Vectorial color

A set of orthonormal color matching functions is developed, in which the first is an all‐positive achromatic function, the second is red–green, and the third can be loosely described as blue–yellow. The achromatic function, proportional to the familiar $ \bar y $ , is a sum of red and green cones. The red–green function uses the same cone sensitivities, but subtracted, with coefficients so that it is orthogonal to the achromatic one. The third function involves all three cones, but is primarily a blue sensitivity. Using this basis to compute the tristimulus vectors of narrow‐band lights at unit power gives Jozef Cohen's locus of unit monochromats, (LUM) an invariant shape now graphed in a space where the axes have intuitive meaning. The extreme points of the LUM reveal the wavelengths that act most strongly in mixtures, a close approximation to William Thornton's Prime Colors. In effect, decades of research converge in three functions and a vectorial schema, demystifying such issues as color rendering and the selection of additive primaries. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2011.     

Camera characterization for improving color archaeological documentation

Determining the correct color is essential for proper cultural heritage documentation and cataloging. However, the methodology used in most cases limits the results since it is based either on perceptual procedures or on the application of color profiles in digital processing software. The objective of this study is to establish a rigorous procedure, from the colorimetric point of view, for the characterization of cameras, following different polynomial models. Once the camera is characterized, users obtain output images in the sRGB space that is independent of the sensor of the camera. In this article we report on pyColorimetry software that was developed and tested taking into account the recommendations of the Commission Internationale de l'Éclairage (CIE). This software allows users to control the entire digital image processing and the colorimetric data workflow, including the rigorous processing of raw data. We applied the methodology on a picture targeting Levantine rock art motifs in Remigia Cave (Spain) that is considered part of a UNESCO World Heritage Site. Three polynomial models were tested for the transformation between color spaces. The outcomes obtained were satisfactory and promising, especially with RAW files. The best results were obtained with a second‐order polynomial model, achieving residuals below three CIELAB units. We highlight several factors that must be taken into account, such as the geometry of the shot and the light conditions, which are determining factors for the correct characterization of a digital camera.     

The use of metamers to compare the color vision of observers

In this research we compare the colorimetric behavior of several observers. For color centers recommended by CIE we have produced large sets of spectral distributions, which are metameric for the CIE 1931 standard observer. For each one of the color centers, we compare the clouds of chromaticity coordinates with the chromaticity thresholds. We define a parameter that provides a quantitative measure of the interobserver variability. This parameter is used to arrange the observers by their degree of likeness. A similar procedure has been used to compare two real observers. It is shown how there is no reciprocity between the colorimetric behavior of two real observers. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 262–269, 2001     

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     

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     

Numerical methods for smoothest reflectance reconstruction

Three numerical methods are presented for finding the smoothest reflectance curve associated with a given triplet of tristimulus values. The methods differ in how “smooth” is defined, and also differ in the domain of colors over which they are applicable. The first method is very quick and applies to any tristimulus values, but sometimes can yield reflectance curves with portions that fall outside the range 0 to 1. The second method applies to colors within the spectral locus (real colors) and guarantees that the reflectances produced are positive. The third method applies to colors within the object color solid (object colors) and guarantees that the reflectances fall within the range 0 to 1. The methods are shown to create reflectances that closely resemble those of real colors (natural and synthetic). Focus is given to implementing the numerical methods in very short MATLAB/Octave functions and to understanding the numerical behavior of the methods near the limits of their respective domains of applicability in terms of matrix conditioning and discretization artifacts.     

Color rendering: A calculation that estimates colorimetric shifts

Lights vary in their ability to render object spectral reflectances into color contrasts. When a light L1 is replaced by another L2, even if L2 matches L1 in chromaticity, systematic color shifts may occur, including a loss or gain of chromatic color. For instance, many familiar lights, when compared to daylight, dull red and green objects, rendering them closer to gray. An opponent colors method is appropriate to this discussion because it brings to the surface the notion of chromatic color, meaning actual departure from white or gray. In this article, an opponent‐colors analysis leads to a matrix formulation that serves two purposes. The effects of replacing L1 by L2 are estimated with a 3×3 “rendering matrix” P . Given an object's tristimulus vector under L1, the method makes an approximate prediction of the new tristimulus vector under L2. Thanks to the opponent formulation, matrix element P22 quantifies the gain or loss of redness and greenness, while P33 expresses gain or loss of blueness and yellowness. These in fact are major effects, so the method is both quantitative and explanatory. © 2003 Wiley Periodicals, Inc. Col Res Appl, 29, 43–56, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10213     

Color rendering: Asking the question

Two white lights may have the same chromaticity, and yet when used to light an array of objects may differ in their ability to reveal colors. For example, any white light can be matched by a mixture of two narrow‐band lights, a yellow plus a blue. In this extreme case, reds and greens become black or brown and the red‐green dimension is lost. At the other extreme, a light with three narrow bands, at the proper wavelengths, can brighten reds and greens and increase red‐green contrast, relative to a broad‐band light such as daylight. Many commercial lights tend to dull reds and greens, relative to broad‐band sources, a central reason that color rendering is a practical concern. A telling example is neodymium glass, a yellow‐absorbing filter that is sometimes used to improve color rendering. This article seeks to bring these ideas to life through detailed graphical examples. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 403–412, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10193     

An attempt to reconstruct the meaning of al‐Tusi's color words

In a text dating between 1259 and 1277, the Persian scholar al‐Tusi presented a systematic arrangement of 26 color terms. We propose a reconstruction of all color terms from al‐Tusi's scheme, in terms of preferred translation, mean CIEL*a^*b^* coordinates and digital representation. This reconstruction is based on a visual experiment with 30 subjects, who identified the Munsell chip best representing each color term. Persian words for which the meaning changed since the time of al‐Tusi were substituted by direct translations. The results show considerable interobserver variability in the colors selected when identifying color terms. This relatively large variation was shown to be a characteristic for memory matching experiments in general. Several specific color terms for which the resulting color variation was particularly large are discussed in more detail, and possible explanations for these variations are proposed. The proposed reconstruction suggests that al‐Tusi's list is largely consistent in modern colorimetric terms, although some large hue shifts are observed for color terms corresponding to green. We found no evidence for blue‐green (“grue”) confusion. © 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 206–216, 2016     

Impact of matching field size on color matching (functions) accuracy

Accurate colorimetry starts with accurate color matching functions (CMFs). Due to changes in the macular pigment and cone pigment optical densities at different retinal locations, different CMFs are required for different stimulus field sizes. To characterize the accuracy of the CIE recommendation for the use of 2° and 10° standard CMFs and the field-size dependent CIEPO06 model, in this study, a series of achromatic matching experiments were performed with 2°, 4°, 6°, 8°, and 10° bipartite fields using spectrally narrowband primaries. Using the CIEPO06 model, optimal field sizes were estimated that minimize the chromaticity differences between the spectrally narrowband observer matches and the spectrally broadband achromatic target. It was found that the optimal field size estimated using the CIEPO06 model is close to half the actual bipartite field size in most cases, except for the 2° field. The discrepancy between the 10° bipartite field in Stiles & Burch's experiments and our optimal field size (6.54°) was assumed to be due to different individual color comparison strategies. However, the results of experiments requiring specific observer gaze positions did not support this assumption and the reason for the discrepancy remains unclear. Confirming our earlier results, the primary set (636, 521, 447 nm) was again found to be largely insensitive to changes in CMFs and to provide the most accurate matches under various fields of view. The inter- and intra-observer variability ellipses for 2° matches are larger than those for 10°, consistent with Brown's finding for color discrimination ellipses. The magnitude of the intraobserver variability was similar for all field sizes, except for 2° field size, where matching errors were larger for some primary sets.     

CIELAB color space boundaries under theoretical spectra and 99 test color samples

A color space is a three-dimensional representation of all the possible color percepts. The CIE 1976 L*a*b* is one of the most widely used object color spaces. In CIELAB, lightness L* is limited between 0 and 100, while a* and b* coordinates have no fixed boundaries. The outer boundaries of CIELAB have been previously calculated using theoretical object spectral reflectance functions and the CIE 1931 and 1964 observers under the CIE standard illuminants D50 and D65. However, natural and manufactured objects reflect light smoothly as opposed to theoretical spectral reflectance functions. Here, data generated from a linear optimization method are analyzed to re-evaluate the outer boundaries of the CIELAB. The color appearance of 99 test color samples under theoretical test spectra has been calculated in the CIELAB using CIE 1931 standard observer. The lightness L* boundary ranged between 6 and 97, redness-greenness a* boundary ranged between −199 and 270, and yellowness-blueness b* boundary ranged between −74 and 161. The boundary in the direction of positive b* (yellowness) was close to the previous findings. While the positive a* (redness) boundary exceeded previously known limits, the negative a* (greenness) and b* (blueness) boundaries were lower than the previously calculated CIELAB boundaries. The boundaries found here are dependent on the color samples used here and the spectral shape of the test light sources. Irregular spectral shapes and more saturated color samples can result in extended boundaries at the expense of computational time and power.     

Dependence of the color appearance of some flowers on illumination

Seven flower colors perceived by five color experts using visual color measurement under 2800 K warm white fluorescent lamps, 3500 K plant growth lamps, and 6500 K light‐emitting diodes (LEDs) were compared with those under 6500 K fluorescent lamps, which represented illuminants in florist shops. Fluorescent lamps (6500 K, 1000 lx) were found to be effective for displaying flower colors and were used as the standard condition. The colors of flowers generally shifted in the same direction as those of the illuminants in CIELAB space. The color differences were highest under the 3500 K fluorescent lamp at both 500 and 2000 lx. At 500 lx, the ΔE values under the 6500 K LED were higher than those under the 2800 K lamp. The C* and ΔE values revealed that the 2800 K lamp was unsatisfactory for purple‐blue and purple flowers and was more suitable for floral displays at lower illuminance. Under the 3500 K lamp, the highest color distortion occurred in cool‐colored flowers, but C* increased for purple‐blue and purple flowers. The 6500 K LED tended to decrease C* for warm‐colored flowers under both illuminances, but it was effective for displaying purple‐blue and purple flowers with increased C*. © 2012 Wiley Periodicals, Inc. Col Res Appl, 39, 28–36, 2014     

Refinement of the RLAB color space

The prediction of color appearance using the RLAB color space has been tested for a variety of viewing conditions and stimulus types. These tests have shown that RLAB performs well for complex stimuli and not-so-well for simple stimuli. This article reviews the various psychophysical results, interprets their differences, and describes evolutionary enhancements to the RLAB model that simplify it and improve its performance. © 1996 John Wiley & Sons, Inc.     

Optimization of color reproduction on CRT‐color monitors

In the present experimental study, we quantify the influence of the brightness and contrast levels of a CRT‐color monitor in the color reproduction of 60 Munsell chips distributed throughout the chromatic diagram. The images were captured by two CCD cameras, and the color differences were evaluated after reproducing the chips on a color monitor (the experiment was performed with 3 different monitors) for 9 combinations of brightness‐contrast levels. We evaluated the color differences with 3 different formulas: CIELAB, CIELUV, and CIE94. The results indicate that the optimal settings of a monitor, to minimize the color differences, is a medium or minimum brightness level in combination with a maximum contrast level. This combination ensures a more faithful color reproduction with respect to the original image. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 207–213, 1999     

水泥颜色的定量表示及测定

介绍了以色彩学理论为基础建立的水泥颜色表示方法———R.S.Hunter提出的Lab空间色彩体系。该方法可以明确表示出水泥色彩的色调、彩度、明度等色彩特征,并且与目视观察的结果具有很好的一致性。使用色差计可以定量测定水泥Lab空间色彩体系的参数,这些参数可以为水泥颜色的评价和控制提供依据。介绍了色度测定方法。     

Light and color,some ethical issues

This is a comment to the editorial by J. Hutchings on “Talking about Color… and Ethics.” © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 233–235, 2007     

Spectral spaces and color spaces

It has long been known that color experiences under controlled conditions may be ordered into a color space based on three primary attributes. It is also known that the color of an object depends on its spectral reflectance function, among other factors. Using dimensionality reduction techniques applied to reflectance measurements (in our case a published set of 1 nm interval reflectance functions of Munsell color chips) it is possible to construct 3D spaces of various kinds. In this article we compare color spaces, perceptual or based on dimensionality reduction using color matching functions and additional operations (uniform color space), to spectral spaces derived with a variety of dimensionality reduction techniques. Most spectral spaces put object spectra into the ordinal order of a psychological color space, but so do many random continuous functions. In terms of interval scales there are large differences between color and spectral spaces. In spectral spaces psychophysical metamers are located in different places. © 2003 Wiley Periodicals, Inc. Col Res Appl, 29, 29–37, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10211     

Calibrated color mapping between LCD and CRT displays: A case study

The primary goal of a color characterization model is to establish a mapping from digital input values d_i (i = R,G,B) to tristimulus values such as XYZ. A good characterization model should be fast, use a small amount of data, and allow for backward mapping from tristimulus to d_i. The characterization models considered here are for the case of an end user who has no direct knowledge of the internal properties of the display device or its device driver. Three characterization models tested on seven different display devices are presented. The characterization models implemented in this study are a 3D look up table (LUT) (Raja Balasubramanian, Reducing the Cost of Lookup Table Based Color Transformations, Proc IS&T/SID 7th Color Imaging Conference 1 ), a linear model (Fairchild MD, Wyble DR. Colorimetric Characterization of the Apple Studio Display (Flat Panel LCD). Munsell Color Science Laboratory Technical Report, 1998), and the masking model (Tamura N, Tsumura N, Miyake. Masking Model for accurate colorimetric characterization of LCD. Proc IS&T/SID 10th Color Imaging Conference 3 ). The devices include two CRT monitors, three LCD monitors, and two LCD projectors. The results of this study indicate that a simple linear model is the most effective and efficient for all devices used in the study. A simple extension to the linear model is presented, and it is demonstrated that this extension improves white prediction without causing significant errors for other colors. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 438–447, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.     

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     

Categorical color constancy under RGB‐LED light sources

The light‐emitting diode (LED)‐based light sources have been widely applied across numerous industries and in everyday practical uses. Recently, the LED‐based light source consisting of red, green and blue LEDs with narrow spectral bands (RGB‐LED) has been a more preferred illumination source than the common white phosphor LED and other traditional broadband light sources because the RGB‐LED can create many types of illumination color. The color rendering index of the RGB‐LED, however, is considerably lower compared to the traditional broadband light sources and the multi‐band LED light source (MB‐LED), which is composed of several LEDs and can accurately simulate daylight illuminants. Considering 3 relatively narrow spectral bands of the RGB‐LED light source, the color constancy, which is referred to as the ability of the human visual system to attenuate influences of illumination color change and hold the perception of a surface color constant, may be worse under the RGB‐LED light source than under the traditional broadband light sources or under the MB‐LED. In this study, we investigated categorical color constancy using a color naming method with real Munsell color chips under illumination changes from neutral to red, green, blue, and yellow illuminations. The neutral and 4 chromatic illuminants were produced by the RGB‐LED light source. A modified use of the color constancy index, which describes a centroid shift of each color category, was introduced to evaluate the color constancy performance. The results revealed that categorical color constancy under the 4 chromatic illuminants held relatively well, except for the red, brown, orange, and yellow color categories under the blue illumination and the orange color category under the yellow illumination. Furthermore, the categorical color constancy under red and green illuminations was better than the categorical color constancy under blue and yellow illuminations. The results indicate that a color constancy mechanism in the visual system functions in color categories when the illuminant emits an insufficient spectrum to render the colors of reflecting surfaces accurately. However, it is not recommended to use the RGB‐LED light source to produce blue and yellow illuminations because of the poor color constancy.