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     

Colorimetric study of SCOTDIC colour specifier

In this study, SCOTDIC cotton standard colours (a physical exemplification of the Munsell system) were studied extensively. L*, a*, b* values were measured and plotted to check the uniformity of the Munsell (SCOTDIC) hue, value and chroma values in a CIELAB diagram. Although for some borderline hues the hue angles were quite different than expected (around 0° or 360°), the correlation between SCOTDIC hue and CIELAB hue angle was fairly good and the correlation between SCOTDIC value and CIELAB lightness was also quite high. However, the correlation between SCOTDIC chroma and CIELAB chroma was only moderate. In the CIELAB diagram, the constant SCOTDIC hue and constant chroma loci took the shape of approximately linear radial lines starting from the origin and approximately concentric circles with the origin as their centres, respectively. However, some deviations were observed for high chroma colours and yellow hues in the respective cases. The instrumentally predicted Munsell notations were compared with the actual SCOTDIC notations. Some deviations of the SCOTDIC system from the Munsell system were observed.     

A structural comparison of the Munsell renotation and the OSA–UCS uniform color systems

A structural comparison has been made of the lightness, chroma, and hue scales of the Munsell system, as expressed in the Munsell Renotations, and of the OSA‐UCS system. While the lightness scales are similar (except for the adjustment for the Helmholtz–Kohlrausch effect and the inclusion of a “crispening” effect in OSA–UCS), there are significant differences in the chroma scales along the major chromatic axes. Unlike in CIELAB, the increments in X and Z along these axes for equal chroma steps in both systems do not fall on a continuous function. In the two systems, as well as in CIELAB lines connecting colors of equal chroma differences at different Y values point to nonreal origins. These differ among the three systems. A major difference between Munsell and OSA–UCS is the size of the first chroma step away from gray. An experiment has been performed with the result that the OSA–UCS system is in much better agreement with the average observer in this respect than the Munsell system. OSA–UCS exhibits considerably more internal uniformity in terms of X and Z increments between steps than the Munsell system. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 186–192, 2000     

Prediction of Munsell appearance scales using various color‐appearance models

The chromaticities of the Munsell Renotation Dataset were applied to eight color‐appearance models. Models used were: CIELAB, Hunt, Nayatani, RLAB, LLAB, CIECAM97s, ZLAB, and IPT. Models were used to predict three appearance correlates of lightness, chroma, and hue. Model output of these appearance correlates were evaluated for their uniformity, in light of the constant perceptual nature of the Munsell Renotation data. Some background is provided on the experimental derivation of the Renotation Data, including the specific tasks performed by observers to evaluate a sample hue leaf for chroma uniformity. No particular model excelled at all metrics. In general, as might be expected, models derived from the Munsell System performed well. However, this was not universally the case, and some results, such as hue spacing and linearity, show interesting similarities between all models regardless of their derivation. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 132–144, 2000     

Spacing in the Munsell Color System Relative to the Coloroid Color Systems

Spacing defined by various Munsell hue and chroma steps are analyzed, applying diagrams resulting from transformations between the Colorid and the Munsell color systems, displaying colors of both color systems with the same Y tristimulus values. After comments on spacings derived from identities, similarities and differences between both color systems, unevennesses uninter-pretable from differences of color system constructions are attributed either to uniform variation of color stimult followed by uneven variation of color perceptions, or to uncertainties of human color perception at several spots of the color space sufficient to be noticeable in spacings in perceptually uniform color system, such as the Munsell color order system © 1994 John Wiley & Sons, inc.     

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     

Geodesic calculation of color difference formulas and comparison with the munsell color order system

Riemannian metric tensors of color difference formulas are derived from the line elements in a color space. The shortest curve between two points in a color space can be calculated from the metric tensors. This shortest curve is called a geodesic. In this article, the authors present computed geodesic curves and corresponding contours of the CIELAB ( ), the CIELUV ( ), the OSA‐UCS (ΔE_E) and an infinitesimal approximation of the CIEDE2000 (ΔE₀₀) color difference metrics in the CIELAB color space. At a fixed value of lightness L*, geodesic curves originating from the achromatic point and their corresponding contours of the above four formulas in the CIELAB color space can be described as hue geodesics and chroma contours. The Munsell chromas and hue circles at the Munsell values 3, 5, and 7 are compared with computed hue geodesics and chroma contours of these formulas at three different fixed lightness values. It is found that the Munsell chromas and hue circles do not the match the computed hue geodesics and chroma contours of above mentioned formulas at different Munsell values. The results also show that the distribution of color stimuli predicted by the infinitesimal approximation of CIEDE2000 (ΔE₀₀) and the OSA‐UCS (ΔE_E) in the CIELAB color space are in general not better than the conventional CIELAB (ΔE) and CIELUV (ΔE) formulas. © 2012 Wiley Periodicals, Inc. Col Res Appl, 38, 259–266, 2013     

Relative wavelength metric for the complete hue cycle: Derivation from complementary wavelengths

In recent research, it has been increasingly necessary to employ an extended wavelength metric to cover the complete hue cycle so as to research or represent data as a function of relative wavelength rather than psychological scales such as CIELAB or Munsell hue angle. This article describes such a relative wavelength metric and its derivation from complementary wavelength functions. The metric provides a useful psychophysical, wavelength‐based, ratio scale for the hue cycle allowing nonspectrals to be treated in the same coherent scale as spectral hues. Several indicators, e.g., color order hue cycles, infer the (optimally efficient) spectral hues comprise about 71% and the nonspectrals about 29%, of the hue cycle interval. This gives a hue cycle whose relative wavelength interval is about 240 nm for illuminant D65. To relate to CIE colorimetry, spectral complementary wavelengths to the nonspectrals' relative wavelengths are identified for seven illuminants including D65,D50, C, and A. Data are given for CIE 1931, and briefly 1964, colorimetry. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

Predictions of Munsell values with the same perceived lightness at any specified chroma irrespective of hues—Determination of any tonal colors

Simple formulas are proposed for predicting the Munsell value of colors with the same tone (the same values for whiteness‐blackness, perceived lightness, and chroma irrespective of hue). The formulas can be used for any tone. In other words, the method can determine the Munsell value with the same perceived lightness at any specified chroma irrespective of hue. The chromatic strength (CS) function is only used for the derivations. The formulas are very simple, and can be used not only in the colorimetry but also in the color design field. The concept described in this study is that a common CS function can be used for transforming each of the three color attributes (hue, lightness, and chroma) from their uniform color space metric to their corresponding color appearance space attribute. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2011     

Color space and its divisions

A synthesis of the author's recent work on color‐order systems and color‐difference evaluation is provided in context of current knowledge and practices. The development of a colorimetric model is demonstrated using Munsell “Celtic crosses” as a model of perceptual space. Issues surrounding color‐matching functions, unique hues, the Helmholtz–Kohlrausch effect, and lightness and chroma crispening are addressed, as is the difficulty of reconciling a difference‐based hue, chroma, lightness model with an Euclidean model. A new lightness scale and treatment of lightness crispening is proposed. The results indicate that, despite problems, relatively simple modified opponent‐color models provide good accuracy in predicting color‐order system and supra‐threshold small color‐difference data. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 209–222, 2001     

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     

The munsell color system in fundamental color space

The Munsell color system is investigated as a structure in fundamental color space. The entire collection of samples from the 1929 Munsell Book of Color is mapped into fundamental color space and surfaces of constant hue, value, and chroma are identified. An algorithm, based on these surfaces, is presented for estimating the Munsell specification of an arbitrary reflectance curve.     

Whiteness,chromaticness, and blackness symmetries for CIELAB,with a numerical example

Whiteness, chromaticness, and blackness are defined for CIELAB. These NCS‐like color attributes offer an alternative to lightness and chroma for describing color. Their hue‐preserving symmetries are derived for tristimulus color space. A numerical example provides what theory predicts are visually uniform sequences of colors with constant lightness, whiteness, chromaticness, or blackness. Numerical approximation is unnecessary. Such sets of symmetric colors in one hue are visually interesting, and useful for computer aided design. The appropriateness of such attributes for CIELAB is briefly discussed. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

Whiteness perception under different types of fluorescent lamps

The effects of correlated color temperature and the chromaticity of light sources on the perception of surface whiteness were investigated. For the experiment, a Munsell N9.25 chip and 11 nearly white chips (V = 9.25, Munsell chroma ≦ 1.0) were selected. The interval scale of the whiteness of these chips was determined from the results of pair comparisons under eight different fluorescent lamps with correlated color temperatures from 2800 to 6700 K. The Munsell 3PB, 10PB, 7P, and N chips gained high scores under 6700 K illumination, whereas the 3PB, 5B, 7BG, and 9G chips scored higher under the 2800 K illumination. The 12 chips were divided into two groups. In one group, the interval scale from the bottom was found to increase as the correlated color temperature increased, whereas in the other group, it decreased with the temperature. The Munsell 3PB/9.25/1.0 chips fell into the latter group but consistently exhibited the highest or at least high‐order scores for all the illuminations examined. In those cases in which the correlated color temperature was held constant, the chromaticity of the light source was found to have no significant effect on the whiteness interval scale. A high correlation was identified between the interval scale of the whiteness and the two metrics, the metric chroma of CIELAB, and CIECAM97s chroma C. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 96–102, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10129     

Correlations between color attributes and children's color preferences

This study examined the role of color attributes (lightness and saturation) on children's color preferences for interior room colors. It also investigated children's most preferred colors among each of the five major hue families in the Munsell color system using scale‐models. Previous color preference studies have typically been done with small color chips or papers, which are very different from seeing a color applied on wall surfaces. A simulation method allowed for investigating the value of color in real contexts and controlling confounding variables. Forty‐five color samples were displayed on scale‐models to 63 children ages 7–11 years old. This study identified children's most preferred colors among each of the five major hue families in Munsell color system. It also demonstrated that saturation was positively correlated with children's preferences in the red, green, blue, and purple hue families. In the yellow hue family, interestingly, lightness has a positive correlation with preferences. Children's gender differences were found in that girls prefer red and purple more than boys. These findings lead to color application guidelines for designers to understand better color and eventually to create improved environments for children and their families. © 2013 Wiley Periodicals, Inc. Col Res Appl, 39, 452–462, 2014     

Design and performance of a color chart based in digitally processed images for sensory evaluation of piquillo peppers (Capsicum annuum)

A chart of color standards for visual color evaluation of the piquillo pepper (Capsicum annuum) has been designed. The chart comprises six rectangular regions of digitally processed images of piquillo peppers covering the observed visual range of variability in this product. Colorimetric characterization of piquillo peppers and the color chart has been made using instrumental color measurements. Both trained and untrained sensory panels tested the reliability of the designed color chart. The Pearson correlation coefficient between color chart scores and subjective color quality scores is 0.831 (P < 0.01). Correlation between all instrumental color coordinates, with the exception of CIELAB a*, and visual color chart scores are significant at P< 0.001 and Pearson correlation coefficients range from ?0.747 with CIELAB chroma C* to ?0.926 with CIELAB hue angle h. Repeatability of visual color chart scores is completely satisfactory, having found no statistically significant differences between color chart scores in samples evaluated twice by panelists. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 305–311, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20026     

Color effect of light sources on peridot based on CIE1976 L*a*b* color system and round RGB diagram system

Previous research indicated that the peridot's color is dominated by the selective absorption of visible light caused by ferrous ion, the hue angle of which is in an inverse ratio of the concentration of Fe²⁺. This article focuses on the color effect of peridot under different standard light sources based on the CIE1976 L*a*b* color space system and round RGB diagram system and tries to find the best one for its grading and display. Based on the results of a series of experiments, including electron microprobe analysis, spectrophotometer, UV‐Vis spectrum, standard illumination box, and Munsell neutral color chips, it was suggested that the spectral power distribution and color temperature of a standard light source significantly influence the color of peridot in terms of lightness and chroma, particularly in the hue of peridot. As for color grading and displaying of peridot, standard light source A fails to fit in, and the color of peridot under a fluorescent light source has a higher chroma but a lower hue angle than that under daylight light source. The best choice for grading and displaying peridot is the standard light source D₆₅. It is better to distinguish the hue of peridot when it is calculated by the round RGB diagram system.     

Color analysis of natural colorant‐dyed fabrics

Colors from naturally dyed fabrics recently have attracted both consumers and manufacturers in fashion markets. Even though color attributes of the fabrics have been partially observed in some literature, a data base of colors for natural colorants in fabrics needs to be established and the colors to be characterized according to systematic color notations and tones in order to relate the traditional natural colors to contemporary color communication systems. Therefore, a study was performed to investigate color characteristics for a given large set of natural colorants‐dyed fabrics based on the Munsell color notations, to analyze their tones with relation to the notation such as hue, value, and chroma, and finally to identify the effects of mordanting, an important coloring auxiliary, on the colorimetric properties of the fabrics. As a result, the dominant hue for a total of 350 naturally dyed fabrics was yellowish families followed by reddish and purplish ones in the Munsell notation owing to the use of leaves and plant as usual natural dyestuff, which confirms the limit of color hues of the fabrics. Color value for most of naturally dyed fabrics was generally higher whereas the chroma was lower, which means that most of colors for naturally dyed fabrics tended to be bright and weak shaded. Grayish, light grayish, and soft tones were the main tones of natural colorant‐dyed fabrics. All of hue, value, and chroma were found as being influenced by mordanting in that more particularly; iron mordanting was likely to cause the decrease of both value and chroma for most of naturally dyed fabrics. These results could provide a systematic color data for naturally dyed fashion fabrics and suggest a future direction of color development for them. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 148–157, 2008     

A hypothesis regarding the poor blue constancy of CIELAB

The poor blue constancy of the CIELAB equations has been noted by a number of researchers, and various proposals have been made to address this shortcoming. The specific issue is the tendency for highly chromatic blues to appear more purple as the chroma is reduced for a constant hue angle. The root cause for the poor CIELAB blue constancy has been an open question, although one possibility is a basic deficiency in the CIELAB equations. An alternative hypothesis is that the equations, in combination with color matching functions with a distinct secondary lobe on the x‐bar or long‐wavelength sensitive channel, such as those found on the International Commission on Illumination (CIE) 1931 and 1964 Standard Observers, are problematic. The spectral curves of a constant hue IPT (Intensity, Protan, and Tritan) blue step ramp displayed on a CRT are used to explore this hypothesis. Additional discussion examines the use of sharpened sensors and achieving parallel tritanopic confusion lines in the CIELAB color space. The results suggest that use of the CIE Standard Observers with the CIELAB equations results in poor blue constancy and distorted tritanopic confusion lines. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 371–378, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10180     

Comparison of unique hue stimuli determined by two different methods using Munsell color chips

Unique hue stimuli were determined by male and female observers using two different visual experimental procedures involving Munsell color chips of varying hue but identical chroma and value. The hypothesis was that unique hues can be more reliably established by explicit selection from a series of ordered stimuli than implicitly by hue scaling a series of stimuli in terms of neighboring UHs and this was statistically confirmed. The implicit selections based on long term memory of UHs appears to have been more challenging to observers since variability was increased by nearly 50% compared to when UHs were explicitly selected. The ranges of unique hues selected in the two methods were, however, comparable and no statistically significant difference was found between the results of females and males. The intra‐observer variability in picking a stimulus to represent a unique hue, for all observers and averaged for all hues, was approximately 12% of the mean spread of unique hues, confirming that the large inter‐observer variability is driven by differences in color vision and perhaps cognitive processes. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010