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     

Euclidization of the first quadrant of the CIEDE2000 color difference system for the calculation of large color differences

The calculation of colour distances in the first quadrant of the CIEDE2000 space can be realized now after the author succeeded in working out such calculations in the CIE94 and CMC space in preceeding articles. The new system is presented and then the Euclidean line element is established, from which terms are derived for the new coordinates of lightness, hue, and hue angle. The calculations of colour distances are carried out with the new Euclidean coordinates according to a well‐known method and are demonstrated by examples guided by CIE94 and CMC distances from the preceeding articles. Finally, proposals are given for the eventual improvement of the CIEDE2000 formula. © 2005 Wiley Periodicals, Inc. Col Res Appl, 31, 5–12, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20168     

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     

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     

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     

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     

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

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

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     

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.     

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     

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.     

Uniform colour spaces based on the DIN99 colour‐difference formula

Several colour‐difference formulas such as CMC, CIE94, and CIEDE2000 have been developed by modifying CIELAB. These formulas give much better fits for experimental data based on small colour differences than does CIELAB. None of these has an associated uniform colour space (UCS). The need for a UCS is demonstrated by the widespread use of the a*b* diagram despite the lack of uniformity. This article describes the development of formulas, with the same basic structure as the DIN99 formula, that predict the experimental data sets better than do the CMC and CIE94 colour‐difference formulas and only slightly worse than CIEDE2000 (which was optimized on the experimental data). However, these formulas all have an associated UCS. The spaces are similar in form to L*a*b*. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 282–290, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10066     

Optimization of color reproduction on CRT‐color monitors

In the present experimental study, we quantify the influence of the brightness and contrast levels of a CRT‐color monitor in the color reproduction of 60 Munsell chips distributed throughout the chromatic diagram. The images were captured by two CCD cameras, and the color differences were evaluated after reproducing the chips on a color monitor (the experiment was performed with 3 different monitors) for 9 combinations of brightness‐contrast levels. We evaluated the color differences with 3 different formulas: CIELAB, CIELUV, and CIE94. The results indicate that the optimal settings of a monitor, to minimize the color differences, is a medium or minimum brightness level in combination with a maximum contrast level. This combination ensures a more faithful color reproduction with respect to the original image. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 207–213, 1999     

Application of improved back propagation algorithm in color difference detection of fabric

Color is an indispensable indicator of product quality evaluation. To detect the color difference of fabrics, the Levenberg–Marquardt optimized back propagation (BP) algorithm is adopted to extract the color feature values of fabric images. First, RGB values are three inputs of BP neural network, and L*a*b* values measured by spectrophotometer are three outputs of the network. The trained network can obtain the corresponding L*a*b* values conveniently. Then the color difference can be calculated through color difference formula and the characteristic values obtained above. Finally, compared with the color difference calculated by the spectrophotometer, the most appropriate formula can be selected from the four formulas listed in the article (CIEDE2000, CMC, CIE94, and CIELAB) to acquire satisfying results. The experimental results reveal that the color difference of fabrics can be detected with a high accuracy and efficiency with this method. Plenty of duplication workloads and some complex conversion formulas can be avoided, making the acquirement of color difference more efficiently. © 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 311–317, 2015     

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     

An evaluation of the Hunt94 color appearance model under different light sources at low photopic to low mesopic light levels

Color appearance models allow for the quantification of color appearance under a variety of viewing conditions. Such models may ultimately provide a measure for accurate assessments of the color‐rendering properties of light sources. This article evaluates the Hunt94 color appearance model using a new set of color‐naming and magnitude‐rating data. At one photopic level (10 cd/m²), the evaluations showed that for a xenon lamp and an enhanced metal halide lamp that have chromaticities and spectra close to an equal energy spectrum, the Hunt94 model provided good predictions of the primary and secondary color names and hue magnitudes for a wide range of color chips under the two illuminants. However, for other light sources the Hunt94 model predictions deviated considerably from the evaluations. Three modifications were applied to the Hunt94 color appearance model to predict color‐naming and magnitude‐rating data better for all light sources. The modified Hunt94 model gave good predictions (correlation coefficients r ～ 0.95) of the secondary hue magnitude of the color chips used in the experiment at photopic light levels (10 cd/m² and 1 cd/m² background luminances) under “white” light sources. However, the modified model was still unable to predict color appearances at low mesopic light levels (0.1 cd/m² and 0.01 cd/m²). © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 107–117, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20088     

Effect of luminance of samples on color discrimination ellipses: Analysis and prediction of data

Four data sets are analyzed to quantify three effects of luminance of samples on chromaticity discrimination: on ellipse area, axis dimensions (a and b), and a/b ratio. Ellipses for aperture, surface, and simulated surface colors in CIE 1931 and 1964 x, y, Y color spaces are shown to reduce axis dimensions with higher luminance by different functions for the major and minor axes. Reduction is greater for major than minor axes, thus improving ellipse circularity. The functions plot straight lines in log‐log scale as power law equations, except luminances below 3 cd/m². We give formulae to predict a and b axes, a/b ratio, and ellipse area for almost any luminance in x, y, Y spaces. Effect of luminance is remarkable on ellipse area, which on average halves with every 3.5 times higher luminance. To illustrate the substantial effects of luminance, RIT‐DuPont ellipses are predicted for three levels of equal luminance at 42, 212, and 2120 cd/m². In the latter, ellipses are much smaller and are nearer circular than in the former. Higher luminance is known to improve color discrimination, so reduced ellipse area is to be expected but does not occur in CIELAB and DIN99 spaces because of lack of luminance‐level dependency. We discuss our results' implications on uniform color space. Weber fraction ΔY/Y indicates brightness discrimination decreases with increasing luminance and is thus independent of chromaticity discrimination. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 186–197, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20107     

A quantitative network model for color categorization

To clarify the higher‐order mechanism of human color perception, we measured the color appearances of 78 colored lights by an elemental color‐scaling method and by a categorical color naming method. The colors covered nearly the entire CIE 1931 xy‐chromaticity diagram with three different surrounds. The results showed that firm basic color zones derived by categorical color naming can be mapped with no overlap in an opponent‐color response space. We propose a network model with a threshold selector, maximum selectors, and multiplication units with gain factors to generate the categorical color responses quantitatively from the elemental color responses. The model can predict the categorical color naming results in different surround conditions with no change of parameters. This suggests that a nonlinear color vision mechanism for color categorization exists between the primary visual cortex (V1) and the inferior temporal cortex (IT) in the human brain. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 225–232, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10060     

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