centers. Regarding the results, the maximum (50%) and the minimum (4%) amount of the Crispening effect belong to the gray and the purple centers, respectively. According to the results of a comparative test, the Crispening intensifies when two stimuli have just lightness difference instead of just chromaticity difference. The highest variation was for the gray samples, in which the amount of the Crispening effect increased from 35% to 65%. By using PF/3 and STRESS index, it is also concluded that CMC and CIEDE2000 perform better than CAM02‐SCD and CAM02‐UCS in prediction of the Crispening effect on the dark gray and gray backgrounds. According to the results, the significant differences between the performances of the CDFs disappear when the luminance of the background increases. Huang's power functions also do not improve these results significantly. Furthermore, the results indicate that the traditional L* equation used in CIELAB performs similar to the Whittle's formula in prediction of the Crispening effect for reflective samples, and no significant difference was obtained.     

Investigation of parametric effects using small colour differences

This experiment was carried out to investigate some viewing parameters affecting perceived colour differences. It was divided into eight phases. Each phase was conducted under a different set of experimental conditions including separations, neutral backgrounds, and psychophysical methods. Seventy‐five wool sample pairs were prepared corresponding to five CIE colour centers. The mean colour difference was three CIELAB units. Each pair was assessed by a panel of 21 observers using both the gray scale and pair comparison psychophysical methods. The assessments were carried out using the three different backgrounds (white, mid‐gray, and black) and a hairline gap between the samples. Assessments on the gray background were repeated using a large (3‐inch) gap between the samples. It was found that the visual results obtained from both psychophysical methods gave very similar results. The parametric effect was small, i.e., the largest effect was only 14% between the white and gray background conditions. These visual data were also used to test four colour‐difference formulae: CIELAB, CMC, BFD, and CIE94. The results showed that three advanced colour‐difference formulae performed much better than CIELAB. There was a good agreement between the current results and those from earlier studies. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 331–343, 1999     

Are chroma tolerances dependent on hue‐angle?

Relationships between suprathreshold chroma tolerances and CIELAB hue‐angles have been analyzed through the results of a new pair‐comparison experiment and the experimental combined data set employed by CIE TC 1–47 for the development of the latest CIE color‐difference formula, CIEDE2000. Chroma tolerances have been measured by 12 normal observers at 21 CRT‐generated color centers L*₁₀ = 40, C*_ab,10 = 20 and 40, and h_ab,10 at 30° regular steps). The results of this experiment lead to a chroma‐difference weighting function with hue‐angle dependence W_CH, which is in good agreement with the one proposed by the LCD color‐difference formula [Color Res Appl 2001;26:369–375]. This W_CH function is also consistent with the experimental results provided by the combined data set employed by CIE TC 1–47. For the whole CIE TC 1–47 data set, as well as for each one of its four independent subsets, the PF/3 performance factor [Color Res Appl 1999;24:331–343] was improved by adding to CIEDE2000 the W_CH function proposed by LCD, or the one derived by us using the results of our current experiment together with the combined data set employed by CIE TC 1–47. Nevertheless, unfortunately, from the current data, this PF/3 improvement is small (and statistically nonsignificant): 0.3 for the 3657 pairs provided by CIE TC 1–47 combined data set and 1.6 for a subset of 590 chromatic pairs (C*_ab,10>5.0) with color differences lower than 5.0 CIELAB units and due mainly to chroma. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 420–427, 2004; Published online in Wiley Interscience (www.interscience.wiley.com). DOI 10.1002/col.20057     

Correlation between visual and colorimetric scales ranging from threshold to large color difference

Psychophysical experiments of color discrimination threshold and suprathreshold color‐difference comparison were carried out with CRT‐generated stimuli using the interleaved staircase and constant stimuli methods, respectively. The experimental results ranged from small (including threshold) to large color difference at the five CIE color centers, which were satisfactorily described by chromaticity ellipses as equal color‐difference contours in the CIELAB space. The comparisons of visual and colorimetric scales in CIELAB unit and threshold unit indicated that the colorimetric magnitudes typically were linear with the visual ones, though with different proportions in individual directions or color centers. In addition, color difference was generally underestimated by the Euclidean distance in the CIELAB space, whereas colorimetric magnitude was perceptually underestimated for threshold unit, implying the present color system is not a really linear uniform space. Furthermore, visual data were used to test the CIELAB‐based color‐difference formulas. In their original forms CIEDE2000 performed a little better than CMC, followed by CIELAB, and with CIE94 showing the worst performance for the combined data set under the viewing condition in this study. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 349–359, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10081     

Development of a comprehensive visual dataset based on a CIE blue color center: Assessment of color difference formulae using various statistical methods

The objectives of this work were to develop a comprehensive visual dataset around one CIE blue color center, NCSU‐B1, and to use the new dataset to test the performance of the major color difference formulae in this region of color space based on various statistical methods. The dataset comprised of 66 dyed polyester fabrics with small color differences ($\Delta E_{{\rm ab}}^* < 5$ ) around a CIE blue color center. The visual difference between each sample and the color center was assessed by 26 observers in three separate sittings using a modified AATCC gray scale and a total of 5148 assessments were obtained. The performance of CIELAB, CIE94, CMC(l:c), BFD(l:c), and CIEDE2000 (K_L:K_C:K_H) color difference formulae based on the blue dataset was evaluated at various K_L (or l) values using PF/3, conventional correlation coefficient (r), Spearman rank correlation coefficient (ρ) and the STRESS function. The optimum range for K_L (or l) was found to be 1–1.3 based on PF/3, 1.4–1.7 based on r, and 1–1.4 based on STRESS, and in these ranges the performances of CIEDE2000, CMC, BFD and CIE94 were not statistically different at the 95% confidence level. At K_L (or l) = 1, the performance of CIEDE2000 was statistically improved compared to CMC, CIE94 and CIELAB. Also, for NCSU‐B1, the difference in the performance of CMC (2:1) from the performance of CMC (1:1) was statistically insignificant at 95% confidence. The same result was obtained when the performance of all the weighted color difference formulae were compared for K_L (or l) 1 versus 2. © 2009 Wiley Periodicals, Inc. Col Res Appl, 2011     

Evaluating the 1931 CIE color‐matching functions

The use of colorimetry within industry has grown extensively in the last few decades. Central to many of today's instruments is the CIE system, established in 1931. Many have questioned the validity of the assumptions made by Wright¹ and Guild,² some suggesting that the 1931 color‐matching functions are not the best representation of the human visual system's cone responses. A computational analysis was performed using metameric data to evaluate the CIE 1931 color‐matching functions as compared to with other responsivity functions. The underlying assumption was that an optimal set of responsivity functions would yield minimal color‐difference error between pairs of visually matched metamers. The difference of average color differences found in the six chosen sets of responsivity functions was small. The CIE 1931 2° color‐matching functions on average yielded the largest color difference, 4.56 ΔE. The best performance came from the CIE 1964 10° color‐matching functions, which yielded an average color difference of 4.02 ΔE. An optimization was then performed to derive a new set of color‐matching functions that were visually matched using metameric pairs of spectral data. If all pairs were to be optimized to globally minimize the average color difference, it is expected that this would produce an optimal set of responsivity functions. The optimum solution was to use a weighted combination of each set of responsivity functions. The optimized set, called the Shaw and Fairchild responsivity functions, was able to reduce the average color difference to 3.92 ΔE. In the final part of this study a computer‐based simulation of the color differences between the sets of responsivity functions was built. This simulation allowed a user to load a spectral radiance or a spectral reflectance data file and display the tristimulus match predicted by each of the seven sets of responsivity functions. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 316–329, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10077     

Color‐difference formula performance for several datasets of small color differences based on visual uncertainty

Visual uncertainty, while reported, is not used routinely when evaluating color‐difference formula performance in comparison with visual data; rather, data are analyzed assuming no uncertainty; that is, repeating the experiment would result in the identical average results. Previously, Shen and Berns developed three methods to determine whether a color‐difference formula was well‐fitting, under‐fitting, or over‐fitting visual data when visual uncertainty was considered, the method dependent on how the uncertainty was reported and the colorimetric sampling of the color‐difference stimuli. The “nonellipsoid standard error method” was used in the current analyses. Three datasets were evaluated: BFD‐P, Leeds, and Witt. For the BFD‐P data, incorporating visual uncertainty led to the same performance results as the average results, that CIEDE2000 was an improvement over CIE94, which was an improvement over CIELAB. For the Witt data, incorporating visual uncertainty led to the same performance results as the average results, that CIEDE2000 and CIE94 had equivalent performance, both an improvement over CIELAB. However, both formulas under‐fitted the visual results; thus, neither formula was optimal. For the Leeds dataset, the visual uncertainty analysis did not support the improvement of CIEDE2000 over CIE94 that occurred when evaluating the average results. Both formulas well fit the visual data. These analyses also provided insight into the tradeoffs between the number of color‐difference pairs and the number of observations when fitting a local contour of equal perceived color difference: In particular, increasing the number of observations was more important than increasing the number of color‐difference pairs. Finally, average standard error could be used to approximate visual uncertainty defined using STRESS. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2011     

Visual evaluation at scale of threshold to suprathreshold color difference

Visual evaluation experiments of color discrimination threshold and suprathreshold color‐difference comparison were carried out using CRT colors based on the psychophysical methods of interleaved staircase and constant stimuli, respectively. A large set of experimental data was generated ranged from threshold to large suprathreshold color difference at the five CIE color centers. The visual data were analyzed in detail for every observer at each visual scale to show the effect of color‐difference magnitude on the observer precision. The chromaticity ellipses from this study were compared with four previous published data, of CRT colors by Cui and Luo, and of surface colors by RIT‐DuPont, Cheung and Rigg, and Guan and Luo, to report the reproducibility of this kind of experiment using CRT colors and the variations between CRT and surface data, respectively. The present threshold data were also compared against the different suprathreshold data to show the effect of color‐difference scales. The visual results were further used to test the three advance color‐difference formulae, CMC, CIE94, and CIEDE2000, together with the basic CIELAB equation. In their original forms or with optimized K_L values, the CIEDE2000 outperformed others, followed by CMC, and with the CIELAB and CIE94 the poorest for predicting the combined dataset of all color centers in the present study. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 198–208, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20106