RIT‐DuPont supra‐threshold color‐tolerance individual color‐difference pair dataset

The RIT‐DuPont dataset has been used extensively for formula development and testing since its inception during the 1980's, for example, in the development of CIE94 and CIEDE2000. The dataset was published as 156 color‐tolerances, T₅₀, along specific vector directions about 19 color centers. Probit analysis was used to transform judgments of 958 color‐difference pairs by 50 observers to these 156 tolerances. For most statistical significance testing, the number of samples determines the confidence limits. Thus, there was an interest in publishing the individual color‐difference pair visual and colorimetric data to improve the precision of significance testing. From these 958 pairs, 828 pairs had determinable visual differences. The others had either excessive visual uncertainty or had unanimous visual judgments such that visual differences were undefined. In addition, a method was devised to assign visual uncertainty to each of these pairs using the principles of maximum likelihood and the T₅₀ values. Comparisons were made between the T₅₀ and individual color‐difference pair data both including and omitting uncertainty weightings. The weighted dataset was found to be equivalent to the T₅₀ tolerances. © 2009 Wiley Periodicals, Inc. Col Res Appl, 2010     

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     

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     

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     

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     

Color discrimination results from a CRT device: Influence of luminance

In this article, we report new color discrimination ellipsoids calculated from two normal observers, using a CRT device and five values of luminance at each of the five centers recommended by the CIE in 1978 (Col Res Appl 1978;3:149–151). Our main goal was to test the weighting function for lightness adopted by the CIE94 color‐difference model (CIE Publication 116, 1995). Although some of the experimental conditions employed here (CRT monitor, small size of the visual field, and controlled exposure time) did not fit those recommended by this model, our results support the weighting function for lightness proposed by CIE94. The only robust trends observed in the ellipsoids obtained were a confirmation of Weber's law and a decrease in the area of the x, y chromaticity ellipses, when the luminance of each reference stimulus increased towards the one of the surround. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 38–44, 1999     

Analysis of five sets of color difference data

In a systematic optimization process five sets of recent color difference data have been analyzed for commonalities. Adjustment of the X tristimulus values and application of a systematic, surround dependent S_L function was found to be beneficial in all cases. Other modifications of the CIE94 color‐difference formula were found to bring improvements only in some cases and may be spurious. Application of what seem to be nonsystematic scale factors in a range of 0.78–1.38 improve correlation between calculated and visual color differences in all cases. After optimization, calculated color difference values explain between 80–90% of the variation in visual color differences. Some of the datasets are shown not to be well suited for formula optimization. Optimization in all cases by set, for three sets of data by quadrant in the a^*b^* diagram, and for one set by subset did not reveal any additional systematic trends for improvement. It appears that the basic structure of CIE94, with the recommended modifications, is a good approximation as a model for color‐difference evaluation in the range from 0.5–10 units of difference. The model is surround dependent. A number of issues remain to be resolved. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 141–150, 2001     

Deriving instrumental tolerances from pass-fail and colorimetric data

Equations such as CIE94 and CMC are now in common use to set instrumental tolerances for industrial color control. A visual experiment was performed to generate a data set to be used in evaluating typical industrial practices. Twenty-two observers performed a pass-fail color tolerance experiment for a single high-chroma yellow color. Thirty-two glossy samples varying in all three CIE-LAB dimensions were compared with a single standard. A near-neutral anchor pair was used to define the quality of match criterion. The pooled pass data were used to fit a 95% confidence ellipsoid. The chromaticness dimension was well estimated by either CMC or CIE94. The lightness dimension was poorly estimated by either equation. Evaluating the sampling distribution of the 32 test samples via a covariance matrix revealed a poor sampling, particularly in the ΔL*Δb* plane. This sampling may have biased the visual experiment. The visual data were used to optimize various color-difference equations based on CIE94 and CMC, where the l:c and total color difference were adjustable parameters. Several methods of optimization are described including minimizing the number of instrumental wrong decisions and logistic multiple-linear regression. Some methods require only pass response data, while others require both pass and fail data. Because industrial tolerances are usually based on a single observer, ellipsoids were fitted for three observers to demonstrate the large variability between observers in judging color differences. It was concluded that when tolerances need to be set based on a single observer's visual responses of samples not well distributed about the standard, typical industrial occurences, one should only adjust the tolerance magnitude based on a statistically valid equation such as CIE94. One should not change l:c or derive a new ellipsoid. © 1996 John Wiley & Sons, Inc.     

Precision in the reproduction of colored coatings

The objective of this study was to apply Hotelling's T²‐statistics to color measurement data of colored coatings. It is described, how outliers can be detected by comparing T² with an appropriate statistical distribution function. As an example, the precision in the reproduction of colored coatings produced in laboratory and prepared by a robot for high‐throughput experimentation was investigated on a turquoise coating. After elimination of outliers the precision of reproduction of the coatings color was determined by the sample color differences to the average color coordinates in CIELAB and DIN99 color spaces as well as with CIEDE2000 color differences. As expected, laboratory experimentation (reproducibility conditions) showed a lower precision of color reproduction as samples prepared with the high‐throughput experimentation device (repeatability conditions).     

Research on the detection of fabric color difference based on T‐S fuzzy neural network

T‐S fuzzy neural network algorithm is used to establish the mapping relationship from the RGB space to the L*a*b* space, which avoids the complex process of color space conversion. Meanwhile, the block method is adopted to detect color difference of dyed fabric that is wide format and wide viewing angle. Color differences in different regions can be calculated with Color Measurement Committee color difference formula based on T‐S fuzzy neural network. Experimental results are in accordance with the spectrophotometer measurement, which proves that T‐S fuzzy neural network algorithm used in real‐time color detection process is effective and feasible. Workers can make corresponding adjustment on‐line according to the deviation to ensure the quality of fabric color and reduce the loss.     

A test of uniformities in the OSA‐UCS and the NCS

In the OSA‐UCS (Optical Society of America–Uniform Color Scales), except for colors on the boundary of the three‐dimensional solid (L, j, g), each color is surrounded by the 12 nearest neighboring colors that are supposed to be perceptually equally different (local uniformity). In the Swedish NCS (Natural Color System), colors are arranged so as to gradually vary in each of the three perceptual attributes: hue, ?; blackness, s; and chromaticness, c. The gradual change in an attribute may correspond to change of color difference from one to the next with a constant step (local uniformity). In each of these color‐order systems, the uniformity was tested by a color‐difference formula d? based on color‐component differences. When a coordinate is fixed (e.g., j in OSA‐UCS, or c in NCS), d? for neighboring pairs turned out fairly constant. However, systematic differences were found between d? in one coordinate and d? in another coordinate. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 277–283, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10162     

Design and study of a color sensitivity function

If we study color reproduction, such as computer color matching or the appraisal of metametric index, we wish to understand the characteristic of color differences that are caused by the object spectral reflectivity change at each wavelength. If we simulate the light source, we wish to know the characteristics of color differences that are caused by change in relative power distribution of the light source at each wavelength; if we simulate a human eye instrument, we wish to know the characteristics of color differences that are caused by change in visual sense of human eyes at each wavelength. So, we define the color‐sensitivity functions of an object, a light source, and human eyes. According to the chromatic theory, the color‐sensitive functions of an object, a light source, and human eyes are defined in the widely used CIE1976 (L*a*b*) color space and color difference.¹ Their mathematical formulae are deduced. The three kinds of color‐sensitive functions are studied systematically and comprehensively in the whole color space. The characteristics of the color‐sensitive functions are summarized, and the mathematical models of the three kinds of color‐sensitive functions can be utilized in some fields such as computer color matching, simulation of a standard light source, and humans viewing a colorimeter. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 118–124, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20089     

Testing the differences between two color measurement probability distributions using Hotelling's T2 test and the permutation test

It is common practice in statistics to test the equality of two population means using, for example, the Student's t test, in the univariate case, or the Hotelling's T² Test in the multivariate case. However, tests on the equality of population means are not well developed for testing the difference between two populations of color measurements. Methods for analyzing populations of spectral reflectance and L*a*b* measurements have been described for applications such as analyzing inter-instrument agreement and repeatability. Methods have also been proposed for the analysis of color differences, but there are little written about techniques for testing whether two samples have the same probability distribution. This article focuses on testing the difference between color measurement probability distributions based on color difference. In addition, a metric is proposed called the threshold for color difference discrimination (TCDD, in units of ΔE), the color difference at which two populations can be considered to have different population distributions. A lower TCDD means smaller color differences between two samples can be resolved. Two parametric tests based on Hotelling's T² test and a nonparametric permutation test were used to determine the TCDD for populations of color measurements with different variances and sample sizes. The TCDD was found to be smaller by tests using the Hotelling's T² statistic, compared with a permutation test performed directly on color difference. It was also found, as expected, that larger sample sizes led to smaller TCDDs, as did smaller population variances.     

Three-dimensional threshold of color-difference perceptibility in painted samples: Variability of observers in four CIE color regions

In four of the five CIE color regions, the correlation of perceptibility of color differences and colorimetric measures is studied for painted samples at threshold. Sample pairs resulting in three-dimensional color differences ranging from zero to just clearly perceptible were used. The variability of color-difference ellipsoids is shown for single observers and for observer groups. Randomisation of mean results by a Monte-Carlo method produces deviation ellipsoids that describe shells of uncertainty inherent in the data. Interobserver and inter-group variability turns out to be widely covered by random noise, but the variances leave some stability of ellipsoid shapes. Color-difference formulas should be able to predict color differences within the shells of uncertainty.     

Comparison of the metrics between the CIELAB and the DIN99 uniform color spaces using dental resin composite material values

The sizes for the perceptible or acceptable color difference measured with instruments vary by factors such as instrument, material, and color‐difference formula. To compensate for disagreement of the CIELAB color difference (ΔE^*_ab) with the human observer, the CIEDE2000 formula was developed. However, since this formula has no uniform color space (UCS), DIN99 UCS may be an alternative UCS at present. The purpose of this study was to determine the correlation between the CIELAB UCS and DIN99 UCS using dental resin composites. Changes and correlations in color coordinates (CIE L*,a*, and b* versus L₉₉, a₉₉, and b₉₉ from DIN99) and color differences (ΔE^*_ab and ΔE₉₉) of dental resin composites after polymerization and thermocycling were determined. After transformation into DIN99 formula, the a value (red–green parameter) shifted to higher values, and the span of distribution was maintained after transformation. However, the span of distribution of b values (yellow–blue parameter) was reduced. Although color differences with the two formulas were correlated after polymerization and thermocycling (r = 0.77 and 0.68, respectively), the color coordinates and color differences with DIN99 were significantly different from those with CIELAB. New UCS (DIN99) was different from the present CIELAB UCS with respect to color coordinates (a and b) and color difference. Adaptation of a more observer‐response relevant uniform color space should be considered after visual confirmation with dental esthetic materials. © 2006 Wiley Periodicals, Inc. Col Res Appl, 31, 168–173, 2006     

Color matching of fiber blends: Stearns‐Noechel model of digital rotor spun yarn

Stearns‐Noechel model was utilized as a primary reference to study color matching principles of digital rotor spun yarn. Three primary colored (red, yellow and blue) cotton fibers were used to spin blended yarns. Spectral reflectance of the two‐component and three‐component samples was measured with data color spectrophotometer. For these samples, the Stearns‐Noechel model parameter M was determined. Four methods were employed to calculate the M value to improve accuracy of the model, 1.Classical method, named as M1; 2.Optimizing the M1 value obtained by the classical method considering the wavelength factor, named as M2; 3.Simplified M2 according to the linear correlation with the wavelength, named as M3; 4. Simplified M2 according to the segmentation correlation with the wavelength, named as M4. The study shows that average color difference of the two‐component decreases from 2.7 to 1.48, and for three‐component samples from 3.32 to 1.66, by using M2 instead of M1. While calculated using M3, the color difference of the two types of samples will be 1.73 and 2.19, correspondingly. This cannot meet color matching needs. As for M4, the average color difference of the two categories will be 1.54 and 1.91, better than the result obtained using M1 and M3, worse than M2.     

Setting tolerances on color and texture for automotive coatings

In the automotive industry, color quality control is increasingly done by reflection measurements. We discuss how color tolerances are set in specifications to suppliers of add‐on parts and to paint suppliers. We mention several factors that often lead to unrealistically tight settings, and therefore to incorrect rejections and unnecessary high productions costs. We show that this is likely to occur when the dE_ab color difference equation is used, or when a strict criterion separating pass from fail is used instead of specifying a “grey area” where instrumental monitoring needs to be followed by visual assessments. Unrealistically, tight tolerances also result from halving tolerances in the supply‐customer chain in an attempt to compensate color variations due to uncontrolled application conditions. Tolerances should be widened further when a gap separates an add‐on part from the car body, making visual discrimination of color differences less critical. Other common situations where tolerances should be widened are the presence of visual texture in effect coatings, the lightness of metallic coatings becoming very high (L*> 100) and measurement geometries close to the gloss angle. Finally, we address the issue that instrumental color tolerances should not be tighter than what is allowed by instrumental reproducibility, repeatability, and inter‐instrument agreement. Accounting for these factors, we provide a set of reasonable values for tolerances on color and on visual texture parameters, based on our own practical experience. But realistic tolerance values depend very much on actual conditions, and should be agreed in tripartite discussions among automotive industry, suppliers of add‐on parts, and paint supplier. © 2012 Wiley Periodicals, Inc. Col Res Appl, 39, 88–98, 2014     

Michromatic scope for enhancement of color difference

A michromatic (microscope plus chromatic) scope is a device that enhances the color discrimination between two spectral color datasets. Three spectral filters are required, instead of the conventional red, green, and blue filters, for the implementation of a michromatic camera. In this study, we describe two approaches to the design of these filters: in the first case, the design is based on the direct optimization of the filter characteristics (transmittance), whereas in the second case, the design is based on the nonnegative tensor factorization (NTF) of the spectral datasets. A michromatic camera can be implemented using these filters along with compatible postprocessing in‐camera firmware. Here, we performed experiments with two color datasets: one comprising skin and vein colors, and one comprising skin and cosmetics colors. These were further divided into a training set and a test set. The filters were defined using the training set, and the operation of the filters was tested and magnified using the test set. Our experiments demonstrated that the proposed approaches are suitable for color discrimination. For the first color dataset, the enhancement produced using the optimized filters was up to 252% of the original value, and the average color difference ΔE was increased from 2.82 to 9.93. NTF and preprocessing further enhanced the ΔE up to 21.84. For the second color dataset, NTF and postprocessing enhanced the ΔE from 4.33 to 29.19. The proposed discrimination enhancement could be physically implemented in a designated digital charge‐coupled device camera with proper filter installation and compatible postprocessing. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

Ultra‐large color difference and small subtense

Color difference calculations are usually applied to match or tolerance of small differences between large (>2°) visual fields. In contrast, we examine here the application of ultra‐large color differences to enhance conspicuousness and discriminability of small (1° subtense or smaller) visual targets, e.g., in visual information displays. We show that CIEDE2000, and color difference metrics based on the OSA Uniform Color Space and CIECAM02 are superior to CIELAB and CIELUV. Considering gray scale only, we show that Whittle's JND metric of achromatic contrast is as good as L* for this purpose, while also modeling contrast polarity and “crispening.” Furthermore, using this JND metric, we replicate Highnote's finding that elongation of small targets affects their apparent contrast. We discuss the perceived fading of color differences when targets become smaller, and suggest practical methods to mitigate the adverse effect on color conspicuousness and discriminability. © 2009 Wiley Periodicals, Inc., Col Res Appl, 2010.