Evaluating the 1931 CIE color‐matching functions

The use of colorimetry within industry has grown extensively in the last few decades. Central to many of today's instruments is the CIE system, established in 1931. Many have questioned the validity of the assumptions made by Wright¹ and Guild,² some suggesting that the 1931 color‐matching functions are not the best representation of the human visual system's cone responses. A computational analysis was performed using metameric data to evaluate the CIE 1931 color‐matching functions as compared to with other responsivity functions. The underlying assumption was that an optimal set of responsivity functions would yield minimal color‐difference error between pairs of visually matched metamers. The difference of average color differences found in the six chosen sets of responsivity functions was small. The CIE 1931 2° color‐matching functions on average yielded the largest color difference, 4.56 ΔE. The best performance came from the CIE 1964 10° color‐matching functions, which yielded an average color difference of 4.02 ΔE. An optimization was then performed to derive a new set of color‐matching functions that were visually matched using metameric pairs of spectral data. If all pairs were to be optimized to globally minimize the average color difference, it is expected that this would produce an optimal set of responsivity functions. The optimum solution was to use a weighted combination of each set of responsivity functions. The optimized set, called the Shaw and Fairchild responsivity functions, was able to reduce the average color difference to 3.92 ΔE. In the final part of this study a computer‐based simulation of the color differences between the sets of responsivity functions was built. This simulation allowed a user to load a spectral radiance or a spectral reflectance data file and display the tristimulus match predicted by each of the seven sets of responsivity functions. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 316–329, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10077     

Development of a comprehensive visual dataset based on a CIE blue color center: Assessment of color difference formulae using various statistical methods

The objectives of this work were to develop a comprehensive visual dataset around one CIE blue color center, NCSU‐B1, and to use the new dataset to test the performance of the major color difference formulae in this region of color space based on various statistical methods. The dataset comprised of 66 dyed polyester fabrics with small color differences ($\Delta E_{{\rm ab}}^* < 5$ ) around a CIE blue color center. The visual difference between each sample and the color center was assessed by 26 observers in three separate sittings using a modified AATCC gray scale and a total of 5148 assessments were obtained. The performance of CIELAB, CIE94, CMC(l:c), BFD(l:c), and CIEDE2000 (K_L:K_C:K_H) color difference formulae based on the blue dataset was evaluated at various K_L (or l) values using PF/3, conventional correlation coefficient (r), Spearman rank correlation coefficient (ρ) and the STRESS function. The optimum range for K_L (or l) was found to be 1–1.3 based on PF/3, 1.4–1.7 based on r, and 1–1.4 based on STRESS, and in these ranges the performances of CIEDE2000, CMC, BFD and CIE94 were not statistically different at the 95% confidence level. At K_L (or l) = 1, the performance of CIEDE2000 was statistically improved compared to CMC, CIE94 and CIELAB. Also, for NCSU‐B1, the difference in the performance of CMC (2:1) from the performance of CMC (1:1) was statistically insignificant at 95% confidence. The same result was obtained when the performance of all the weighted color difference formulae were compared for K_L (or l) 1 versus 2. © 2009 Wiley Periodicals, Inc. Col Res Appl, 2011     

Inter‐observer comparison of color‐matching functions

The colorimetric difference between pairs of observers is simulated by a proper filtering of the stimulating radiation, and their comparison is made on properly defined Common Reference Frames in the tristimulus space. As examples, two comparisons are proposed: (1) Comparison between the Vos modification of the CIE 1931 Standard Colorimetric Observer and the CIE 1964 Supplementary Standard Observer: in this case, it is supposed that the difference between these two color‐vision systems is due to the macula lutea only, which with a spectral selective absorbance alters the power spectral distribution of the color stimuli. The optical density of the macular pigment is well reproduced. (2) Comparison between the Vos modification of the CIE 1931 Standard Colorimetric Observer and the CIE 1931 Standard Colorimetric Observer: in this case, the difference between these two observers could be simulated by different calibration of the photodetectors. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 177–184, 1999     

Spectral sensitivities of the normal human visual system,color‐matching functions and their principles,and how and why the two sets should coincide

The objectives of this article are (1) to help reestablish in technical thinking the three spectral sensitivity curves, dating from Helmholtz, of the normal human visual system (particularly their peak wavelengths); (2) to remind the reader of the principles of the sets of three color‐matching functions (CMFs) comprising a CIE Standard Observer, and to make these principles more easily understandable; (3) to show how the visual data comprising today's Standard Observers lead directly to the peak wavelengths of the spectral sensitivity curves; (4) to use modern color‐matching data to restore essential details to CMFs damaged by manipulation over the years; (5) to suggest that coincidence of corrected CMFs and the actual spectral sensitivities of the normal human visual system (a feature long tacitly assumed by color scientists of the past) is close at hand; and (7) to point out that CMFs embody a wealth of significance concerning the nature of the spectral response of the normal human visual system, despite the fact that they do not work well as weighting functions in the practice of colorimetry. The color‐matching data of the CIE 1964 10° Standard Observer are used to reproduce the visual matches upon which it is based, and to model the principles of CMFs in general. The CIE 1964 data are treated as if they had been collected directly from modern‐day visual matching experiments, in which an accurate, high‐resolution, absolute spectral power distribution (SPD) of every viewed light is measured, and power content of each component of the light determined. The experimental units and dimensions of the resulting three CMFs are established. The significance of CMF plots above and below the zero‐power level, and of the spectral shapes of the CMFs, is shown. The positions in wavelength of the nominal maximum of the red, green, and blue CMF, for a wide range of wavelengths of real spectral primaries, are noted (following MacAdam) to be “amazingly similar.” Then the much‐manipulated data of the CIE Standard Observers are left behind, and modern raw unmanipulated visual data are analyzed in the same manner. The results yield characteristics of CMFs that are more representative of the normal human visual system than are those of the CIE Standard Observers. The peak heights of the nominal maxima of the red, green, and blue CMF, for the same wide range of primaries, are importantly significant also. They serve to define, at least approximately, the forms of the three spectral sensitivities, assuming the traditional model of the visual system. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 139–156, 1999     

Visual evaluation at scale of threshold to suprathreshold color difference

Visual evaluation experiments of color discrimination threshold and suprathreshold color‐difference comparison were carried out using CRT colors based on the psychophysical methods of interleaved staircase and constant stimuli, respectively. A large set of experimental data was generated ranged from threshold to large suprathreshold color difference at the five CIE color centers. The visual data were analyzed in detail for every observer at each visual scale to show the effect of color‐difference magnitude on the observer precision. The chromaticity ellipses from this study were compared with four previous published data, of CRT colors by Cui and Luo, and of surface colors by RIT‐DuPont, Cheung and Rigg, and Guan and Luo, to report the reproducibility of this kind of experiment using CRT colors and the variations between CRT and surface data, respectively. The present threshold data were also compared against the different suprathreshold data to show the effect of color‐difference scales. The visual results were further used to test the three advance color‐difference formulae, CMC, CIE94, and CIEDE2000, together with the basic CIELAB equation. In their original forms or with optimized K_L values, the CIEDE2000 outperformed others, followed by CMC, and with the CIELAB and CIE94 the poorest for predicting the combined dataset of all color centers in the present study. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 198–208, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20106     

Grassmann's laws and individual color‐matching functions for non‐spectral primaries evaluated by maximum saturation technique in foveal vision

Over time, much work has been carried out to ascertain the validity of Grassmann's laws, Abney's law, CIE standard color‐matching functions and, up to now, no definitive answer has been given. Some of the phenomena subject of this debate are considered. An apparatus for color matching in 1.8° visual field has been realized with two sets of primary lights with broad spectral bands. This kind of primaries is the great difference with respect to other laboratories because it allows an indirect check of the Grassmann additivity law on the basis of the spectra and individual color‐matching functions by evaluating: (1) the tristimulus values of the primary lights; (2) the transformation matrices between the two reference frames defined by the two primary sets; and (3) the tristimulus values associated to all the pairs of matching lights in the bipartite field produced in the evaluation of the two sets of color‐matching function. The discrepancies of the data resulting in the check (1) and (2) are all compatible with the range defined by the uncertainty propagation of the individual color‐matching functions. In the check (3) fifteen tristimulus values over 18 have a discrepancy lower than one standard uncertainty. Grassmann's proportionality law is checked directly by reducing the matching lights with a neutral filter and holds true. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 271–281, 2008.     

Correlation between visual and colorimetric scales ranging from threshold to large color difference

Psychophysical experiments of color discrimination threshold and suprathreshold color‐difference comparison were carried out with CRT‐generated stimuli using the interleaved staircase and constant stimuli methods, respectively. The experimental results ranged from small (including threshold) to large color difference at the five CIE color centers, which were satisfactorily described by chromaticity ellipses as equal color‐difference contours in the CIELAB space. The comparisons of visual and colorimetric scales in CIELAB unit and threshold unit indicated that the colorimetric magnitudes typically were linear with the visual ones, though with different proportions in individual directions or color centers. In addition, color difference was generally underestimated by the Euclidean distance in the CIELAB space, whereas colorimetric magnitude was perceptually underestimated for threshold unit, implying the present color system is not a really linear uniform space. Furthermore, visual data were used to test the CIELAB‐based color‐difference formulas. In their original forms CIEDE2000 performed a little better than CMC, followed by CIELAB, and with CIE94 showing the worst performance for the combined data set under the viewing condition in this study. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 349–359, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10081     

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     

Testing the behavior for metamerism of the new deviate observer (JF‐DO)

Recently,in our laboratories, a set of color‐matching functions (cmfs) has been formulated for small fields by using two groups of real observers: JAM, MM, CF and AY, JR, MR, JL, JA, FP. The measurements of these cmfs have been made using different experimental devices and methods and it has enabled us to propose a New Deviate Observer for small fields (JF‐DO). This new JF‐DO was derived from the average observer of our nine real observers, following the technique used by the CIE to establish the Standard Deviate Observer (CIE‐1989 SDO), which was established for fields of 10°, despite the CIE's assumption that it can be applied to smaller fields. In the present work, we report experimental results of the JF‐DO using metameric reflectances in comparison to the CIE‐1931 Standard Observer and to the CIE‐1989 SDO. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 363–370, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.     

Design and study of a color sensitivity function

If we study color reproduction, such as computer color matching or the appraisal of metametric index, we wish to understand the characteristic of color differences that are caused by the object spectral reflectivity change at each wavelength. If we simulate the light source, we wish to know the characteristics of color differences that are caused by change in relative power distribution of the light source at each wavelength; if we simulate a human eye instrument, we wish to know the characteristics of color differences that are caused by change in visual sense of human eyes at each wavelength. So, we define the color‐sensitivity functions of an object, a light source, and human eyes. According to the chromatic theory, the color‐sensitive functions of an object, a light source, and human eyes are defined in the widely used CIE1976 (L*a*b*) color space and color difference.¹ Their mathematical formulae are deduced. The three kinds of color‐sensitive functions are studied systematically and comprehensively in the whole color space. The characteristics of the color‐sensitive functions are summarized, and the mathematical models of the three kinds of color‐sensitive functions can be utilized in some fields such as computer color matching, simulation of a standard light source, and humans viewing a colorimeter. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 118–124, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20089     

Color‐difference formula performance for several datasets of small color differences based on visual uncertainty

Visual uncertainty, while reported, is not used routinely when evaluating color‐difference formula performance in comparison with visual data; rather, data are analyzed assuming no uncertainty; that is, repeating the experiment would result in the identical average results. Previously, Shen and Berns developed three methods to determine whether a color‐difference formula was well‐fitting, under‐fitting, or over‐fitting visual data when visual uncertainty was considered, the method dependent on how the uncertainty was reported and the colorimetric sampling of the color‐difference stimuli. The “nonellipsoid standard error method” was used in the current analyses. Three datasets were evaluated: BFD‐P, Leeds, and Witt. For the BFD‐P data, incorporating visual uncertainty led to the same performance results as the average results, that CIEDE2000 was an improvement over CIE94, which was an improvement over CIELAB. For the Witt data, incorporating visual uncertainty led to the same performance results as the average results, that CIEDE2000 and CIE94 had equivalent performance, both an improvement over CIELAB. However, both formulas under‐fitted the visual results; thus, neither formula was optimal. For the Leeds dataset, the visual uncertainty analysis did not support the improvement of CIEDE2000 over CIE94 that occurred when evaluating the average results. Both formulas well fit the visual data. These analyses also provided insight into the tradeoffs between the number of color‐difference pairs and the number of observations when fitting a local contour of equal perceived color difference: In particular, increasing the number of observations was more important than increasing the number of color‐difference pairs. Finally, average standard error could be used to approximate visual uncertainty defined using STRESS. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2011     

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.     

Investigating the effect of texture on the performance of color difference formulae

To predict the perceived color differences, the effect of the surface texture on the performance of the color difference formulae was investigated. To this end, knitted polyester fabrics with eight different textures were prepared. The fabrics were dyed by seven dyestuffs in five different depths. The selected pairs from the five samples with different depths in each hue covered small to large color differences. The assessed pair of samples had the same texture and hue, but different depths. A panel of 23 observers assessed the color differences of the pairs by gray scale method. The results showed that for the textile samples with different texture structures, the CIEDE2000 (2:1:1) performed the best followed by CMC (2:1:1), CIE94 (2:1:1), and CIELAB with approximately same performance. In addition, the magnitude of color difference influenced the ability of the formulae to predict the visual assessments and the best performance obtained for medium color differences. The comparison between eight different texture groups indicated that the texture structures of the pairs significantly affected the performance of the color difference formulae. For instance, the PF/3 measures obtained for the eight texture groups by CIEDE2000 (2:1:1) color formula could be varied between 21.98 and 33.37 PF/3 units. © 2009 Wiley Periodicals, Inc., Col Res Appl, 2010.     

Evaluation of the quality of different D65 simulators for visual assessment

In this study psychophysical experiments were conducted to investigate the visual color differences of 77 textile metamers using a gray‐scale rating method under five D65 simulators. The quality of each of the D65 simulators was quantified according to the method provided in CIE Publication No. 51.2 using the visible range metamerism index (MI_vis). The five D65 simulators were categorized from A to D according to their MI_vis values. The color difference of each metameric pair was calculated using the spectral power distribution (SPD) of CIE illuminant D65 and artificial SPDs of D65 simulators. The performance factor (PF/3) was used to indicate the agreement between visual differences under five D65 simulators as well as between instrumental color difference and visual difference. Observer accuracy and observer repeatability were also analyzed by PF/3 measure. The experiment results showed that the visual data obtained from category A and B D65 simulators were in good agreement with the PF/3 measure and had no statistical difference in a pair comparison t test. The results also indicated that better agreement between instrumental and visual color differences was obtained using the artificial SPDs of the D65 simulator than with the SPD of CIE illuminant D65. The general color rendering index, Ra, for each D65 simulator was calculated by the CIE No. 13.3 method. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 243–251, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10061     

A top down description of S‐CIELAB and CIEDE2000

Recent work in color difference has led to the recommendation of CIEDE2000 for use as an industrial color difference equation. While CIEDE2000 was designed for predicting the visual difference for large isolated patches, it is often desired to determine the perceived difference of color images. The CIE TC8‐02 has been formed to examine these differences. This paper presents an overview of spatial filtering combined with CIEDE2000, to assist TC8‐02 in the evaluation and implementation of an image color difference metric. Based on the S‐CIELAB spatial extension, the objective is to provide a single reference for researchers desiring to utilize this technique. A general overview of how S‐CIELAB functions, as well as a comparison between spatial domain and frequency domain filtering is provided. A reference comparison between three CIE recommended color difference formulae is also provided. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 425–435, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10195     

A hypothesis regarding the poor blue constancy of CIELAB

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

The study of visual image improvement of an organic light‐emitting diode by dye‐polarizer composed of optical film

The visual image improvement of an organic light‐emitting diode (OLED), which is based on some theoretical frameworks and the optical property of the dye‐polarizer composed of optical film, is investigated. The key performance indexes of visions, i.e., visual reflective sensitivity, contrast ratio, and color saturation are focused. First, the reflectance and color saturation of an OLED were simulated and calculated by using the transfer matrix method with thin‐film optical filters and the definition rule of color performances in the 1931 index proposed by the Commission International de l'Eclairage (CIE₁₉₃₁). The results clearly showed excellent performance when using the dye‐polarizer on the panel of an OLED in the theoretical calculation and practical application. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1755–1763, 2012     

Field trials for assessing the method of observer metamerism adopted by CIE

The following field trials are made for assessing the method of observer metamerism adopted by CIE. (1) The individual variation of metameric match was assessed between a fluorescent-lamp light and each of three different matching stimuli by the CIE method. The high precision of visual color match was confirmed for the 6-primary Donaldson colorimeter. The prediction was compared with experimental results for a similar fluorescent lamp. (2) The individual variation predicted by the CIE method was compared with that directly derived by using the Stiles original 20 color-matching functions. The effectiveness of the CIE method was confirmed. (3) It was clarified that the individual variation of colorimetric values on a single test stimulus corresponds to that for the metameric match between the test stimulus and a mixture of the CIE 10° r, g, b primaries. (4) The actual observer variation found by Stiles and Wyszecki in the field trial on the CIE 1964 color-matching functions was tested using the CIE method. The method is effective to assess the intrusion of other factors in actual color match, in addition to the individual variation of color-matching functions.