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.     

Visual determination of hue suprathreshold color-difference tolerances

This research extends the previous RIT-DuPont research on suprathreshold color-difference tolerances in which CIELAB was sampled in a balanced factorial design to quantify global lack of visual uniformity. The current experiments sampled hue, specifically. Three complete hue circles at two lightnesses (L* = 40 and 60) and two chroma levels ( = 20 and 40) plus three of the five CIE recommended colors (red, green, blue) were scaled, visually, for hue discrimination, resulting in 39 color centers. Forty-five observers participated in a forced-choice perceptibility experiment, where the total color difference of 393 sample pairs were compared with a near-neutral anchor-pair stimulus of 1.03 A supplemental experiment was performed by 30 additional observers in order to validate four of the 39 color centers. A total of 34,626 visual observations were made under the recently established CIE recommended reference conditions defined for the CIE94 color-difference equation. The statistical method logit analysis with three-dimensional normit function was used to determine the hue discrimination for each color center. A three-dimensional analysis was required due to precision limitations of a digital printer used to produce the majority of colored samples. There was unwanted variance in lightness and chroma in addition to the required variance in hue. This statistical technique enabled estimates of only hue discrimination. The three-dimensional analysis was validated in the supplemental experiment, where automotive coatings produced with a minimum of unwanted variance yielded the same visual tolerances when analyzed using one-dimensional probit analysis. The results indicated that the hue discrimination suprathresholds of the pooled observers varied with CIELAB hue angle position. The suprathreshold also increased with the chroma position of a given color center, consistent with previous visual results. The results were compared with current color-difference formulas: CMC, BFD, and CIE94. All three formulas had statistically equivalent performance when used to predict the visual data. Given the lack of a hue-angle dependent function embedded in CIE94, it is clear from these results that neither CMC nor BFD adequately predict the visual data. Thus, these and other hue-suprathreshold data can be used to develop a new color-difference formula with superior performance to current equations. © 1998 John Wiley & Sons, Inc. Col Res Appl, 23, 302–313, 1998     

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     

Publications Sponsored by the Colour Measurement Committee—III

Two further sets of results, including data from measurements made with several tristimulus colorimeters (Colormaster and Color-Eye) and visual assessments by a relatively large number of observers, have been obtained for (a) a series of matt paint surfaces and (b) a series of gloss paint surfaces in approximately the same region of colour-space as the wool and viscose rayon samples discussed previously (l). All samples in any set have been assessed by a ranking method, with reference to a standard, and a statistical approach has been used to provide a quantitative estimate of the visual spacing. The number of colour-difference equations employed has been increased to include the four equations (1964 CIE; Glasser Cube Root; MacAdam Modified Friele; Munsell Renotation) recommended by the CIE for further study. In all cases an estimate has been made of the degree of correlation between instrumental and visual results for all samples (wool, viscose rayon and matt and gloss paints). The established equations all show poor correlation with the visual results, whereas an equation similar to that reported (l) in Part II of this series, which places much less emphasis on lightness weighting, provides a reasonable fit for all samples. There is little evidence that any significant differences exist in the assessment by colourists of paint and textile surfaces, although the reproducibility of instrumental measurements is much better for the former. The results from a single instrument and, in particular, the Colormaster are at least as reliable as the assessments of a single observer and are more reproducible. These and other relevant points are discussed in some detail.     

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     

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     

The new deviate visual functions improving the instrumental estimation on the visual color difference for the metamers with about 1° field size

Although the CIE1931 and 1964 color matching functions have been used in color specification for decades, many researchers, from Allen in 1970 to Hu and Houser in 2006, have found that there still exists a great visual mismatch on the discrimination of color difference as in terms of the CIE color matching functions. Hence, some significant error would be made on color specification due to employing the CIE1931 and 1964 color matching functions. Therefore, six color difference formulae developed from different experimental methods are used to derive various deviate visual functions (DVFs) respectively, and to investigate the effect of these DVFs on the performance of the color difference formulae tested in estimating visual color difference. The results indicate that the performance of the color difference formulae in estimating color difference is significantly improved by the deviate visual functions derived in this study. The CIE94 color difference formula has the best performance in predicting the total visual color difference (ΔV_T) using the DVFs and DVFIIs having the mean values 29 and 27 in PF/4 unit, respectively, while the CMC(l:c) the worst the ones 37 and 38. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 115–127, 2009     

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     

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).     

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.     

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.     

Improvement of CMC upon CIEDE2000 for a new experimental dataset

This communication reports additional analyses of the dataset presented in the article “A preliminary comparison of CIE color differences to textile color acceptability using average observers” by Mangine, Jakes, and Noel © 2006 Wiley Periodicals, Inc. Col Res Appl, 31, 239–241, 2006     

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.     

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     

Effect of texture on color variation in inkjet‐printed woven textiles

Inkjet‐printed textiles are influenced by a wide range of parameters due to highly diverse textile structures and the resulting textures. The goal of this study is to understand the effect of texture on color appearance in inkjet‐printed woven textiles. Cotton‐woven samples were constructed with nine different weave structures. Each sample was digitally printed with identical squares of primary colors cyan, magenta, and yellow and secondary colors red, green, and blue. The amount of ink applied was controlled consistently with an image editing software. CIE L* values were calculated from the measured reflectance. 25 observers ranked the perceived texture and color lightness of each sample. Perceived visual texture and perceived color lightness scales were estimated from the rankings using the rank order method. The measured CIE L* values and the scale of perceived lightness were positively related for the primary and secondary colors. Instrumental measurements of the textile surface characteristics were positively related to the visual scale. Texture was demonstrated to cause a measurable effect on color results in inkjet printing, both using instrumental and perceptual measures. To investigate if the color differences were substantial enough to cause “out of tolerance” ratings in textiles based on common textile industry color acceptance procedures, color differences among the samples were calculated and compared to a reference sample. Results demonstrated that color variation due to texture was sufficient to lead to rejection of a printed color in comparison to a color specification. © 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 297–303, 2015     

Testing CIELAB‐based color‐difference formulas

The CMC, BFD, and CIE94 color‐difference formulas have been compared throughout their weighting functions to the CIELAB components ΔL*, ΔC*, ΔH*, and from their performance with respect to several wide datasets from old and recent literature. Predicting the magnitude of perceived color differences, a statistically significant improvement upon CIELAB should be recognized for these three formulas, in particular for CIE94. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 49–55, 2000     

Some aspects of the visual scaling of large colour differences

The formulation of a metric to provide numbers that correlate with visually perceived colour differences has proved a very difficult task. Most early experimental work was concerned with just-perceptible colour differences. Later the concept of perceptibility was expanded to acceptability, it being argued that many industrial tolerances were larger than just-perceptible. This led naturally to the concept of large colour differences and the question as to whether the current CIE colour-difference formulae, specified as appropriate for just-perceptible differences, can be applied to larger differences than those concerned with, for instance, colour matches experienced in the fabric dyeing industry. This article investigates the application of four colour-difference formulae to visual scaling of large colour differences between photographically prepared reflection colour samples at approximately constant lightness. It is shown that the scaling of colour differences depends on the directions of hue and chroma differences of a test sample when compared with a reference. It is also shown that, of the four candidate colour-difference metrics, the modified CIE 1976 L*a*b* colour difference, referred to as CIE1994 or , correlates best with visual scaling. © 1997 John Wiley & Sons, Inc. Col Res Appl, 22, 298–307, 1997     

An Analysis of the HATRA Acceptability Data

Data on the acceptability as matches of textile samples determined and published by the Hosiery and Allied Trades Research Association (HATRA) are analyzed by near-optimal fitting of ellipsoids to the colorimetric data in CIE color space. The resulting ellipsoids are compared to those of similar data published earlier.     

Color scales in simulated daylight

The pigmentation plan used for production of the color cards made available by the Optical Society of America (OSA) for its Committee on Uniform Color Scales (UCS) was designed in such a manner that the color scales should, within the production tolerances, appear uniform in all phases of daylight. The production specifications were based on D₆₅ of the Commission International de L'Eclairage (CIE) and the CIE supplementary observer (1964) for 10° visual-field subtense. To test for the intended invariance of uniformity of the scales in daylight, for normal observers, the effects on color differences between all nearest neighbors of the OSA colors have been studied for CIE Illuminant C with the 1931 observer, and for a “daylight” fluorescent luminaire (color temperature 6500 K) with both the 1931 and 1964 CIE observers. Although the colorimetric specifications (Y, x, y) of each color card are different for those three illuminant + observer combinations, the color differences computed with the formula of the OSA-UCS committee are, within the production tolerances, unchanged. The purpose of this article is to show how well the aim and expectation is fulfilled—that the uniformity of color differences between nearest neighbors in the scales of the OSA-UCS colors be essentially unchanged for normal observers and for ordinary variations of the quality of natural and artificial daylight. This invariance is found, even for daylight-quality fluorescent-lamp light.