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     

A preliminary comparison of CIE color differences to textile color acceptability using average observers

Ninety‐six nylon pairs were prepared, including red, yellow, green, and blue standards, each at two lightness levels with CIE94 ΔE units ranging from 0.15 to 4.01. Visual assessments of acceptability were carried out by 21 females. Logistic regression compared visual results to four color‐difference equations, CIELAB, CMC, CIE94, and CIEDE2000. It was found that CMC most closely represented judgments of average observers. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 288–294, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20124     

A Euclidean color space in high agreement with the CIE94 color difference formula

Many consider it futile to try to create color spaces that are significantly more uniform than the CIELAB space, and, therefore, efforts concentrate on developing estimates of perceived color differences based on non‐Euclidean distances for this color space. A Euclidean color space is presented here, which is derived from the CIELAB by means of a simple adjustment of the a* and b* axes, and in which small Euclidean distances agree to within 10.5% with the non‐Euclidean distances given by the CIE94 formula. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 64–65, 2000     

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     

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     

Investigating the effect of texture on the performance of color difference formulae

To predict the perceived color differences, the effect of the surface texture on the performance of the color difference formulae was investigated. To this end, knitted polyester fabrics with eight different textures were prepared. The fabrics were dyed by seven dyestuffs in five different depths. The selected pairs from the five samples with different depths in each hue covered small to large color differences. The assessed pair of samples had the same texture and hue, but different depths. A panel of 23 observers assessed the color differences of the pairs by gray scale method. The results showed that for the textile samples with different texture structures, the CIEDE2000 (2:1:1) performed the best followed by CMC (2:1:1), CIE94 (2:1:1), and CIELAB with approximately same performance. In addition, the magnitude of color difference influenced the ability of the formulae to predict the visual assessments and the best performance obtained for medium color differences. The comparison between eight different texture groups indicated that the texture structures of the pairs significantly affected the performance of the color difference formulae. For instance, the PF/3 measures obtained for the eight texture groups by CIEDE2000 (2:1:1) color formula could be varied between 21.98 and 33.37 PF/3 units. © 2009 Wiley Periodicals, Inc., Col Res Appl, 2010.     

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     

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     

Evaluation of colour difference formulae

Values obtained by using five colour difference formulae in a set of 106 pairs of textile samples are compared with visual assessments. These included not only total colour difference, but also their psychophysical components (lightness, chroma and hue differences). Visual data used for the comparisons are the average from more than eight observers' assessments, carried out under standardised conditions by means of the grey scale method. Linear regression calculations show that the new CIEDE2000 formula gives similar results to the CMC(2:1) formula, with the differences between correlation coefficients not being statistically significant. The application of performance factors helps to ascertain the superiority of these two formulae over the other three tested. This is valid not only for total colour difference, but also for its individual components.     

Different transformation methods between CIELAB coordinates and Munsell hue

This research aims to convert CIE L*C*_abh_ab coordinates into corresponding Munsell hues. Different transformation methods for colour mapping from CIELAB colour space to Munsell hues are proposed. Polynomial equations that predict Munsell hue from CIELAB h_ab suffer from poor performance as there is no direct one‐to‐one mapping. Polynomial methods that predict Munsell hue from all three L*C*_abh_ab values also show limited performance. However, a distance‐weighted look‐up‐table model based upon the CIEDE2000 colour‐difference equation is able to predict Munsell hue to an accuracy of 1 unit of root mean square error. All transformation methods in this paper were developed using CIE illuminant C and the 2° standard observer conditions and were based on 2729 Munsell renotation colour samples.     

Performance of lightness difference formulae

There are large variations between different previously published lightness difference experimental data sets. Two hundred and eight pairs of matt and glossy paint samples exhibiting mainly lightness differences were accumulated. Each pair was assessed about twenty times by a panel of fourteen observers using the grey scale method. The results were used to derive a new lightness difference formula (CII), and to a large extent, a possible new CIE lightness difference formula (CMC99). Both formulae were found to be more accurate than the typical deviation of an individual assessment from the mean of a panel of 20 observers, and outperformed the existing formulae using the present data set. The new CMC99 lightness difference formula is integrated into the new CIE colour difference equation CIEDE2000. The results also showed that special attention should be paid to measuring very dark samples. This is caused by poor instrument repeatability and inter-instrument agreement in this colour region.     

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     

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     

Vector-based modelling of colour difference: a pilot study of the DE2000 colour difference model

A novel approach to colour difference modelling is presented whereby for any given CMC (1:1) or CIE DE2000 ∆E, ∆C, ∆H, and ∆L colour difference, the equivalent CIE XYZ, L*a*b*, and L*C*h coordinate changes are derived by optimising the input RGB stimuli from which they are all calculated. Single-dimension L or C or H difference loci expressed in DE2000 difference units are thus generated, and the additive equivalence of tristimulus values is likewise projected forward onto each locus and also onto a set of CIE DE2000 three-unit ellipse boundaries. Using the datasets thus generated, it is then shown firstly that the derived ellipses have well-defined semi-axes, which explain the detailed orientation of the MacAdam ellipses in x,y,Y space. Unit CIE DE2000 difference is confirmed as a successful quantifying constant of visual difference over a wide range of chroma, hue, and lightness differences. As a constant, CIE DE2000 unit difference is shown to have a significantly variable value at high and low chroma: evidence is established for systematic changes in both chroma and hue difference sensitivity. A hitherto unresolved non-linearity is revealed in the C* dimension of L*C*h space that is not replicated in the CIE DE2000 model. The derived difference loci appear to specify physically reproducible experimental stimuli that could be used in the estimation of visual difference magnitude. Overall, the data derived by the new approach and presented in this paper increase the probability that a true vector model of the visual difference response may eventually be derived.     

Iris color and texture: A comparative analysis of real irises,ocular prostheses,and colored contact lenses

In this work, we analyzed the color and texture of irises, ocular prostheses, and cosmetic colored contact lenses measured by means of a multispectral system, which provides the CIE L*a*b* colorimetric coordinates of a high resolution image pixel by pixel. The same subject, who has dark brown irises, participated in the measurement of all the contact lenses. The CIE L*a*b* colorimetric coordinates were analyzed to classify the samples into three major groups (brown, blue and green) using a new algorithm developed for this purpose. This classification allowed us to carry out a comparison of the color associated with each set of samples, using the corresponding color gamuts in the CIE L*a*b* color space. Furthermore, we analyzed the iris color reproduction achieved by prostheses and contact lenses in terms of CIEDE2000 color differences, and obtained closer results with prostheses. In addition, we performed an analysis of texture by means of the color spatial distribution of all samples. This was achieved by means of two statistical approaches: first order statistics of image histograms and second order statistics using co‐occurrence matrices. The results suggest that the texture associated with real irises, ocular prostheses and colored contact lenses is very different. This study provides useful information about the color and texture of irises that may help to establish a strategy for improving the techniques used in the manufacturing process of prostheses and colored contact lenses to obtain a better and more realistic appearance. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2011     

A hue rectangle and its color metrics in a modified opponent‐colors system

In the proposed modified opponent‐colors system, the hue regular rectangles show the chromatic coordinates of any chromatic colors better than hue circles. In the hue rectangles equihue and equichroma loci are shown together with equigrayness loci. In the color perception space of the modified opponent‐colors system, a city‐block metric must be used instead of a Euclidean one for distance. The reason for this is described in detail. The proposed color perception space constitutes a regular octahedron. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 171–179, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10046     

Regression analysis to determine the optimum colour tolerance level for instrumental shade sorting

An investigation of the correlation between visual colour assessment and instrumental colour acceptance determination using regression analysis has been carried out. Three colour-difference equations, CIELAB, CMC(2:1) and CIE94(2:1:1), were studied in order to determine which is the best for generating a uniform colour space/microspace for allocating the colour population in shade sorting. Determination of optimum colour tolerance for further shade sorting was also undertaken. Some 1320 pairs of dyed samples distributing around 20 shade standards were measured instrumentally and also evaluated visually by a panel of 32 observers. Percentage rejection was plotted against colour difference and different mathematical regression relationships were then imposed. As a result, both CMC and CIE94 showed better correlation between the two colour assessment methods than the CIELAB colour-difference equation. Consequently, optimum colour tolerance limits were determined for subsequent development of shade sorting, with the findings being equally applicable to colour acceptance (shade passing).     

CIE94-a new colour-difference formula*

The Commission Internationale de I'Eclairage (CIE) has recently published a new colour-difference formula, called CIE94, for use in industrial pass/fail colour-difference work. It is based in CIELAB colour space but on the CMC(l:c) colour-difference formula. In this paper the history behind the development of the new formula is outlined, before the formula itself is described and compared with the CMC(l:c) formula. The role of future work in this area is briefly reviewed and the attitude of the Society's Colour Measurement Committee to CIE94 is outlined.     

A comparison of the colour differences computed using the CIE94, CMC(l:c) and BFD(l:c) formulae

The colour differences computed using three advanced formulae have been compared for numerical standard/sample pairs located at regular intervals throughout the colour space. A ratio method was used to compare the values obtained, so that the regions of the colour space where the greatest disagreements occur could be identified. The level of disagreement between the BFD and the CIE94 formulae was generally lower then that between the CMC and CIE94 formulae. In the latter case, the greatest level of disagreement covered a large part of the colour space, concentrated especially in the orange region. It is recommended that studies of the performance of these formulae in relation to visual assessments are made, for real standard/sample pairs located in this region.     

Revisiting the weighting function for lightness in the CIEDE2000 colour-difference formula

We have used 13 experimental datasets (7420 colour pairs) to study the performance of the weighting function for lightness proposed by the CIEDE2000 colour-difference formula, because it has been suggested that this function can be improved by using the weighting function for lightness S_L = 1 adopted by the CIE94 colour-difference formula. Using the standardised residual sum of squares (STRESS) index, it was found that: (i) replacing the S_L in CIEDE2000 with S_L = 1 improved the results for 7/13 datasets considered, but the improvement was statistically significant only for 1/13 datasets; (ii) a Whittle-type lightness-difference formula can be used to replace the term ∆L*/S_L in CIEDE2000, which led to a new colour-difference formula with no statistically significant difference with respect to CIEDE2000 for any of the 13 experimental datasets. A modification of the CIEDE2000 formula using a Whittle-type lightness formula is proposed.