Chroma,chromatic luminance,and luminous reflectance. Part I: Basic research and illustration of relations

Chromatic luminance carries both wavelength and radiance of light, is the source of all psychophysical dimensions and all color attributes, and is a key to understand their relations. It has long attracted research, hindered in the past by flawed definitions of colorimetric purity (p_c), remedied in a recent article. This article investigates relations between luminous reflectance Y (i.e., total luminance, chromatic plus achromatic), chromatic luminance (calculated from Y per p_c), and chroma/colorfulness. Relations are clarified, illustrated by formulas and graphs including three‐dimensional schemas of luminance Y, chromatic luminance, and color solids. A useful new term, relative chromatic luminance, is introduced. Munsell chroma is shown to resemble inverted log luminance much more closely than inverted log colorimetric purity as claimed by previous researchers. The relationship is used in Part II to model chroma, colorfulness, and brightness. © 2008 Wiley Periodicals, Inc. Col Res Appl, 34, 45–54, 2009.     

Color constancy from invariant wavelength ratios. II. The nonspectral and global mechanisms

Given the spectral mechanism of color constancy (Part I of this series), the remaining nonspectral mechanism is formulated here in Part II by the constraint of correlation with known spectral illuminant–invariant functions, i.e., invariant wavelength ratios between constant hues, which plot straight parallel lines in the plane of wavelength and reciprocal illuminant color temperature (MK^?1). The same is assumed to apply to nonspectral constant hues in the same plane and dominant wavelength scale extended to cover the nonspectrals (see accompanying article “Relative wavelength metric for the complete hue cycle …”). To simplify analysis, stimuli are optimal aperture colors; their monochromatic stimuli lie between 442 and 613 nm, common boundaries with optimal compound stimuli (nonspectrals). It is shown that the wavelengths and invariant ratios of spectral constant hues can be formulated exactly (±0.5%) from the ratios of an harmonic period, which shifts wavelength with MK^?1. The formula implies this color‐constant hue cycle is isomorphic across illuminants and allows prediction of nonspectral constant hues. To identify these colorimetrically, their spectral complementary wavelengths are specified for various illuminants. This completes theglobal color constancy mechanism for the illuminant color temperature range 2800 to 25,000 K. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

Why higher resolution graphics cards are needed in colour vision research

The colour resolution of a 14‐bit and an 8‐bit per channel graphics card were evaluated and compared with the just noticeable difference between colours (varying only in luminance) for: (1) a standard observer (based on the CIE 1976 L*u*v* colour space) and (2) real observers in a colour discrimination task. The results of this study show that an 8‐bit per channel graphics card seems adequate for colour discrimination experiments where stimuli only vary in luminance. However, considering that the resolution of the graphics card should be equal to the Nyquist rate, an 8‐bit per channel card turns out to be inadequate. For colour discrimination experiments where stimuli only vary in chromaticity, there is an undersampling of the colour space with respect to MacAdam ellipses when using 8‐bit per channel graphics cards. The extremely fine colour resolution of a 14‐bit per channel graphics card overcomes these problems. Its use allows more accurate measurements of achromatic and chromatic discrimination thresholds and avoids experimental (spatial or luminance) artefacts, such as bandings that can occur on achromatic or chromatic gradients. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2011     

Chroma,chromatic luminance,and luminous reflectance. Part II: Related models of chroma,colorfulness, and brightness

Part I of this article found, inter alia, that chroma resembles log inverted luminance. This article develops three math models of Munsell chroma and associated colorfulness from (1) inverted luminous reflectance Y, (2) inverted chromatic luminance, and (3) inverted chromatic luminance combined (over the mid‐spectrum 480–580 nm) with the unimodal curve for spectral absorptance of M cones. The first two models are simple but of limited accuracy and demonstrate that inverted luminance (of any form) cannot fully account for varying relative chroma around the hue cycle, particularly the minor minimum and maximum about 490 and 520 nm (which also feature in B:L functions). The third model is rather complex but very accurate, apparently the only accurate model of Munsell chroma or other experimentally based scales of relative chromaticness in the literature. It adjusts to any level of luminance or purity, as demonstrated for several levels. Three models of brightness (B:L ratio) for 2⁰ field aperture colors are given, based on either Munsell chroma or log inverted chromatic luminance. The former provides two accurate and simple models of the CIE B:L function: (1) log chroma = B:L ratio ±0.1, and (2) (chroma/k)^x = B:L ratio ±0.1. The latter also predicts B:L for nonspectral colors and those of lower purities, e.g., object colors. The results finally solve the relationship between brightness and chroma and demonstrate that B:L ratio (a contrast in constant luminance) arises directly from chroma (also a form of contrast in constant luminance), or the reverse. © 2008 Wiley Periodicals, Inc. Col Res Appl, 34, 55–67, 2009.     

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.     

Concerning the calculation of the color gamut in a digital camera

Several methods to determine the color gamut of any digital camera are shown. Since an input device is additive, its color triangle was obtained from their spectral sensitivities, and it was compared with the theoretical sensors of Ives‐Abney‐Yule and MacAdam. On the other hand, the RGB digital data of the optimal or MacAdam colors were simulated to transform them into XYZ data according to the colorimetric profile of the digital camera. From this, the MacAdam limits associated to the digital camera are compared with the corresponding ones of the CIE‐1931 XYZ standard observer, resulting that our color device has much smaller MacAdam loci than those of the colorimetric standard observer. Taking this into account, we have estimated the reduction of discernible colors by the digital camera applying a chromatic discrimination model and a packing algorithm to obtain color discrimination ellipses. Calculating the relative decrement of distinguishable colors by the digital camera in comparison with the colorimetric standard observer at different luminance factors of the optimal colors, we have found that the camera distinguishes considerably fewer very dark than very light ones, but relatively much more colors with middle lightness (Y between 40 and 70, or L* between 69.5 and 87.0). This behavior is due to the short dynamic range of the digital camera response. © 2006 Wiley Periodicals, Inc. Col Res Appl, 31, 399–410, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20245     

Changes in color appearance with variations in chromatic adaptation

Chromatic adaptation has been studied by applying methods of direct scaling to color appearances of invariant stimuli seen under different conditions of adaptation. The influence on color appearance of correlated color temperature of illumination, sample luminance factor, illuminance, and surround induction was studied. Perceived hue [expressed as proportions of unitary hues] varies with color temperature of illumination but not significantly with luminance factor or illuminance for the conditions of these experiments. Colorfulness varies with color temperature and also with luminance factor and illuminance, although relative colorfulness does not change significantly with illuminance. Lightness varies with luminance factor but is essentially independent of color temperature and illuminance over the ranges investigated here. Achromatic and chromatic lightnesses for samples of equal luminance differ in systematic ways that depend upon dominant wavelength and excitation purity. Color appearance data for daylight adaptation are highly correlated with Munsell Renotation specifications. The results may be used to determine corresponding colors for the adaptation conditions studied [equivalent to CIE Illuminants D₆₅, D₅₀, A, and dark adaptation]. They may also be used to determine color appearances under those conditions throughout a color solid. It is anticipated that they will be used as the basis for developing mathematical expressions for predictions of corresponding colors under other illumination conditions as well.     

A simple estimation method for effective adaptation coefficient

A method was proposed in a previous article (CRA, 22, 240–258, 1997) to estimate the state of incomplete adaptation by using the effective chromatic adaptation coefficient α_min. The method could be applied to any experiment on chromatic adaptation using object-color or luminous-color stimuli, but its computational procedure was rather tedious. For this reason, the two simple methods, Methods I and II, are proposed to give the approximate estimates of α_min. Method I uses the corresponding reference color under reference illuminant to a test achromatic color under test illuminant. Method II uses the two kinds of relation equations between test adapting luminance and α_min. The estimates of α_min by each of the two methods agree fairly well with those given in the previous article to the three experiments studied. © 1997 John Wiley & Sons, Inc. Col Res Appl, 22, 259–268, 1997     

Chromatic discrimination in relation to luminance level

We have measured the chromatic‐discrimination ellipses with different luminances for 66 stimuli distributed throughout the CIE‐1931 chromatic diagram. The distribution of these stimuli enabled us to analyze the influence of luminance on discrimination from clearly photopic levels to levels that could enter the mesopic range. The results show a clear influence of the luminance level on the areas of the chromatic‐discrimination ellipses. These areas remain almost constant when the luminance level is clearly photopic, and clearly increase when the luminance diminishes. However, it is not necessary that the luminance level diminish far below 2–3 cd/m² to detect a substantial increase in the area of the ellipses. According to our data, within the photopic range appears a transition interval of luminance above which the most pronounced increase in the area of the ellipse would be appreciable. Other parameters characteristic of discrimination ellipses, such as orientation and relation to semi‐axes, vary with the luminance level, although without clearly following any rule. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 123–131, 2001     

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     

Further investigation on the modified hyperbolic function in the CAM16 color appearance model

In the International Commission on Illumination (CIE) color appearance model CIECAM02, a modified hyperbolic function is used to represent luminance adaptation. The same nonlinear function is also used in the new color appearance model CAM16 [Color Res Appl., 2017;42:703‐718]. Although the modified hyperbolic function seems reasonable based on physiological evidence, it has an infinite slope at the origin, which causes instability for both the forward and inverse modes of the CIECAM02/CAM16 models. In this article, various possible extensions to the nonlinear luminance adaptation function in CIECAM02/CAM16 are reviewed and evaluated. Based on these investigations, the Gill extension to the hyperbolic function that is used to represent luminance adaptation [Proceedings of 16th Color and Imaging Conference, pp. 327‐331, 2008], is recommended at both the lower end (q < q_L ) and the upper end (q > q_U ), where q is the appropriate R_c , G_c , B_c (or R_wc , G_wc , B_wc ) response. In addition, the new recommended function can be readily inverted for use in the appropriate inverse appearance model. From an extensive analysis using available experimental data sets, we also propose that, for the lower and upper limits of the luminance range in the extended model, the values q_L = 0.26 and q_U = 150 be used, respectively.     

A shift of the perceptual attributes of color due to the manifestation of the simultaneous contrast effect on a display

This research shows the effect of simultaneous contrast on a design solution that generates it, and it also shows how its manifestation affects the shift of perception attributes of the observer's color. In the conducted research, 55 subjects had to harmonize the primary stimuli from the reproduction obtained with the help of digital printing technology, with the primary stimuli presented on two computer screens. As a visual harmonization technique, simultaneous binocular harmonization was used. The primary stimuli were made achromatic, with a 50% Raster Tone value (RTV), and are surrounded by achromatic secondary stimuli whose values increase in steps from 10% RTV up to 100% RTV. A shift in the perceptual attributes of color has been shown with the help of the CIEDE2000 system. Using ANOVA with repeated-measures and Fisher's post hoc analysis, statistically significant differences were found between the perceived means of shift in the ΔC₀₀ chroma and ΔL₀₀ lightness on defined samples on both computer screens, while in the case of the ΔH₀₀ hue, no statistically significant differences were observed. The research also determined colorimetric differences in the ΔE₀₀ color difference. Moreover, the student's t test was used to determine that the effect is stronger when manifested on the Lenovo computer than on the Asus computer screen (P < .05).     

On the conditions affecting the contribution of color to brightness perception

Colored stimuli appear to be brighter than an achromatic stimulus of the same luminance as the colored stimuli. We have studied this effect using similarity judgments in a triadic scaling task. Several instructions and stimulus configurations were used. the color sets contained colors at three luminance levels. When subjects are instructed to attend to brightness differences, the contribution of the brightness axis is strongly increased relative to the contribution of the color channels. Moreover, a correction to the color input is necessary when subjects are instructed to attend to brightness similarities between saturated colors. For a fixed adaptation level, the chromatic input is relatively stronger for the lower luminance levels. This correction is absent in all other investigated conditions. the correction found here confirms an earlier report by Fairchild and Pirotta (1991).     

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     

The Specification of Colour Appearance. I. Concepts and Terms

Concepts necessary for the specification of the appearance of colours are described, and the corresponding colour terms collected. Psychometric and psychoquantitative terms are listed that correlate with the perceptual and psychophysical terms used. The perceptual term colourfulness is proposed to denote the attribute of a visual sensation according to which an area appears to exhibit more or less chromatic colour; for a given chromaticity, as the luminance increases, colourfulness generally increases. For related colours, the CIE 1976 Colour Spaces are used to systematize some psychometric variables that are independent of absolute luminance level, including metric saturation, metric purity, and metric chroma, and formulae are given for calculating their amounts. (In Part II, to appear in the next issue, the effects of changes in viewing conditions will be discussed).     

An adaptive color similarity function suitable for image segmentation and its numerical evaluation

In this article, we present an adaptive color similarity function defined in a modified hue‐saturation‐intensity color space, which can be used directly as a metric to obtain pixel‐wise segmentation of color images among other applications. The color information of every pixel is integrated as a unit by an adaptive similarity function thus avoiding color information scattering. As a direct application we present an efficient interactive, supervised color segmentation method with linear complexity respect to the number of pixels of the input image. The process has three steps: (1) Manual selection of few pixels in a sample of the color to be segmented. (2) Automatic generation of the so called color similarity image (CSI), which is a gray level image with all the gray level tonalities associated with the selected color. (3) Automatic threshold of the CSI to obtain the final segmentation. The proposed technique is direct, simple and computationally inexpensive. The evaluation of the efficiency of the color segmentation method is presented showing good performance in all cases of study. A comparative study is made between the behavior of the proposed method and two comparable segmentation techniques in color images using (1) the Euclidean metric of the a* and b* color channels rejecting L* and (2) a probabilistic approach on a* and b* in the CIE L*a*b* color space. Our testing system can be used either to explore the behavior of a similarity function (or metric) in different color spaces or to explore different metrics (or similarity functions) in the same color space. It was obtained from the results that the color parameters a* and b* are not independent of the luminance parameter L* as one might initially assume in the CIE L*a*b* color space. We show that our solution improves the quality of the proposed color segmentation technique and its quick result is significant with respect to other solutions found in the literature. The method also gives a good performance in low chromaticity, gray level and low contrast images. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 156–172, 2017     

Preference index for Japanese complexion under illuminations

This article proposes a useful evaluation method based on preferred complexion as one of color‐rendering methods of light sources. A relational equation between subjective evaluation values of preferred Japanese complexion under various illuminations and the D65 corresponding colors by adopting CIE94 chromatic adaptation transform on the CIE 1976 u′v′ chromaticity diagram was derived by using multiple regression. Then, preference index of skin color or PS was developed in order to evaluate quantitatively the degrees of preferred complexion from the equation. Furthermore, a new index PS_(ac,bc) was derived by using CAM02 color appearance model instead of the CIE94. Each relationship of R_a, R₁₅, CQS, MCRI, FCI, CCRI, and HCR to PS was examined. Then, the PS was found as an independent index which was quite different from the other indices when the PS was more than or equal to 80. Therefore, it is useful to develop and evaluate light sources to realize more comfortable lighting environments by applying the concept of the PS. © 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 143–153, 2016     

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.     

Unique hue data for colour appearance models. Part III: Comparison with NCS unique hues

In this study, Swedish Natural Color System (NCS) unique hue data were used to evaluate the performance of unique hue predictions by the CIECAM02 colour appearance model. The colour appearance of 108 NCS unique hue stimuli was predicted using CIECAM02, and their distributions were represented in a CIECAM02 a_c–b_c chromatic diagram. The best‐fitting line for each of the four unique hues was found using orthogonal distance regression in the a_c–b_c chromatic diagram. Comparison of these predicted unique hue lines (based on the NCS data) with the default unique hue loci in CIECAM02 showed that there were significant differences in both unique yellow (UY) and unique blue (UB). The same tendency was found for hue uniformity: hue uniformity is worse for UY and UB stimuli in comparison with unique red (UR) and unique green (UG). A comparison between NCS unique hue stimuli and another set of unique hue stimuli (obtained on a calibrated cathode ray tube) was conducted in CIECAM02 to investigate possible media differences that might affect unique hue predictions. Data for UY and UB are in very good agreement; largest deviations were found for UR. © 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 256–263, 2015