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     

Revision of the chroma and hue scales of a nonlinear color-appearance model

The following questions were raised to chroma and hue scales of the nonlinear color-appearance model: 1) significant nonuniformities of the chroma scales for different hues, and 2) deviations of hue scale between the model and the Munsell and the NCS schemes. It was suggested that the problems were caused by the use of the coefficient e_s(0) proposed by Hunt. Instead of e_s(0), a new coefficient E_s(0) was proposed, which corresponds to the chromatic strengths of spectral colors (including colors on the redpurple locus). By using E_s(0), the nonlinear color-appearance model could predict the hue and chroma scales of the Munsell and the NCS schemes quite nicely. the method in the present study is generally applicable for determining hue and chroma perceptions of object colors irrespective of the color-appearance model used.     

Different transformation methods between CIELAB coordinates and Munsell hue

This research aims to convert CIE L*C*_abh_ab coordinates into corresponding Munsell hues. Different transformation methods for colour mapping from CIELAB colour space to Munsell hues are proposed. Polynomial equations that predict Munsell hue from CIELAB h_ab suffer from poor performance as there is no direct one‐to‐one mapping. Polynomial methods that predict Munsell hue from all three L*C*_abh_ab values also show limited performance. However, a distance‐weighted look‐up‐table model based upon the CIEDE2000 colour‐difference equation is able to predict Munsell hue to an accuracy of 1 unit of root mean square error. All transformation methods in this paper were developed using CIE illuminant C and the 2° standard observer conditions and were based on 2729 Munsell renotation colour samples.     

Interrelation of the natural color system and the munsell color order system

The CIE tristimulus values of the aim points of the Natural Color System (NCS) were converted to Munsell notations using a computer program. The values so converted were those from the four elementary hues R, Y, G, and B, and the intervening hues for which full pages of colors exist in the NCS Colour Atlas. The resulting notations were plotted on Munsell Value-Chroma and Hue-Chroma charts and analyzed for several features of interest, for example the locations of the points with 100% chromaticness and the relative spacing of the hue circles. Analytical equations are presented relating Munsell Chroma and NCS chromaticness, and Munsell Value and NCS blackness, for both achromatic and chromatic samples. Such analytical relationships could not be derived between the hues of the two systems, since a relatively wide range of hue in either system corresponds to constant hue in the other. This range appears to include both systematic and random components that must be removed before analytical relations between the two hues can be derived.     

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     

Unique hue judgments using saturated and desaturated Munsell samples under different light sources

Past studies investigating the unique hues only used samples with a relatively high saturation levels under standard illuminants. In this study, 10 observers selected the four samples with unique hues from 40 V6C8 (Value 6 Chroma 8) and 40 V8C4 (Value 8 Chroma 4) Munsell samples under six light sources, comprising three levels of D_uv (i.e., 0, ?0.02, and ?0.04) and two levels of correlated color temperature (i.e., 2700 and 3500 K). Significant differences were found between the two chroma levels for unique blue and yellow, with the hue angles of unique yellow and blue judged using the desaturated samples being significantly different from those defined in CIECAM02. The iso‐lines of unique yellow, blue, and green did not always go through the origin of the a*‐b* or a′‐b′ planes in CIELAB and CAM02‐UCS. Thus, the problems of CIECAM02, CIELAB, and CAM02‐UCS identified in this study need further investigations.     

Proposal of an opponent‐colors system based on color‐appearance and color‐vision studies

A new theoretical color order system is proposed on the basis of various studies on color appearance and color vision. It has three orthogonal opponent‐colors axes and an improved chromatic strength of each hue. The system has color attributes whiteness w, blackness bk, grayness gr, chroma C, and hue H. A method is given for determining Munsell notations of any colors on any equi‐hue planes in the system. A method is also given for determining grayness regions and grayness values on hue‐chroma planes in the system. It is concluded that colors with the same color attributes [w, gr, bk, C] but with different hues in the theoretical space have approximately the same perceived lightness, the same degree of vividness (“azayakasa” in Japanese), and also the same color tone. The tone concept, for example used in the Practical Color Coordinate System (PCCS), is clarified perceptually. The proposed system is a basic and latent color‐order system to PCCS. In addition, the concept of veiling grayness by a pure color with any hue is introduced. Further, relationships are clarified between generalized chroma c(gen) and grayness. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 135–150, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10234     

Interrelation of the Swiss Colour Atlas (SCA-2541) and the Munsell Color Order System

The CIE tristimulus values of measured Swiss Colour Atlas samples were converted to Munsell notations using a colour notation conversion program. A selected subset of SCA-2541 sample points was chosen: the samples on the fully populated regularly spaced hues 6, 12, 18, 24, 30, 36, 42, 48, 54, and 60. The resulting Munsell notations were plotted onto Munsell Value-Chroma and Hue-Chroma planes and analysed for regularity of spacing and hue distribution around the achromatic axis. An earlier article has detailed the interrelation between the Natural Color System (NCS) and the Munsell Color Order System using similarly constructed charts. Comparison is made with the sample spacing of the NCS and SCA-2541 points when mapped into Munsell colour space, to determine similarities and differences between these two geometrically similar systems; both are double cones forming equilateral triangular constant hue planes. © 1997 John Wiley & Sons, Inc. Col Res Appl, 22, 111–120, 1997     

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     

A model of colour vision for predicting colour appearance

A set of possible cone spectral sensitivity functions has been used to obtain combinations of responses that provide good predictions for loci of constant hue, simple criteria for unique hues, and good approximations to the NCS and Munsell schemes for surface colours, and to data on the appearance of spectral colours.     

Determination of unique hues using Munsell color chips

Forty observers determined their unique hues from arrays of Munsell chips in a standard surround under artificial daylight. There was some discrepancy in the results of males and females. Essentially no variability due to age of observer was found. The standard deviation around the total mean was less than 1 Munsell 40 hue step. Simple linear opponent‐color a and b values were calculated. The ranges were found to straddle in all but the red color the system axes for the CIE 2°observer, but not for the 10°observer. NCS unique hues determined at similar chroma and lightness values fell in all cases within the ranges. The shifts in cross‐over wavelengths of the color‐matching functions necessary to match the extreme range values were determined to be between 6–11 nm. The results provide support for an opponent‐color system based on subtractions of color‐matching functions. They also point to significant variation in color normal observers. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 61–66, 2001     

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     

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 fallacy in the definition of ΔH*

When a color differs from the reference, it is desirable to ascribe the difference to differences in the perceptual attributes of hue, chroma, and/or lightness through psychometric correlates of these attributes. To this end, the CIE has recommended the quantity ΔH* as a psychometric correlate of hue as defined by ΔH* = [(ΔE*)² - (ΔL*)² - (ΔC*)²]^1/2, where the correlates correspond to either the 1976 CIELAB or CIELUV color spaces. Since ΔH* is defined as a “leftover,” this definition is valid only to the extent that ΔE* comprises exclusively ΔL*, ΔC*, and ΔH* and that ΔL*, ΔC*, and ΔH* are mutually independent compositionally, both psychophysically and psychometrically. It will be shown that as now defined ΔH* lacks psychometric independence of chroma and always leads to incorrect hue difference determination. Such a deficiency causes problems, especially in the halftone color printing industry, since it can suggest an incorrect adjustment for the hue of the inks. A revised definition herein of ΔH* provides a psychometric hue difference independent of chroma, valid for large and small psychometric color differences regardless of chroma. However, for small chromas, the seldom used metric ΔC might be a better color difference metric than ΔH* because complex appearance effects make the perceptual discrimination of lightness, chroma, and hue components more difficult than for high chromas.     

Color appearance of a large homogenous visual field

In this article, the color appearance of a large (85°) homogeneous self‐luminous visual stimulus was studied in a psychophysical experiment. Large stimuli were displayed on a plasma display panal (PDP) monitor. The large stimuli were viewed with a fixed viewing time (2 s). They were compared with 2° and 10° stimuli presented on a grey background on a CRT monitor. The so‐called “color size effect” was found to be significant. The color stimulus was perceived to be lighter when it was large compared with the 2° and 10° situation. But we did not find the general increase of chroma claimed in previous literature. We found only small hue changes. A model of the color appearance of large‐field stimuli is presented in terms of the CIELAB L*, a*, and b* values of the corresponding 2° and 10° stimuli. © 2007 Wiley Periodicals, Inc. Col Res Appl, 33, 45–54, 2008     

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     

Equivalent lightness of colored objects of equal munsell chroma and of equal munsell value at various illuminances

Equivalent lightness was determined for 26 colored surfaces by heterochromatic brightness matching with a grey scale. The illuminance for observation was varied from 0.01 to 1000 lx to cover scotopic, mesopic, and photopic vision, and the equivalent lightness-versus-log illuminance curve was obtained for every stimulus. The shape of the curves did not change if the surfaces had the same Munsell hue and chroma. It differed significantly if they had different hues or different chroma. The curves were interpreted in terms of achromatic lightness and chromatic lightness, which are both subject to change with illuminance level. The achromatic lightness was assumed to follow the Purkinje shift and the chromatic lightness monotonically increased with illuminance. The chromatic lightness was larger for larger Munsell chroma within a single hue.     

Absolute Identification of Colors in the Munsell Notation: Trainability and Systematic Shifts

Subjects were asked to identify colors in the Munsell notation, without comparing with the samples of the Munsell Book of Color, and then were immediately told the values of H, V, and C. This training was carried out with 520 colors identified twice by each of five subjects, two experienced and three completely naive with the Munsell system. The effect of training was noticeable over the series of 1040 estimations, and the means of absolute deviations at the end were 3.1, 0.5, and 1.25 for H, V, and C, respectively. Systematic shifts of mean estimations from the Munsell notations were noted: saturated colors tend to be judged lighter when V < 5, there is a tendency to scale compression in the estimation of C, and colors of hue between 7.5B and 7.5B tend to shift toward B, and colors of 10PB and 2.5P, toward P.     

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     

Use of regression methods for determining the relation between theoretical–linear and spectrophotometrical colour values of bicolour woven structures

In this paper, new approaches for evaluating the entire colour effect of optical mixing of bicolour woven structures are presented. Simple woven structures with constant colour in the warp direction and different colours in the weft direction were prepared and analysed. The constructional parameters of these woven fabrics were systematically changed, which resulted in the variations of the fractions of colour components and, consequently, also in the changes of colour properties (lightness, hue, chroma) of bicolour optical mixtures. The position of colours of the bicolour structures and the approximate direction (linear) of colour changes in CIELAB colour space were theoretically determined with a simple geometrical model and additive method. Furthermore, the bicolour optical effects were determined spectrophotometrically. The differences between the linear–theoretical and the spectrophotometrical colour values of bicolour woven fabrics were mathematically analysed with linear and non‐linear regression methods to determine the positions of colour coordinates L*, a* and b* of bicolour woven fabrics in the a*b* plane by increasing or reducing the cover factors of warp and weft threads (addition or reduction of colour components). The results present, on the one hand, the strong influence of original colours of warp and weft threads and, on the other hand, the minor influence of constructional parameters on the form of linear/non‐linear behaviour of colours of bicolour compositions. When the characteristics of a specific colour combination are taken into account, the spectrophotometrical colour values of bicolour woven fabrics can be also mathematically determined with additive–theoretical colour values and, to some extent, with predictable colour deviations.