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.     

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     

Practical demonstration of the CIEDE2000 corrections to CIELAB using a small set of sample pairs

A set of 10 color pairs was proposed and produced in 2002 to show the advantages of the CIEDE2000 color‐difference formula with respect to CIELAB. These 10 color pairs illustrated each of the five corrections to CIELAB proposed by CIEDE2000. The 10 color pairs were visually assessed, under reference conditions close to those proposed by CIEDE2000, by two groups of 31 and 21 inexperienced observers, using two different gray scales. Average visual results in these experiments fitted CIEDE2000 predictions much better than CIELAB, as shown by a decrease of Standardized Residual Sum of Squares values of about 20 units. Current visual results showed only the improvement of CIEDE2000 upon CIELAB in predictions of perceived color differences, but they are not recommended for testing new advanced color‐difference formulas. © 2012 Wiley Periodicals, Inc. Col Res Appl, 38, 429–436, 2013.     

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     

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     

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 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     

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     

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     

Evaluation of colour‐difference formulae for different colour‐difference magnitudes

Most of the colour‐difference formulae were developed to fit data sets having a limited range of colour‐difference magnitudes. Hence, their performances are uncertain when applying them to a range of colour differences from very small to very large colour differences. This article describes an experiment including three parts according to the colour‐difference magnitudes: large colour difference (LCD), small colour difference (SCD), and threshold colour difference (TCD) corresponding to mean ΔE values of 50.3, 3.5, and 0.6, respectively. Three visual assessment techniques were used: ratio judgement, pair comparison, and threshold for LCD, SCD, and TCD experiments, respectively. Three data sets were used to test six colour‐difference formulae and uniform colour spaces (CIELAB, CIE94, CIEDE2000, CAM02‐SCD, CAM02‐UCS, and CAM02‐LCD). The results showed that all formulae predicted visual results with great accuracy except CIELAB. CIEDE2000 worked effectively for the full range of colour differences, i.e., it performed the best for the TCD and SCD data and reasonably well for the LCD data. The three CIECAM02 based colour spaces gave quite satisfactory performance. © Wiley Periodicals, Inc. Col Res Appl, 2012     

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.     

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     

Geodesic calculation of color difference formulas and comparison with the munsell color order system

Riemannian metric tensors of color difference formulas are derived from the line elements in a color space. The shortest curve between two points in a color space can be calculated from the metric tensors. This shortest curve is called a geodesic. In this article, the authors present computed geodesic curves and corresponding contours of the CIELAB ( ), the CIELUV ( ), the OSA‐UCS (ΔE_E) and an infinitesimal approximation of the CIEDE2000 (ΔE₀₀) color difference metrics in the CIELAB color space. At a fixed value of lightness L*, geodesic curves originating from the achromatic point and their corresponding contours of the above four formulas in the CIELAB color space can be described as hue geodesics and chroma contours. The Munsell chromas and hue circles at the Munsell values 3, 5, and 7 are compared with computed hue geodesics and chroma contours of these formulas at three different fixed lightness values. It is found that the Munsell chromas and hue circles do not the match the computed hue geodesics and chroma contours of above mentioned formulas at different Munsell values. The results also show that the distribution of color stimuli predicted by the infinitesimal approximation of CIEDE2000 (ΔE₀₀) and the OSA‐UCS (ΔE_E) in the CIELAB color space are in general not better than the conventional CIELAB (ΔE) and CIELUV (ΔE) formulas. © 2012 Wiley Periodicals, Inc. Col Res Appl, 38, 259–266, 2013     

Establishment of a color tolerance for yarn-dyed fabrics from different color-depth yarns

Yarn-dyed fabric is often woven from warp and weft yarns in the same color depth to ensure a uniform color appearance. The difference in color depth between warp and weft tends to result in the uneven color of the yarn-dyed fabric. This article aims to establish a color tolerance for yarn-dyed fabric that can be woven with a qualified color appearance but from the warp and weft yarns in different color depths. A total of 27 yarn-dyed fabric samples in three color series (red, yellow, and blue) were evaluated by using the yarn-dyed fabric from warp and weft yarns in the same color depth of 2% (on weight of fabric, owf) as the standard. Visual assessment and instrumental measurement of color were carried out to establish the color tolerance ellipse that was defined as CMC (Color Measurement Committee) color differences (2:1) of no more than 1.00. It was found that the color strengths (K/S) and color differences (ΔE_CMC(2:1)) of these fabric samples for each color series had linear relationships with the color depths of warp and weft yarns. The color tolerance ellipses indicated that, even though the warp and weft yarns had an apparent color difference, they could be woven in fabrics with relatively uniform color appearance and meet the requirements for yarn-dyed fabric. This work provided valuable insight into the production of qualified yarn-dyed fabrics from unqualified dyed yarns.     

Setting up acceptability tolerances: A case study

Current acceptance of goods for color by the United States Army depends on visual comparison against a standard and as many as eight limit samples. The Army wished to have a numerical method of setting color tolerances to be used with instrumental measurement. Preliminary work with the standards and limit samples indicated that acceptability ellipsoids oriented in the hue, chroma, and lightness directions in CIELAB color space should be set up. To establish the tolerances, we selected pairs of samples from a large number of previous submissions by industry. These pairs represented four graduated lightness steps, four graduated chroma steps, and four graduated hue steps. Six observers looked at each pair ten times, randomly interspersed with other pairs, and issued a pass-or-fail judgment each time. From these data we established lightness, chroma, and hue tolerance limits. For an olive green and a tan shade, these tolerances were roughly in the ratio 3:2:1; for a dark blue, the ratios were roughly 2:2:1. We wrote simple equations that can be used in order to determine quickly whether a sample passes or fails.     

Are we able to distinguish color attributes?

The perception and understanding of the three color attributes have been analyzed from two experiments using pairs of Munsell samples, where only one of the three color attributes were changed/unchanged (Experiment I/II) at a time. In each experiment, 36 pairs with color differences of 3 different sizes (average values of 15.8 and 21.7 CIELAB units for Experiments I and II, respectively) were assessed under standardized conditions by 40 normal observers, 20 of them with previous knowledge and experience in colorimetry. At a 95% confidence level, the results from the two experiments were not significantly different, indicating that color attributes were not easily distinguished: for example, for experienced observers, the percentage of correct answers for identifying the color attribute responsible for a color difference was only 72.4%, the random probability being 33.3%. There were no significant differences between the results found by men and women. The worst distinguished attribute was Chroma, that is, the least frequent confusion was between Hue and Value or vice versa. Value differences were more easily detected for achromatic than for chromatic pairs, both for experienced and inexperienced observers. With respect to the size of the color differences, we observed that large hue differences were more easily identifiable than smaller ones, and a constant Hue was more identifiable when the entire color difference was small. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 356–367, 2000     

Color appearance modeling of bicolor striped woven fabrics considering neighboring color effects

In this article, the effect of the spatial and colorimetric attributes of neighboring color on color appearance shift in bicolor striped woven fabrics is investigated. A total of 240 test/neighboring woven color combinations were constructed in four different striped paradigms. Each test color in the combinations was visually assessed by 12 observer panels with the use of the magnitude estimation method estimating the magnitude of perceptual color attributes lightness, colorfulness, and hue. The visual estimates obtained were analyzed statistically by employing correlation and simple regression methods, and, as a result, the following significant neighboring color effects were detected and individually defined: (1) neighboring color's size, lightness, colorfulness, and hue on test color's lightness, (2) neighboring color's colorfulness and hue on test color's colorfulness, and (3) neighboring color's hue on test color's hue. Furthermore, through multiple regression analysis, color appearance models by which the lightness, colorfulness, and hue of bicolor woven fabrics can be predicted were derived. The predictive performance of the models was evaluated by calculating the difference between the visually estimated and the predicted color appearances, using ΔL*, ΔC*, Δh°, and ΔE_CMC(2:1). Among all the derived models, the model producing the smallest mean error was chosen as a final model, and its great accuracy in color appearance predictions was verified through further statistical evaluation. It is envisaged that the findings of this research are of benefit to design textile products with bicolor striped woven fabrics to have desired color appearances. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 512–521, 2017     

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.     

Wpt (waypoint) shift manifold difference metrics for evaluation of varying observing-condition (observer + illuminant) metamerism and color inconstancy

Metamerism is a critical color phenomenon which can cause serious problems for products assembled by various parts. Customers generally expect all parts are color-matched under different observing conditions. This article extends the concepts of illuminant and observer metamerism to observing-condition metamerism, that is, objects are color-matched under one observing condition but not under others. The color inconstancy of a single object is also expanded to be evaluated under multiple observing conditions. Moreover, four Waypoint (Wpt) Shift Manifold difference metrics are proposed to evaluate not only observing-condition metamerism of metamers and paramers but also observing-condition color inconstancy of single objects: The Mean Object Inconstancy Index (MOII), The Mean Object Color Difference (MMOCD), Object Metamer Index (OMI), and Object Hue Similarity Index (OHSI). Existing indices of metamerism and color inconstancy employ appearance matching using a Chromatic Adaptation Transform (CAT) and color difference formulas such as CIEDE76 or CIEDE2000. The proposed metrics utilize material matching based upon the Waypoint Material Adjustment Transform (Wpt-MAT) and Euclidian color difference in the perceptually uniform Material Color Equivalency Space WLab. Conceptual comparisons between these approaches are discussed and evaluated. Additionally, computational evaluation results under observing conditions composed by 99 illuminants and 70 observers show that MOII provides a measure of color inconstancy for single objects, MMOCD provides a measure of metamerism between metamers and paramers with a generalized assessment of color difference between two objects, OMI provides a measure of paramers, and OHSI provides a quantitative measure of hue characteristics for different observing conditions.     

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.