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 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     

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     

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     

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     

Evaluation of Uniform Color Spaces Developed after the Adoption of CIELAB and CIELUV

Since the adoption of the color spaces CIELAB and CIELUV by the CIE in 1976, several other uniform spaces have been developed. We studied most of these spaces and evaluated their uniformity for small as well as larger color differences. Therefore, several criteria have been defined based on color discrimination data and appearance systems. The main difference between color spaces based on discrimination data and spaces that model appearance systems is reflected in a different size of the chroma distance unit compared with the lightness unit. If spaces based on the same kind of data (discrimination data or appearance systems) are compared with each other, they are all almost equally uniform. BFD (l:c), for example, is said to be more uniform than CMC(l:c), but, based on confidence intervals of 65%, there is no significant difference between them. If the proposed color difference formula of the CIE is compared with these distance functions, it also performs equally well. The SVF space and OSA 90 space on the other hand should be better than OSA 74. However, as opposed to what was expected, OSA 74 is slightly better; but, also in this case, the difference between the spaces is insignificant.     

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     

Linearity and additivity of small color differences

The functional relation of visual to colorimetric scaling of small color differences is needed for a realistic interpretation of the perceptual magnitude of a measured color difference. Linearity is usually assumed and differences are expressed in threshold units without adjustment. an experimental plan is described that provides for the application of gray-scale assessment to visual judgments under controlled parameters. Gray scale and test colors were produced from a two-component acrylic lacquer system. A green color center (CIE green) was chosen for a first test with color differences extending from the center in the directions of hue, saturation/chroma, and lightness in steps ranging from -5 to + 5 thresholds. Thirteen observers made 4 judgments of each of 78 color-difference pairs. the resulting scales were typically linear but increasing less steeply than threshold stepping; however, Fstatistics showed some inhomogeneous effects. Scales along the main color directions tended slightly to subadditivity. the vector model of color difference better predicted the magnitude of diagonal jumps between two color directions than did the city-block model. Relations to some recent color-difference formulae were studied and the CIE TCI-29 formula was found to be a good predictor for this color center. © 1995 John Wiley & Sons. Inc.     

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     

Visual determination of suprathreshold color-difference tolerances using probit analysis

As part of a research program to improve the relationship between visual and numerical color-difference evaluation for industrial colorimetry, a color-difference tolerance data set for fitting and testing of color-difference metrics has been extended to include 156 individual color-tolerance determinations. These tolerances were designed to sample 19 color centers over a surface color gamut with balanced sampling of lightness and chromaticness differences. The tolerance determination procedures emphasized accurate estimation of population visual color-difference response and rigorous estimation of tolerance precision. Tolerance accuracy was confirmed by excellent agreement of these results and the majority of previous experiments on five color centers selected for CIE color-difference evaluations. The average uncertainty of the tolerance determinations was ± 11% of the tolerance value at a 2 ó level (95% confidence interval). The completed data set is suitable for estimating the parameters of color-difference metrics or testing the performance of such metrics. The color tolerances indicated the systematic lack of uniformity of the CIELAB space, in general agreement with previous experiments. A simple modification of the CIELAB color-difference metric was shown to account for much of the systematic lack of uniformity.     

Distance metrics for very large color differences

Small, supra-threshold color differences are typically described with Euclidean distance metrics, or dimension-weighted Euclidean metrics, in color appearance spaces such as CIELAB. This research examines the perception and modeling of very large color differences in the order of 10 CIELAB units or larger, with an aim of describing the salience of color differences between distinct objects in real-world scenes and images. A psychophysical experiment was completed to compare directly large color-difference pairs designed to probe various Euclidean and non-Euclidean distance metrics. The results indicate that very large color differences are best described by HyAB, a combination of a Euclidean metric in hue and chroma with a city-block metric to incorporate lightness differences.     

Hue uniformity and the CIELAB space and color difference formula

The hue uniformity of the CIELAB system is investigated using a hue circle of Munsell colors at value 6 and chroma 14 and experimentally determined hue coefficient data. CIELAB hue differences for equal Munsell hue increments are found to vary up to nearly a factor 4, and hue coefficients differ from the experimentally determined ones by up to 40% at certain wavelengths. Dominant wavelengths assigned by the CIELAB system to individual Munsell hues are found to vary up to 35 nm from those of the Munsell Renotations. Four other color space systems are compared with widely differing but comparable results. The CIE 2° color-matching functions are adapted to result in a set of opponent-color functions accurately representing the Munsell Hue and Chroma data. A call is made for the experimental determination of the “standard hue observer” as a step toward an improved color space/color-difference formula. © 1998 John Wiley & Sons, Inc. Col Res Appl, 23, 314–322, 1998     

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.     

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     

Performance testing of color-difference metrics using a color tolerance dataset

A color-difference dataset was developed for testing the performance of color metrics. The dataset comprises 45 color-difference vectors varying in five directions at nine color centers under conditions typical of commercial color decisions. Probit analysis was used to estimate the parameters of the population distribution of tolerances for each vector. In addition to estimating the median tolerance, the anlysis allows one to estimate the uncertainty of a tolerance and to test the adequacy of the underlying model tolerance distribution. The median tolerances were used to specify 45 color-difference pairs with equal visual color-difference magnitudes. The performance of eight color-difference metrics was compared using the normalized standard deviation of the color differences of the visually equal difference pairs as a measure of uniformity. A bootstrap statistical technique was used to quantify the variation in performance with varying samples of color centers and color-difference directions and to determine the significance of observed differences in uniformity performance. Some metrics based on weighted CIELAB dl*, dC*, dH* color-difference components had significantly superior performance compared to the CIE recommended color-difference metrics.     

Suprathreshold color-difference ellipsoids for surface colors

The RIT-DuPont visual color-difference data [Color Res. Appl. 16, 297–316 (1991)] have been used to estimate contours of equal color-differences (ellipsoids) at 19 color centers, in CIELAB and x, y, Y/100 color spaces. The ellipsoid fits are better in the CIELAB space than in x, y, Y/100, since the design of the RIT-DuPont experiment emphasized directional balance in CIELAB. The ellipsoids estimated are hardly tilted with respect to L* or Y/100, and they appear to be in overall good agreement with those reported for object colors in recent publications. From the characteristics and accuracy of the RIT-DuPont experiment, the current ellipsoids can be considered highly reliable and representative of color discrimination under the observational conditions employed, these closely following the “reference conditions” recently suggested by the CIE for industrial color-difference evaluation [Color Res. Appl. 20, 399–403 (1995)]. © 1997 John Wiley & Sons, Inc. Col Res Appl, 22, 148–155, 1997     

Hue scale adjustment derived from the Munsell system

Hue scale adjustment factors have been determined for CIELAB using the Munsell system. They have been found to vary significantly as a function of hue angle. A formula has been derived based on the 2° observer color‐matching functions that models the chroma scale of the Munsell system much more accurately than CIELAB using the same opponent color relationships. In this formula, hue differences can be calculated from hue angle differences, hue scale adjustment factors, and chroma. The hue scale adjustment factors based on hue angle required for the Munsell system have been derived. The variability by hue angle of these factors is such that an analytical hue scale adjustment function as those in CMC or BFD appears insufficient. The adjustment factors are compared to those recently derived by Qiao and coworkers. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 33–37, 1999     

Modified CIELAB formula tested using a textile pass/fail data set

The proposed new color-difference formula of CIE TC 129, which is a modified version of CIELAB, was tested with a recently published data set of textile pass/fail judgments. Goodness of fit is improved, if the parameter of lightness is set near 2, and if, additionally, a weight function for lightness is defined that reduces the weight of a lightness difference with lightness level in relation to chroma or hue scaling. © 1994 John Wiley & Sons, Inc.     

Parametric effects on surface color-difference evaluation at threshold

Experiments on thresholds of perceptible color-difference at CIE color centers have been extended for the parametric effects of the lightness of an achromatic surround and of a separating gap between a pair of painted specimens. Components of perceived color-difference (hue, chroma, lightness) approximately could be assigned to geometric elements of threshold ellipsoids and used for component analysis. A study of ellipsoid and city-block modelling revealed ellipsoid to be slightly better. An increase of total threshold by changed lightness of the achromatic surround was found only in the case of the dark CIE Blue, but in every case a gap increased threshold the darker the CIE color center. The results can be used for a correction in color-difference evaluation.     

Defining a practical method of ascertaining textile color acceptability

The relations between supplier and customer are today more important than they have ever been. However, conflicts do sometimes arise between them, deriving from differences in the judgment of color matchings. Colorimetry's role is precisely to avoid such conflicts through instrument measurements. A study was made on the pass/fail problems, based on 1,830 measurements and observations made in industrial textile firms, followed by 350 new tests. Human judgments are as liable to errors as instrument measurements, because the surface effects are often misleading for the observer. This study proposes a sorting method that combines the differences deriving from measurements by colorimetric instruments and by visual judgment. The Color Measurement Committee (CMC) equation, widely used in the textile field, has given excellent practical results. The CIE94 equation, which uses the same principle of ellipsoid tolerance, offers a mathematical simplification as well as further information on the sample observation conditions in order to determine color differences. Nevertheless, these two equations are different, and the CIE94 indexes must not be interpreted with the same tolerances as those of the CMC. Pending the CIE recommendations concerning textile samples, new acceptability tolerances should be redetermined for the CIE94. This article presents an innovative way of calculating metameric indexes that, when coupled with acceptability equations, allow the agreement rate between visual judgment and automatic selection to be increased.