How strong metamerism disturbs color spaces

Systems for arranging and describing color include “color spaces” and “color order systems.” In a color space, tristimulus values R, G, and B are computable for every light (every point in the space). In familiar color spaces, such computation makes use of three functions of wavelength (the color-matching functions that define one of the CIE Standard Observers), one function corresponding to each of R, G, and B. In the presence of strong metamerism (marked spectral difference between the spectral power distributions of a pair of visually matching lights), the color-matching functions may report that one light of the pair has an entirely different color from that of the other member of the visually matching pair of lights. The CIE Standard Observer embodying those color-matching functions “sees” the two visually matching lights as entirely different in color, that is, it reports entirely different sets of R, G, and B for the two visually matching lights, and, thus, an entirely different chromaticity. In an example given here, each of the CIE Standard Observers assigns a strong green color to lights that are seen by normal human observers as a visual match to a hueless reference white. On the other hand, color order systems comprising sets of real objects in a specified illuminant, and which are assembled (visually arranged) by normal observers, as are the Munsell and OSA sets, do not suffer from the type of trouble discussed here. Color spaces depending on mathematical functions of R, G, and B are at risk: both Standard Observers are shown to plot visually identical lights at widely varying points in familiar color spaces (e.g., delta E*_ab = 40–50). © 1998 John Wiley & Sons, Inc. Col Res Appl, 23: 402–407, 1998     

Color difference predicted by color component differences

A relationship between assessed color differences and assessed components of colors is presented. The perceptual difference between colors j and k is converted to a lightness difference of two Munsell grays, V_A and V_B, and d_jk = |V_A ? V_B|. Scaled values of principal hue components of a color ξ _α(H|V/C), α = R, Y, G, and B, are read from charts based on assessments of observers. Previous charts (Color Research and Application, 1999, 24, 266–279) are enlarged and extended. A linear combination of ΔV = |V_j ? V_k| and Δξ _α = |ξ _α(H_j|V_j/C_j) ? ξ _α(H_k|V_k /C_k)|, d?_jk, is the best to predict d_jk. The root‐mean‐squares of (d_jk ? d?_jk) is 0.34 V, about one third of the lightness difference from V to V + 1 on the Munsell Value Scale.     

Spectral color reproduction minimizing spectral and perceptual color differences

In this article, we are combining minimization criteria in the colorant separation process for spectral color reproduction. The colorant separation is performed by inverting a spectral printer model: the spectral Yule‐Nielsen modified Neugebauer model. The inversion of the spectral printer model is an optimization operation in which a criterion is minimized at each iteration. The approach we proposed minimizes a criterion defined by the weighted sum of a spectral difference and a perceptual color difference. The weights can be tuned with a parameter α ∞ [0, 1]. Our goal is to decrease the spectral difference between the original data and its reproduction and also to consider perceptual color difference under different illuminant conditions. In order to find the best α value, we initially compare a pure colorimetric criterion and a pure spectral criterion for the reproduction, then we combine them. We perform four colorant separations: the first separation will minimize the 1976 CIELAB color difference where four illuminants are tested, the second separation will minimize an equally weighted summation of 1976 CIELAB color difference with the four illuminants tested independently, the third colorant separation will minimize a spectral difference, and the fourth colorant separation will combine a weighted sum of a spectral difference and one of the two first colorimetric differences previously introduced. This last colorant separation can be tuned with a parameter in order to emphasize on spectral or colorimetric difference. We use a six colorants printer with artificial inks for our experiments. The prints are simulated by the spectral Yule‐Nielsen modified Neugebauer model. Two groups of data are used for our experiments. The first group describes the data printed by our printing system, which is represented by a regular grid in colorant space of the printer and the second group describes the data which is not originally produced by our printing system but mapped to the spectral printer gamut. The Esser test chart and the Macbeth Color Checker test chart have been selected for the second group. Spectral gamut mapping of this data is carried out before performing colorant separation. Our results show improvement for the colorant separations combining a sum of 1976 CIELAB color difference for a set of illuminants and for the colorant separation combining a sum of 1976 CIELAB color difference and spectral difference, especially in the case of spectral data originally produced by the printer. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 494–504, 2008     

Spectral color management using interim connection spaces based on spectral decomposition

A feasible approach to spectral color management was previously defined to include lookups performed within an interim connection space (ICS). ICS is relatively low in dimensions and is situated between a high‐dimensional spectral profile connection space and output units. The definition of ICS axes and the minimum number of ICS dimensions are explored here by considering the LabPQR, an ICS described in earlier research. LabPQR has three colorimetric dimensions (CIE L*a*b*) and additional dimensions to describe a metameric black (PQR). Several versions of LabPQR are explored. One type defines PQR axes based on metameric blacks generated from Cohen and Kappauf's spectral decomposition. The second type is constructed in an unconstrained way where metameric blacks are statistically derived based on the spectral characteristics of the target output device. For a six‐dimensional LabPQR, one that uses three colorimetric and three metameric black dimensions, it was found that Cohen and Kappauf‐based LabPQR was inferior for estimating the spectra when compared with the unconstrained method. However, when the limited spectral gamut of an output device was introduced through printer simulation and necessary spectral gamut mapping, the disadvantage of the six‐dimensional Cohen and Kappauf‐based LabPQR dissipated. On the other hand, reducing LabPQR to only five‐dimensions (two metameric black dimensions) reintroduced the advantage of the unconstrained approach even after simulated printing including spectral gamut mapping. Importantly, it was found that the five‐dimensional unconstrained approach achieved equivalent levels of performance to a full 31‐dimensional approach within simulated printer spectral gamut limitations. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 282–299, 2008.     

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     

Munsell reflectance spectra represented in three‐dimensional Euclidean space

In this article we describe the results of an investigation into the extent to which the reflectance spectra of 1269 matt Munsell color chips are well represented in low dimensional Euclidean space. We find that a three dimensional Euclidean representation accounts for most of the variation in the Euclidean distances among the 1269 Munsell color spectra. We interpret the three dimensional Euclidean representation of the spectral data in terms of the Munsell color space. In addition, we analyzed a data set with a large number of natural objects and found that the spectral profiles required four basis factors for adequate representation in Euclidean space. We conclude that four basis factors are required in general but that in special cases, like the Munsell system, three basis factors are adequate for precise characterization. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 182–196, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10144     

Principal hue curves and color difference

The size of perceptual difference of colors (j, k) is scaled as d_jk by selecting a pair of Munsell grays in which the lightness difference matches in size with the color difference. Hence, d is given in terms of Munsell V. The degree of principal hue component α in a color j is scaled as ξ_α(j) by making marks on a line segment and the range of ξ_α is from 0 to 10. By plotting ξ_α(H V/C) on Munsell H‐circle, principal hue curves ξ¯_α(H V/C) are defined, where α = R, Y, G, B, V = 4–7, and C = 2–10. In this process, similar plots of NCS codes (cϕ_α) are used as references. The curves ξ¯_α(H V/C) tell us the appearance of Munsell colors (H V/C) and also enable us to predict color differences. The relationship between d_jk and ΔV = |V_j − V_k|, Δξ¯_α = |ξ¯_α(H_j V_j/C_j) − ξ¯_α(H_k V_k/C_k)| is tested in various ways, e.g., logarithmic, power, Minkowski‐type functions. The best predictor d̃ is given by a simple linear form, d̃ = a_VΔV + {d₀ + Σa_αΔξ¯_α}. For 899 pairs (j, k), 706 differing in H, C and 193 differing in H, V, C, a_V = 0.459, d₀ = 0.610, a_R = 0.199, a_Y = 0.031, a_G = 0.098, a_B = 0.136, and the root‐mean‐squares of (d_jk − d̃_jk) is 0.338 in the matched V‐unit. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 266–279, 1999     

Predictions based on Munsell notation. I. Perceptual color differences

For every pair of colors (j, k), the observers selected a pair of Munsell grays (N_a, N_b) such that the lightness difference matched the color difference in size, and the scaled value of color difference was defined as d_jk = V_a − V_b. On the basis of these data, where (j, k) are limited in the range that can be matched by d_jk < 4.0 V, the procedure was presented to define predicted values d̃_jk for Munsell colors (J, K) between 4V and 7V directly from Euclidean d̂_jk between points P_j and P_k in the current Munsell solid. The procedure is more practical than the multidimensional scaling representation. Inter‐point d̂_jk are measured in the units of C in the (H, C) plane and the contributions d̂_jk of 1C and 1V differences are assumed to be 1 and 2.3. Precision of predictions, RMS = {mean of d_jk − d̃_nk)²}^0.5, is 0.3 V (0.8 C) for 2‐D color differences (V_j = V_k). For the set of data on 3‐D color differences used in the present study, RMS = 0.6 V (1.7 C). These were compared with the precision of predictions by Judd, Adams–Nickerson formulae, CIE 1976(L*, u*, v*), and CIE94. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 10–18, 1999     

The metamerism potentiality of a color recipe

The weighted spectrophotometric color matching method with the optimum weighting to the spectrophotometric equations in each particular wavelength proportional to the viewing condition is applied for minimizing the color difference of instrumental color formulation of textile materials. The work is based on the one‐constant Kubelka–Munk theory. The sensitivity of a recipe to small perturbation of deviation between the reflectance of target and matched samples in the visible spectrum is determined as the metamerism potentiality of proposed recipe. Its correlation with metamerism index was also studied for some metameric pairs. Metamerism potentialities are also appraised under several light sources by using equilibrate matching strategy. The results show that the outputs of colorimetric color matching are exactly identical with the weighted spectrophotometic match under the same viewing condition. According to the numerical results for matching of 58 target samples, there is a good statistical correlation between metamerism indices and the metamerism potentialities of each recipe. Our results show that the quantitative value of the metamerism potentiality of each recipe can reasonably predict the metamerism indices of applied formulation. © 2006 Wiley Periodicals, Inc. Col Res Appl, 31, 483–490, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20261     

Quantifying variations in personal color spaces: Are there sex differences in color vision?

We report a search for group differences in color experience between male and female subjects, focusing on the relative prominence of the axes of color space. Dissimilarity data were collected in the form of triadic (odd‐one‐out) judgments, made with the caps of the D‐15 color deficiency test, with lighting conditions controlled. Multidimensional scaling reduced these judgments to a small number of dimensional‐weight parameters, describing each subject's sensitivity to color axes, i.e., how much each axis contributes to the inter‐color dissimilarities perceived by each subject. Normal trichromatic subjects in two age bands were examined, teenagers and university students, and in both cases males placed significantly less weight on a ‘red‐green’ axis, and more on ‘lightness’. We consider the implications and possible explanations. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 128–134, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10232     

Observer variability in metameric color matches using color reproduction media

Standard color-matching functions are designed to represent the mean color-matching response of the population of human observers with normal color vision. When using these functions, two questions arise. Are they an accurate representation of the population? And what is the uncertainty in color-match predictions? To address these questions in the dual context of human visual performance and cross-media reproduction, a color-matching experiment was undertaken in which twenty observers made matches between seven different colors presented in reflective and transmissive color reproduction media and a CRT display viewed through an optical apparatus that produced a simple split-field stimulus. In addition, a single observer repeated the experiment 20 times to estimate intra-observer variability. The results were used to evaluate the accuracy of three sets of color-matching functions, to quantify the magnitude of observer variability, and to compare intra- and inter-observer variability in color-matching. These results are compared with various techniques designed to predict the range of color mismatches. The magnitude of observer variability in this experiment also provides a quantitative estimate of the limit of cross-media color reproduction accuracy that need not be exceeded. On average, the differences between matches made by two different observers was approximately 2.5 CIELAB units. © 1997 John Wiley & Sons, Inc. Col Res Appl, 22, 174–188, 1997     

Determination of constant Hue Loci for a CRT gamut and their predictions using color appearance spaces

A colorimetrically characterized computer-controlled CRT display was used to determine 24 loci of constant perceived hue for pseudo-object related stimuli, sampling the display's interior color gamut at constant lightness and the edge of its gamut at variable lightness. Nine observers performed three replications generating matching data at 132 positions. the constant hue loci were used to evaluate the correlation between perceived hue and hue angle of CIELAB, CIELUV, Hunt, and Nayatani color appearance spaces. the CIELAB, CIELUV, and Hunt spaces exhibited large errors in the region of the blue CRT primary, while the Nayatani and CIELUV spaces produced large errors in the region of the red primary for constant lightness stimuli. Along the edge of the CRT's color gamut (variable lightness stimuli), all the spaces had a similar trend, large errors in the cyan region. the differences in performance between the four spaces were not statistically significant for the constant lightness stimuli. For the variable lightness stimuli, CIELAB and CIELUV had statistically superior performance in comparison with the Nayatani space and equal performance in comparison with the Hunt space. It was concluded that for imaging applications, a new color appearance space needs to be developed that will produce small hue error artifacts when used for gamut mapping along loci of constant hue angle. © 1995 John Wiley & Sons, Inc.     

Review and evaluation of color spaces for image/video compression

A color space plays an important role in color image processing and color vision applications. While compressing images/videos, properties of the human visual system are used to remove image details unperceivable by the human eye, appropriately called psychovisual redundancies. This is where the effect of the color spaces' properties on compression efficiency is introduced. In this work, we study the suitability of various color spaces for compression of images and videos. This review work is undertaken in two stages. Initially, a comprehensive review of the published color spaces is done. These color spaces are classified and their advantages, limitations, and applications are also highlighted. Next, the color spaces are quantitatively analyzed and benchmarked in the perspective of image and video compression algorithms, to identify and evaluate crucial color space parameters for image and video compression algorithms.     

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     

The CIELAB reversal in calibration and verification

A CIELAB anomaly, in which smaller spectrophotometric errors at all wavelengths lead to larger CIELAB differences, is identified. It is shown that the reversal can occur throughout tristimulus space and is colorimetrically important during calibration procedures. Three numerical examples of the reversal, using data from the BCRA tiles, are given. The reversal cannot be attributed entirely to metamerism, which itself may cause large spectrophotometric error leading to small CIELAB difference. The effect is compounded by the nonlinearity of CIELAB relative to tristimulus coordinates. A recommendation for avoiding the reversal is offered. © 2004 Wiley Periodicals, Inc. Col Res Appl, 30, 66–68, 2005; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/col.20076     

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     

Francis Glisson's color specification system of 1677

What is perhaps the first color specification system, developed in 1677 by the eminent English physician Francis Glisson, is described. Two of the scales for which Glisson provided quantitative data Glisson have been reconstructed: the gray scale in virtual form and the red scale in real form. Reflectance calculations or measurements and calculations of CIELAB L*a*b* values indicate that the two scales have a significant degree of uniformity despite the simple method used by Glisson to construct them. © 2002 John Wiley & Sons, Inc. Col Res Appl, 27, 15–19, 2002     

Evaluation of the performance of metameric indices

Forty three metameric pairs were obtained by comparison, shade-adjustment, and redyeing of 660 self shades dyed with direct, azoic, vat, and reactive dyes. The pairs were regrouped shadewise and ranked visually in increasing order of metamerism. Spearman's rank correlation coefficients were calculated between 11 measures of metamerism and the visual metameric ranking under three illuminants A, D65, and TL84 in pairs. The illuminant-independent general indices included the indices based on reflectance differences (Bridgeman), weighted reflectance differences (Nimeroff and Yurow), Cohen-Kappauf's residual differences (proposed) obtained from the spectral decompositions of the reflectance spectra of the metameric pair. Illuminant-specific special indices included color-differences under test illuminant, addition, subtraction, division, and multiplication of color-differences under test and reference illuminants, indices based on ΔL*, Δa*, Δb* differences under two illuminants, based on chromatic adapted ΔL*, Δa*, Δb* differences with multiplicative corrections for tristimulus differences under reference illuminant (Berns-Billmeyer), differences of the color constancy indices. The present work showed that indices based on ΔL*, Δa*, Δb* differences under two illuminants, both unmodified and modified by Berns-Billmeyer performed best among the existing indices. The differences of color constancy indices showed good correlation with the degree of metamerism in some cases, and this may be utilized for developing newer indices of metamerism. © 1996 John Wiley & Sons, Inc.     

Conversion between the reflectance spectra and the Munsell notations

A novel general transformation between reflectance spectra and the corresponding coordinates of the Munsell Color System is presented. The coefficient values of the transformation were experimentally determined by mapping the actual reflectance spectra of the chips in the Munsell Book of Color into the Munsell Color Order System and by minimizing the distance between calculated and actual coordinates. The experiment was repeated with a selected set of points of the Munsell Renotation System. Both the Smith–Pokorny functions and the CIE 1931 standard color‐matching functions were used as a basis of the transformation. There is a good correspondence between calculated and actual coordinates of the Munsell Color System. It is also shown that the linear part of the same transformation applied to the basis functions results in one achromatic response function and two chromatic response functions in accordance with the opponent‐colors theory. © 2005 Wiley Periodicals, Inc. Col Res Appl, 31, 57–66, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20173