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     

Categorical formation of Mandarin color terms at different luminance levels

This study presents the categorical formation of a set of Mandarin color terms on the International Commission on Illumination (CIE) 1931 chromaticity diagram across six luminance levels. This article conducted a study that employed 44 native Mandarin speakers to perform a force–choice sorting task. The Mandarin color terms for sorting were determined by a free‐recall pretest and are consistent with basic color terms proposed by Berlin and Kay. The square‐sampled stimuli were generated by evenly sweeping the x–y diagram of 5, 10, 25, 50, 100, and 170 cd/m² planes. The categorical sorting results and response time (RT) measurements suggest that: (1) the concepts of green, blue, purple, and gray stably exist at most luminance levels. The voting RT for the green, blue, and purple categories is particularly short. (2) Red, orange, yellow, and pink are highly luminance‐dependent; these can be identified without difficulty only at some restricted luminance levels. (3) The chromaticity areas designated as orange, partial yellow, red, and pink are recognized as brown when the luminance level decreases. (4) Brown and gray serve as representations of two distinct tints in the low saturation condition. (5) The location of boundaries between blue and green are remarkably different than those in a similar study that employed Japanese speakers. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2011.     

Comprehensive color solutions: CAM16, CAT16, and CAM16‐UCS

The CIECAM02 color‐appearance model enjoys popularity in scientific research and industrial applications since it was recommended by the CIE in 2002. However, it has been found that computational failures can occur in certain cases such as during the image processing of cross‐media color reproduction applications. Some proposals have been developed to repair the CIECAM02 model. However, all the proposals developed have the same structure as the original CIECAM02 model and solve the problems concerned at the expense of losing accuracy of predicted visual data compared with the original model. In this article, the structure of the CIECAM02 model is changed and the color and luminance adaptations to the illuminant are completed in the same space rather than in two different spaces, as in the original CIECAM02 model. It has been found that the new model (named CAM16) not only overcomes the previous problems, but also the performance in predicting the visual results is as good as if not better than that of the original CIECAM02 model. Furthermore the new CAM16 model is simpler than the original CIECAM02 model. In addition, if considering only chromatic adaptation, a new transformation, CAT16, is proposed to replace the previous CAT02 transformation. Finally, the new CAM16‐UCS uniform color space is proposed to replace the previous CAM02‐UCS space. A new complete solution for color‐appearance prediction and color‐difference evaluation can now be offered.     

Investigation on effects of adapting chromaticities and luminance on color appearance on computer displays using memory colors

CAT02, the most widely used chromatic adaptation transform to characterize the chromatic adaptation mechanism in the human visual system, includes a factor D to characterize the degree of chromatic adaptation. This factor, however, is only determined by the luminance level of the adapting field and surround. This study was designed to investigate how the change of adapting chromaticities and the simultaneous changes of adapting chromaticities and luminance affect the degree of chromatic adaptation and color appearance on computer displays. The human observers adjusted the color appearance of various familiar objects and cubes on different display backgrounds. A higher degree of chromatic adaptation was found when using familiar objects, which was likely due to the cognitive mechanism. Both the adapting chromaticities and luminance significantly affected the degree of chromatic adaptation, with a lower degree under an adapting condition with a lower adapting correlated color temperature and a lower adapting luminance. In addition, the effect of adapting luminance on colorfulness (known as the Hunt Effect) was likely to be overpredicted in CAM02-UCS, which merits further investigations.     

Preprocessing to CIECAM02 input color with chromatic background

A preprocessing to CIECAM02 input color for color appearance prediction was proposed. In this study, 8640 color appearance matching pairs (NCS color charts with red, green, yellow, and blue backgrounds in a light booth and their reproductions with gray background on a CRT screen) were obtained by psychophysical experiment using the simultaneous‐binocular technique. Because only the lightness of background is included in CIECAM02, a color inducing vector based on opponent‐colors theory was introduced to preprocess CIECAM02 inputs, so that CIECAM02 may predict the corresponding color of an input color with chromatic background as well. By data fitting, a color preprocessing formula describing a relationship between the color inducing vector and the NCS chromaticness was conducted. Furthermore, the formula's performance was tested and the results showed that it was good for implementing the color appearance prediction of input colors with different chromatic backgrounds.© 2006 Wiley Periodicals, Inc. Col Res Appl, 32, 40–46, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20287     

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     

Comments: Number of perceivable object color stimuli

M. Brill, in his comments “Maximum number of discriminable colors in a region of uniform color space,” offers a different calculation method from that used by R. G. Kuehni in “How many object colors can we distinguish?,” one based on close‐packing of just noticeable difference spheres. The number per just noticeable difference (JND) sphere is lower than that derived in Kuehni's study. Based on the resulting number of close‐packed JND spheres in the CIECAM02/D65 object color solid and Brill's described multiplier of 5.923 potential stimuli within a JND sphere, the resulting number of distinguishable color stimuli is 9.114 million. © 2016 Wiley Periodicals, Inc. Col Res Appl, 00, 000–000, 2016     

Color vision model of macLeod and Boynton

MacLeod and Boynton started off with the assumption that the fundamental blue falls on the x' axis of Judd's 1951 chromaticity diagram. This leads to a constant luminance diagram in which the lines that converge at the fundamental blue in Judd's diagram are parallel. MacLeod and Boynton tried to solve this problem by a slight change in one of the constants in the transformation equations. It turns out that what this does is to shift the position of the alychne on Judd's diagram so that it does not coincide with the x' axis. The blue fundamental no longer lies on the alychne. This makes it possible to derive a constant luminance chromaticity diagram in which the fundamental blue falls at one of the corners. After having created this new diagram, they used it to formulate a theory of color vision in which the blue cones contribute nothing to luminance. This procedure needs to be understood because it can be used to convert any theory of color vision in which all three cones contribute to luminance to one in which only two contribute to luminance. This has nothing to do with having the blue fundamental fall on the x' axis. A more serious problem is that Judd has made an error in his assessment of the luminosity coefficients and the concepts of MacLeod and Boynton need to be reformulated in terms of the CIE 1931 chromaticity diagram.     

Visual determination of hue suprathreshold color‐difference tolerances using CRT‐generated stimuli

Suprathreshold hue color‐difference tolerances were measured at four color centers using CRT‐generated stimuli. The tolerances, defined using CIELAB, were measured using two different methods of presentation. In the Absolute Experiment, the stimuli were presented at luminance levels that matched those of the previous object‐color experiments, so that the CRT stimuli were nearly metameric to the originals. In the Relative Experiment, the white point of the monitor was defined as L* = 100 at a corresponding chromaticity to the object‐color viewing environment, but at a lower luminance level. The results from these two experiments followed the same general trends; however, they were significantly different from each other for three of the four color centers. The same trends were seen in the object‐color results, although neither CRT experimental condition produced tolerances that were conclusively more similar to the object‐color results than the other. The feasibility of the use of the CRT has been demonstrated. It is likely that parametric effects of stimulus presentation are the cause of the differences in results among the different experiments, as opposed to differences in the mode of appearance. These parametric effects can be studied more quickly and economically using a computer‐controlled CRT display. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 164–176, 1999     

Quantitative camouflage paint selection for the CH‐47F helicopter

We have determined optimal minimum‐conspicuity monocoat paint colors for the CH‐47F Chinook helicopter, viewed photopically against forest, desert, and sky backgrounds. Our methodology combines use of a validated spectroradiometric model for rigorous 3D signature prediction with statistics of varying background fields and a CIE color difference metric. The study considered a large subset of the Federal Standard 595 (FS595) paint inventory. Each paint color was rigorously modeled with bidirectional reflectance distribution function scattering properties to match existing army paint and spectral reflectances to match spectrophotometer measurements of FS595 reference samples. We devised and validated a method to impute statistical variation in background radiances over environmental conditions consistent with the aircraft radiometric computations. Using a visual jury, we informally calibrated the CIE 1994 color difference formula (which gauges both luminance and chromaticity contrast) to gauge how each paint performed against each background, for varying range, view direction, and sun location. The statistical dispersions in performance were summarized for the CH‐47F Program Manager, who selected the best overall paint for the CH‐47F fleet. We found paints that were optimized to a specific background (forest, desert, etc.) yielded enhanced performance against those backgrounds, as would be expected, and that those paints were better than the paint used on CH‐47s in the current US inventory. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 406–416, 2009     

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     

Effects of luminance,wavelength and purity on the color attributes: Brief review with new data and perspectives

A color stimulus may be characterized by three psychophysical dimensions (luminance, dominant wavelength, and purity), whose corresponding color attributes are lightness, hue, and chroma/colorfulness. The 3 × 3 matrix gives nine basic effects of the psychophysical dimensions on the color attributes (e.g. the effect of luminance on hue), but there are 49 possible combinations as more complex effects (e.g. the effect of luminance on hue and chroma, i.e. on chromaticity). Researching and quantifying such effects enables modelling of the underlying neural mechanisms and of color appearance. Using a simple nomenclature to identify the effects (e.g. Ph denotes the effect of Purity on hue), this paper briefly reviews and interrelates 15 of the commonest effects, giving new data or new graphical perspectives to clarify or fill gaps in the literature. Contrast and no‐contrast effects (stimuli viewed simultaneously or singly, respectively) are differentiated. © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 208–222, 2007     

Model of saturation and brightness: Relations with luminance

The model is simple: For flicker luminance stimuli and maximum purity, the hue cycle's relative luminance (computed from CIE data) is reciprocal to relative saturation. Brightness/luminance ratio B/L is proportional to relative saturation S, i.e., B/L = 1.5 S^1/4. S times B/L ratio gives relative saturation for brightness stimuli; just as relative luminance times B/L ratio gives brightness. Predictions for any purity agree with data on saturation discrimination, color appearance in CIE space, B/L, and CIE brightness V_b. Predictions support Hunt's concept of “colorfulness” and indicate its causal role in proporitionality of S and B/L.     

Relationship between brightness/luminance ratio and additivity‐law failure

The degree of additivity‐law failure of a mixture color consisting of two component chromatic colors has very complex characteristics depending on the used component colors and their mixing conditions. It is significantly affected by the mixture‐color chromaticity and by the brightness/luminance ratio at the chromaticity. A simple relationship was derived between the following quantities: degree of additivity‐law failure, additivity‐law luminance (luminance of the mixture color derived by postulating additivity law), and brightness/luminance ratio at the chromaticity of the mixture color. This relationship can be applied to any additivity‐law failure experiment and any formula on brightness/luminance ratio. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 185–190, 2002; Published online in Wiley Interscience (www.interscience.wiley.com). DOI 10.1002/col.10045     

Testing the performance of CIECAM02 from 100 to 3500 cd/m2

Color appearance models were developed to characterize the color attributes of stimuli under different viewing conditions based on data collected through magnitude estimation or color matching experiments. Although human beings experience very high light levels under daylight and the reproduction of colors under daylight is important in the color and imaging industries, the existing color appearance models were developed based on the data that were collected under the conditions with luminance levels below 700 cd/m² due to the lack of facilities to produce stable illumination at high light levels. A recent study investigating color preference of an artwork under a wide range of light levels from 20 to 15 000 lx suggested that CIECAM02 cannot accurately characterize the color appearance under extremely high light levels. This study was designed to directly test the performance of CIECAM02 from 100 to 3500 cd/m². Human observers performed color match for four hues under a series pairs of adapting conditions with a haploscopic viewing condition. It was found that CIECAM02 had the best performance in characterizing the hue angles but the worse performance in characterizing the brightness with a maximum underprediction around 200% across a wide range of luminance. This was mainly due to the fact that CIECAM02 was developed based on the data collected under relatively low adapting luminance levels. The color appearance model that was proposed to use the adapting luminance levels in characterizing the cone compression in the postadaptation process was found to have a much better performance in characterizing the brightness.     

Categorized color space on CRT in the aperture and the surface color mode

The study was made for structure of categorized color space in the aperture and the surface color modes. The color appearances of two modes were reproduced on a CRT display with or without a surround configuration. Subjects made categorical color naming with 11 basic color terms. The (x,y,L) color space divided with these terms showed structural difference between the two modes. This result indicates that color is categorized by only chromaticity in the aperture color mode but by luminance and chromaticity in the surface color mode. © 1993 John Wiley & Sons, Inc.     

Brightness-to-luminance ratio of colored light in the entire chromaticity diagram

Brightness-to-luminance (B/L) ratios based on the CIE 1924 V (λ) for 195 test stimuli equally sampled from the whole area of the CIE1976(u′, v′) chromaticity diagram were measured for four color normal observers. The results of two observers were similar to results in previous studies in that the B/L ratio increases as purity of the stimulus increases. However, the results of the other two observers showed very low B/L ratios, especially in the reddish region. The B/L ratios based on each observer's sensation luminance were also calculated. Although the contour lines of equal B/L ratio become less atypical for the latter two observers, they still showed low B/L values compared to typical results. Large individual differences of the B/L ratio in the whole area of the chromaticity diagram were indicated. © 1998 John Wiley & Sons, Inc. Col Res Appl, 23, 274–287, 1998     

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     

Chromatic luminance,colorimetric purity,and optimal aperture‐color stimuli

Chromatic luminance (i.e., luminance of a monochromatic color) is the source of all luminance, since achromatic luminance arises only from mixing colors and their chromatic luminances. The ratio of chromatic luminance to total luminance (i.e., chromatic plus achromatic luminance) is known as colorimetric purity, and its measurement has long been problematic for nonspectral hues. Colorimetric purity (p_c) is a luminance metric in contrast to excitation purity, which is a chromaticity‐diagram metric approximating saturation. The CIE definition of p_c contains a fallacy. CIE defines maximum (1.0) p_c for spectral stimuli as monochromatic (i.e., optimal) stimuli, and as the line between spectrum ends for nonspectrals. However, this line has <0.003 lm/W according to CIE colorimetric data and is therefore effectively invisible. It only represents the limit of theoretically attainable colors, and is of no practical use in color reproduction or color appearance. Required is a locus giving optimal rather than invisible nonspectral stimuli. The problem is partly semantic. CIE wisely adopted the term colorimetric purity, rather than the original spectral luminance purity, to permit an equivalent metric for spectrals and nonspectrals, but the parameter of equivalence was never clear. Since 1 p_c denotes optimal aperture‐color stimuli for spectrals, arguably 1 p_c should denote optimal stimuli consistently for all stimuli. The problem reduces to calculating optimal aperture‐color stimuli (“optimal” in energy efficiency in color‐matching) for nonspectrals, shown to comprise 442 + 613 nm in all CIE illuminants. This remedy merely requires redefinition of 1 p_c for nonspectrals as the line 442–613 nm, and gives meaningful p_c values over the hue cycle allowing new research of chromatic luminance relations with color appearance. © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 469–476, 2007     

Color appearance and color connotation models for unrelated colors

The purpose of this research is to investigate the color appearance and color connotation of unrelated colors. To investigate color appearance (i.e., brightness, colorfulness, and hue) for unrelated colors, 22 observers have answered their color appearance for 50 unrelated color stimuli using the magnitude estimation method. Perceptual data obtained by the experiment is compared with the color attributes data estimated by unrelated‐color appearance models, CAM97u and CAM02u. It is found that both models perform reasonably well but the performance of CAM02u is better than that of CAM97u. For investigating color connotation for unrelated colors, 32 observers have judged their color connotation for the 50 unrelated color stimuli using the 10 color connotation scales (i.e., “Warm – Cool,” “Heavy – Light,” “Modern – Classical,” “Clean – Dirty,” “Active – Passive,” “Hard – Soft,” Tense – Relaxed,” “Fresh – Stale,” “Masculine – feminine,” and “like – Dislike”), and semantic differential method is used for measurement. It is found that the color connotation models developed for related colors perform poorly for unrelated colors. Experimental results indicate that brightness attribute is confusing to estimate and does not affect color connotation significantly for unrelated colors. Based on the psychophysical data, new models for “Warm‐Cool”, “Heavy‐Light”, “Active‐Passive” and “Hard‐Soft” were proposed using CAM02u hue, brightness, and colorfulness. Color connotations for unrelated colors are classified into three categories, which “Color solidity,” “Color heat,” and “Color purity.” © 2013 Wiley Periodicals, Inc. Col Res Appl, 40, 40–49, 2015