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.     

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.     

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     

Calculation of metameric reflectances

Object-color metamerism becomes visually apparent if two objects match under one light, but not under a second. In the present article, a method is derived by which metameric object colors can be calculated, given the light under which they are to match, and the light under which they are to mismatch. The method gives practical guidance for avoiding or achieving metamerism. The method is not primarily a matter of trial and error and statistics, but depends on a simple calculation that operates on the spectral power distributions of the two lights, along with a set of three color matching functions. The method can deal as well with “observer metamerism,” meaning the effects of observer differences.     

Comparison of methods for assessing observer metamerism

Studies on observer metamerism reported so far are classified into two series. One is studies based on the color-matching functions of Stiles's 20 observers. The other is experimental studies by using the Davidson and Hemmendinger (D-H) Color Rule and color-normal actual observers. The large discrepancy of the degree of observer metamerism between the above two series of studies was analyzed by using the color-matching functions of Stiles's 20 observers and the D–H Color Rule. The results confirmed that the discrepancy in the observer-metamerism indices was caused by different computational procedures used for deriving the indices.     

Methods for quantifying metamerism. Part 2-Instrumental methods

This is the second part of this series of articles, in which the experimental data described in Part 1 are used to evaluate three types of metamerism indices. The results show that the index based upon one of the three advanced colour-difference formulae (CMC, BFD, and CIE94) gave a quite satisfactory prediction to the visual results. The degree of precision from these formulae is equal to or higher than the typical observer precision found in this study. A set of colour-matching functions was also derived. In comparison with those of the CIE 1964 standard colorimetric observer, the new set gives closer agreement with the visual results, particularly under source D_65. This new set could be used for indicating the degree of observer metamerism. Another set of experimental data was also assessed. Similar tests were conducted and the results confirm the earlier findings. The advanced colour-difference formulae can be confidently used for evaluating the degree of metamerism for industrial applications.     

Methods for quantifying metamerism. Part 1ndashVisual assessment

This work forms part of the Society of Dyers and Colourists' CMC Working Group 1 project on metamerism and colour constancy. The aim of the project is to derive reliable indices for predicting metamerism and colour constancy. Some 76 metamers were prepared by dyeing wool with acid dyes. Two experiments were conducted to quantify the degree of metamerism using a grey-scale method. In the first experiment each metamer's colour difference was assessed against a grey scale by a panel of observers under seven light sources. The second experiment was carried out under three sources: D₆₅, A and TL₈₄. Each observer assessed not only the total colour difference as in the first experiment but also the separate lightness, chroma, and hue components. Observer variations were investigated in terms of observer precision, and within-and between-observer errors. Cross-over wavelengths for each metamer were also examined. It was found that intersections tend to converge on three wavelengths for almost all metamers used here, in agreement with previous findings.     

Wpt (waypoint) shift manifold difference metrics for evaluation of varying observing-condition (observer + illuminant) metamerism and color inconstancy

Metamerism is a critical color phenomenon which can cause serious problems for products assembled by various parts. Customers generally expect all parts are color-matched under different observing conditions. This article extends the concepts of illuminant and observer metamerism to observing-condition metamerism, that is, objects are color-matched under one observing condition but not under others. The color inconstancy of a single object is also expanded to be evaluated under multiple observing conditions. Moreover, four Waypoint (Wpt) Shift Manifold difference metrics are proposed to evaluate not only observing-condition metamerism of metamers and paramers but also observing-condition color inconstancy of single objects: The Mean Object Inconstancy Index (MOII), The Mean Object Color Difference (MMOCD), Object Metamer Index (OMI), and Object Hue Similarity Index (OHSI). Existing indices of metamerism and color inconstancy employ appearance matching using a Chromatic Adaptation Transform (CAT) and color difference formulas such as CIEDE76 or CIEDE2000. The proposed metrics utilize material matching based upon the Waypoint Material Adjustment Transform (Wpt-MAT) and Euclidian color difference in the perceptually uniform Material Color Equivalency Space WLab. Conceptual comparisons between these approaches are discussed and evaluated. Additionally, computational evaluation results under observing conditions composed by 99 illuminants and 70 observers show that MOII provides a measure of color inconstancy for single objects, MMOCD provides a measure of metamerism between metamers and paramers with a generalized assessment of color difference between two objects, OMI provides a measure of paramers, and OHSI provides a quantitative measure of hue characteristics for different observing conditions.     

A proposal of new standard deviate observers

The method of singular-value decomposition analysis of matrices is used to analyze the 20 color-matching functions of Stiles's observers. It is confirmed that the 20 color-matching functions are well reconstituted by the first three decomposed components. A new deviate observer is derived from the first decomposed component. It is shown that the new deviate observer can be used well in the computation of observer-metamerism indices. Furthermore, an optimized deviate observer is developed by modifying the color-matching functions of the new deviate observer slightly. Both the new and the optimized deviate observer give a basis for the further study of the evaluation of observer metamerism.     

Categorical observers for metamerism

A method is proposed to generate categorical colour observer functions (individual colour matching functions) for any field size based on the CIE 2006 system of physiological observer functions. The method combines proposed categorical observer techniques of Sarkar et al with a physiologically-based individual observer model of Asano et al and a clustering technique to produce the optimal set of categorical observers. The number of required categorical observers varies depending on an application with as many as 50 required to predict individual observers' matches when a laser projector is viewed. However, 10 categorical observers are sufficient to represent colour-normal populations for personalized colour imaging. The proposed and recommended categorical observers represent a robust and inclusive technique to examine and quantify observer metamerism in any application of colorimetry.     

Theoretical considerations on small color differences ascribed to the standard observer made on the basis of individual color‐matching functions

An analytical method to determine how color‐matching functions influence the perception of chromaticity differences is proposed. We show that, as a consequence of the observer metamerism, a metameric color‐match perceived by one observer may appear to be a significant mismatch to a different observer. It is also shown that, on average, the differences between the color‐matchings made by two different observers can be estimated to be in the order of 2 CIELAB units. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 194–200, 2009     

Evaluation of daylight simulators. Part 2; Assessment of the quality of daylight simulators using actual metameric pairs†

This paper discusses two methods for evaluating the quality of daylight simulators, namely the band‐value method specified in British standard BS 950 and the CIE metamerism index method. Six daylight simulators of various types and manufacturers were used for the assessment and a psychophysical experiment was conducted to evaluate the two methods. A range of 70 metameric pairs was assessed by a panel of observers under each of the six simulators and the reliability of their visual results was examined in terms of observer accuracy and repeatability. The visual results were also compared for each pair of simulators to reveal how the results could be affected by using different simulators. The effectiveness of four colour difference formulae was tested using the visual results. Finally, four methods were developed using two statistical measures of performance factor, band‐value deviation and CIE metamerism index for evaluating the quality of daylight simulators.     

The proper use of indices of metamerism

General (spectral) and special (colorimetric) indices of metamerism have been developed to evaluate match quality for metameric and parameric specimens. For a parameric pair, in which there is not an exact colorimetric match for a reference observer and illuminant, various corrections can be used to adjust one of the stimuli such that an exact match is achieved. These adjustments can be spectral or colorimetric. In cases where the mismatch is large, the resultant metameric index may be misleading. A small index of metamerism and a large color difference under the reference conditions has a different interpretation than its converse. This is demonstrated for blue, yellow, magenta artist paints matching a spectrally nonselective gray. The implication is that special indices of metamerism should be calculated only for a limited range of color differences under the reference condition. It is suggested that metameric indices should not be calculated for pairs having a mismatch beyond a threshold value, for example, 5 ΔE. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 509–512, 2008     

The impact of viewing conditions on observer variability for cross‐media colour reproduction

This study investigates observer metamerism in cross‐media colour reproduction (CMCR) between monitor and physical colours. An LCD display was placed inside a viewing cabinet. The cabinet had a mid‐grey interior. Observers were asked to match a colour displayed on the monitor to a printed colour patch, which was also inside the viewing cabinet in two configurations, one consisting of two samples separated by a hairline gap (Configuration 1), and the other consisting of two samples separated by a large gap (Configuration 2). Eleven observers were asked to first match the background colour and then 10 test colours for each configuration, and this was repeated five times. The observers’ variability results showed little difference between inter‐ and intra‐variability, and between the two configurations. Comparing the observers’ results with the CIE 1964 standard colorimetric observer, Configuration 1 and Configuration 2 each showed similar agreement. In both configurations, the results of observer variability were smaller than those obtained by Oicherman et al. in 2008. In addition, each configuration's results showed better agreement with the CIE standard colorimetric observer than Oicherman et al.'s results. This implies that both configurations, one with two samples having a hairline gap and with two samples separated by a large gap in a viewing cabinet, could be recommended for future CMCR systems. However, if choosing between the two, then Configuration 2 is recommended rather than Configuration 1.     

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.     

塑料着色中减小同色异谱现象的研究

研究了塑料着色时加入不同的颜料对同色异谱的影响,通过加入同色异谱调节剂使颜色在指定光源下同色异谱指数最小。实验结果表明：调整颜料及加入同色异谱调节剂,可以达到在两个光源下无同色异谱现象。     

The metamerism potentiality of a color recipe

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

塑料着色中减小同色异谱现象的研究

研究了塑料着色时加入不同的颜料对同色异谱的影响,通过加入同色异谱调节剂使颜色在指定光源下同色异谱指数最小。结果表明,调整颜料及加入同色异谱调节剂,可以达到在两个光源下无同色异谱现象。     

Intersections of matching spectra: Applications

Results of the preceding article are used to develop (1) a “characteristic” SPD of a light; (2) a method of spectral correction to remove the simple color difference in a pair of lights or reflectances that embody both metamerism and simple color difference; (3) characterization of typical spectral differences between SPDs of lights that match; and (4) a definition and procedure for specifying “degree of metamerism” of a pair of matching lights or reflectances. © 1993 John Wiley & Sons, Inc.