A multiprimary lighting system for customized color stimuli

In this article, a dual seven-primary lighting system is constructed for color research and education. The system offers sufficient spectral variability to approximate the spectral power distribution of a variety of standard illuminants. More importantly, the constructed multiprimary lighting system was verified to have crucial advantages over conventional displays/projectors to probe observer metamerism through the generation of individualized metameric color stimuli. An observer metamerism index to describe the potential for observer metamerism of any generated stimulus pairs with respect to the population variation of color-normal observers is formulated. The metric is further extended for use in quantifying the potential for observer metamerism of any lighting system or a system-primary combination. Moreover, 10 pairs of lighting stimuli, customized for exhibiting high degrees of observer variability, were produced using the system as a step toward creating a device for the color matching functions characterization of individual observers, a so-called observer calibrator.     

Effect of observer metamerism on colour matching of display and surface colours

We studied the individual variability of asymmetric metameric colour matching between computer displays and object colour stimuli in conditions typical for the surface colour industries. Using two different computational techniques, we assessed the contribution of observer metamerism to this variability. In the studied conditions of spatially separated computer display and surface colour stimuli, this contribution was found to be insignificant for all colours but neutrals. In the chromaticness plane, the range of matches made by different observers practically coincides with the range of matches made by an individual observer. Consequently, we conclude that in the task of matching spatially separated display and surface colours, the range of matches made by a group of observers cannot be determined from variations in their colour‐matching functions, and thus the paradigm of the Standard Deviate Observer is shown to be inapplicable to the studied conditions. We suggest that individual variability in these conditions is governed by mechanisms of chromatic discrimination, and can be modeled by advanced colour difference formulae with suitably adjusted parametric coefficients. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 346–359, 2008     

Color matching experiment for highlighting interobserver variability

Human color vision differs from person to person, not only when color deficiencies occur but also within color‐normal populations. Investigating individual variability in normal color vision is beneficial both for clinical purposes and for quantifying observer metamerism. Researchers have used color matches such as Rayleigh matches, Moreland matches, the D&H color rule, and various combinations of different media for such investigations. However, none of them were originally aimed at investigating the interobserver variability in color‐normal populations, but rather were aimed at screening for color‐deficiencies. The objective of this study was, therefore, to design and carry out a color matching experiment where observer variability appeared as large as possible to detect the interobserver differences in the color‐normal population. Color matching was simulated under different combinations of reference spectrum and matching primaries using ColorChecker patches, different display/projector primaries, and the Stiles and Burch 49 observers. The simulation results showed: (1) The choice of spectra for the matching primaries had a significant effect on observer variability, (2) observer variability was large for near‐neutral reference colors, and (3) observer variability in the lightness direction was small relative to chromatic variability. The color matching experiment highlighting interobserver variability was designed based on these three findings and carried out for 61 color‐normal observers. Typical interobserver variability was 9.2 mean color difference from the mean (MCDM) using CIEDE2000 (spanning about 40 CIELAB units), which was much larger than any previous experiment. The obtained color matching data are useful for derivation, validation, and analysis of color matching functions. © 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 530–539, 2016     

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     

A general metric for the magnitude of observer metamerism

Observer metamerism is defined as a property of a pair of spectrally different stimuli having the same colour sensation for an individual (reference) observer. Frequently, samples in this pair no longer match if the observer is changed. In this article, a linear approximation formula is developed that predicts a metameric effect caused by small changes in the observer's colour‐matching functions. This approximation formula enables a general metric of observer metamerism, the observer metamerism potential, to be defined that is independent of any particular deviated observer but still provides a close link to ‘observer‐metameric’ colour difference. Numerical experiments were conducted to investigate the correlation between the observer metamerism potential and the maximum of 53 metameric colour differences caused by the change from the colour‐matching functions of CIE standard 10° observer to the colour‐matching functions of 49 Stiles and Burch's real 10° test observers. The proposed general metric, together with a previous metric proposed by the present authors, the illuminant metamerism potential, could be taken as a quantitative measure of the performance of spectral approximation methods.     

Colour matching using LEDs as primaries

In our metameric experiment, the colour of a filtered incandescent lamp was matched with the additive mixture of three LEDs in a Lummer–Brodhun‐type visual photometer. Two sets of primaries were used, one had their dominant wavelengths at 467, 533, and 600 nm; the other set had dominant wavelengths at 478, 552, and 635 nm. These values correspond approximately to the characteristic wavelengths of the Prime and Non‐Prime Colour spectral regions defined by W. A. Thornton. 1 Both the light of the incandescent lamp and that of the LED clusters were seen monocularly in a centrally divided bipartite field at a visual angle of 2°. The luminance of the matching fields was in the order of 20 cd/m² to provide sufficient gamut for the LED mixture. Ten young observers with normal colour vision participated in the experiment. The emission spectra of the viewing fields were measured with an array‐type spectroradiometer, and two sets of colour‐matching functions were used to calculate the chromaticity of the matching stimuli: the CIE 1931 standard colorimetric observer and the Judd–Vos modification of the colour‐matching functions. We found that the Judd–Vos modification of the CIE 1931 standard observer represents more accurately the real observers in the evaluation of our results. No systematic differences between the use of the two sets of LEDs were detected in contradiction to Thornton's findings. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 360–364, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20044     

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.     

Hybrid extended Luenberger-asymptotic observer for bioprocess state estimation

State observers generate estimates of non-measured variables based on a mathematical model of the process and some available hardware sensor signals. On the one hand, exponential observers, such as Luenberger observers or Kalman filters, have an adjustable rate of convergence, but strongly rely on the accuracy of the process model. On the other hand, asymptotic observers use a state transformation in order to avoid using the (usually uncertain) kinetic model, but have a rate of convergence imposed by the process dilution rate. In an attempt to combine the advantages of both techniques, a hybrid observer is developed, which evaluates a level of confidence in the process model and, accordingly, evolves between the two above-mentioned limit cases (exponential or asymptotic observer). In particular, attention is focused on a hybrid “Luenberger-asymptotic” observer, for which a rigorous stability/convergence analysis is provided. The efficiency and usefulness of the proposed observer is demonstrated with a bioprocess application example.     

Minimizing observer metamerism in display systems

Observer metamerism has long been known to be an issue of concern for color engineers. With the advent and mass proliferation of narrow‐band display devices, this article addresses the issue of observer metamerism and puts it in the context of first understanding the implication of interobserver variations in the color matching functions (CMFs) and additionally designing the ideal set of primary illuminant spectral power distributions (SPDs) such that observer metamerism is minimized. The article also suggests the use of the Full Width Half Maximum (FWHM) and the number of modes (peaks) in the primary SPDs as a means of assessing the susceptibility to observer‐to‐observer variations between various modern display technologies. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 391–398, 2009     

The usability of the CIE colour‐matching functions in the case of CRT monitors

During the past years, several papers have been published that question the use of the CIE colour‐matching functions in the case of metameric samples. Visually matching samples produced on CRT (Cathode Ray Tube) monitors are metameric to most colour stimuli created by illuminating reflecting materials. As CRT monitors are often used in colour design applications, it seemed important to check how well CIE colorimetry will predict such colour matches. To investigate this problem, we set up an experiment in which painted samples were matched with samples produced on a CRT monitor. The colour of incandescent lamp irradiated Munsell samples were visually matched to the mixture of the RGB primaries of a CRT monitor. Both the reflected colour stimuli of the Munsell samples and the emitted stimuli of the monitor were measured spectroradiometrically. Our results imply that there is an observer‐dependent variability among the matches, but we could not find a major difference between the tristimulus data of the hard copy and soft copy presentations that would indicate errors in the CIE colour‐matching functions. The measurement accuracy, quantization errors of the monitor, and the achieved accuracy of the colour matches are treated in this study. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 436–441, 2001     

Comparing observers

Color‐matchingfunctions may be considered dimension reduction functions that project a spectral reflectance function into the desired space of colors. Using a gray metameric pair with maximal spectral difference we compare the abilities of various human and other observers with regard to the transition wavelengths for that metameric pair. Transition wavelengths are shown to be a convenient tool for comparing and classifying observers regardless of the number of dimension reduction functions. Four human observers were identified as differing in a comparable manner from the CIE 2° standard observer. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 183–186, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20004     

The Measurement and Assessment of Colour Differences for Industrial Use. IV—The Accuracy of Visual Assessments

The magnitude of the errors in the visual assessment of colour differences is discussed. The errors are likely to vary with the particular form of visual assessment. Methods are described for estimating visual errors from data in which the visual assessments are expressed as percentage acceptance and rank orders as well as ratios of other colour differences. The results indicate that experienced observers tend to have a greater degree of discrimination than inexperienced observers. Between-observer variation is greater than within-observer variation, suggesting that the mean of many repeat observations by a single observer may differ significantly from the mean derived from a number of different observers. For colour passing, the error of a single observer varies with the size of the colour difference and is given by the equation: σ=0.4+ 0.25 δν where δν is the true visual difference expressed in units equivalent to the average unit given by the AN40 equation.     

Quantifying the suitability of CIE D50 and a simulators based on LED light sources

In this study, two psychophysical experiments, colour‐difference assessment and colour‐appearance estimation, were conducted to investigate the perceived quality of four CIE illuminant simulators, including two simulators based on LED light sources. The perceived colour‐differences of 30 metameric pairs, seen under the different simulators, were evaluated by 10 colour‐normal observers using the gray scale method and the colour appearance of the colour inconstant sample in each pair assessed in a magnitude estimation method. Colorimetric measures revealed that LED simulators can achieve the desired quality according to the relevant ISO and CIE standards. The results of the experiments showed that an LED simulator outperformed the conventional fluorescent lamp‐based simulator for the CIE illuminant D50 condition. In addition, an LED simulator worked almost equally well as a conventional simulator for simulating CIE illuminant A. These findings strongly indicated the good quality of LED simulators based on a limited number of channels, and the superiority of LED technology. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 408–418, 2017     

A cross‐cultural comparison of colour emotion for two‐colour combinations

Psychophysical experiments were conducted in the UK, Taiwan, France, Germany, Spain, Sweden, Argentina, and Iran to assess colour emotion for two‐colour combinations using semantic scales warm/cool, heavy/light, active/passive, and like/dislike. A total of 223 observers participated, each presented with 190 colour pairs as the stimuli, shown individually on a cathode ray tube display. The results show consistent responses across cultures only for warm/cool, heavy/light, and active/passive. The like/dislike scale, however, showed some differences between the observer groups, in particular between the Argentinian responses and those obtained from the other observers. Factor analysis reveals that the Argentinian observers preferred passive colour pairs to active ones more than the other observers. In addition to the cultural difference in like/dislike, the experimental results show some effects of gender, professional background (design vs. nondesign), and age. Female observers were found to prefer colour pairs with high‐lightness or low‐chroma values more than their male counterparts. Observers with a design background liked low‐chroma colour pairs or those containing colours of similar hue more than nondesign observers. Older observers liked colour pairs with high‐lightness or high‐chroma values more than young observers did. Based on the findings, a two‐level theory of colour emotion is proposed, in which warm/cool, heavy/light, and active/passive are identified as the reactive‐level responses and like/dislike the reflective‐level response. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2012     

Assessing the reliability of ordered categorical scales using kappa-type statistics

Methods for the analysis of reliability of ordered categorical scales are discussed, focussing on the limitation of the single summary-weighted kappa coefficients. A symmetric matrix of kappa-type coefficients is suggested as an alternative. The method is proposed as being suitable for ordinal scale where there is no underlying continuum. Their application is illustrated using two data sets from reliability studies. If, instead, distances between categories can be specified, a weighted mean of the matrix terms can be used as a summary measure. This is equal to a weighted kappa coefficient with squared weights, provided distances between adjacent categories are equal. When a study design corresponds to a one-way random effects model, estimates of precision of kappa-type coefficient, including the coefficients described here, can be obtained using the delta-method, bootstrap resampling by subjects or jack-knifing by subjects. In the case of interobserver reliability studies, where there may be systematic differences between observers, the investigator may wish to generalise to a population of observers and subjects. In this case, jack-knifing by observer and subject is suggested. Empirical comparisons are made between standard error estimates based on the delta-method, on jack-knifing by subjects and a two-way jack-knife by subjects and observers. The results suggest that standard errors based on the delta-method or jack-knifing by subject alone may be overly precise.     

Nonlinear observer design for two-time-scale systems

A two-time-scale system involves both fast and slow dynamics. This article studies observer design for general nonlinear two-time-scale systems and presents two alternative nonlinear observer design approaches, one full-order and one reduced-order. The full-order observer is designed by following a scheme to systematically select design parameters, so that the fast and slow observer dynamics are assigned to estimate the corresponding system modes. The reduced-order observer is derived based on a lower dimensional model to reconstruct the slow states, along with the algebraic slow-motion invariant manifold function to reconstruct the fast states. Through an error analysis, it is shown that the reduced-order observer is capable of providing accurate estimation of the states for the detailed system with an exponentially decaying estimation error. In the last part of the article, the two proposed observers are designed for an anaerobic digestion process, as an illustrative example to evaluate their performance and convergence properties.     

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     

Measuring color-matching functions. Part I

A visual colorimeter was designed to implement a new model for the determination of color-matching functions developed in the Munsell Color Science Laboratory. An instrument utilizing laser primaries was originally developed. The instrument was later improved to incorporate CRT primaries and seven interference filters to make matches to simulated daylight in a 2° bipartite field. The system was designed to minimize the strain on observers. Color-matching functions of naïve observers can be measured in approximately 30 minutes. Results from an individual observer correlate well with data collected on the National Research Council of Canada's Trichromator. Part II of this article gives the color-matching functions results for 18 observers and 20 repetitions by a single observer.     

Image‐based spectral reflectance reconstruction using the matrix R method

The ultimate goal of spectral imaging is to achieve high spectral accuracy, so that the spectral information can be used to calculate colorimetrically accurate images for any combination of illuminant and observer. A new spectral reconstruction method, called the matrix R method, was developed to reconstruct spectral reflectance factor accurately while simultaneously achieving high colorimetric performance for a defined illuminant and observer. The method combines the benefits of both colorimetric and spectral transformations. Tristimulus values were predicted by a colorimetric transformation from multi‐channel camera signals, while spectral reflectance factor was estimated by a spectral transformation from the same signals. The method reconstructed reflectance factor by combining the fundamental stimulus from the predicted tristimulus values with the metameric black from the estimated spectral reflectance, based on the Wyszecki hypothesis. The experimental results verified the new method as a promising technique for building a spectral image database. © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 343–351, 2007