In a study, involving laboratories from seven geographic regions, the memory colors of eleven familiar objects were investigated. Based on that study, one global and seven regional memory color rendition indices (MCRIs) are created and the impact of cross-regional differences on the evaluation of color rendition was investigated. A first analysis focuses on the impact on MCRI index values by comparing the regional index values, calculated for 401 light sources, with those of the global index. A second analysis examines the impact on predictive performance in terms of the visual appreciation and naturalness of rendered objects colors as evaluated in respectively twenty-one and fifteen experiments published in literature. Both analyses show that, although there are small differences in absolute level of color rendition, the regional metrics are generally comparable in terms of predicting light source rank order and correlation with visual data. Therefore, ànd considering between-region variability to be smaller than or of the same size as the within-region variability, a globally valid memory color rendition metric can be proposed without introducing substantial errors. Finally, Smet’s Rm index, obtained using real objects, is suggested as a good approximation to that globally valid metric.
© 2015 Optical Society of America
The concept of memory colors, i.e. the colors associated with familiar objects in long-term memory, was first introduced by Hering in the late 19th century who stated that we view the world through the spectacles of memory . Because of their potential use as an internal reference to assess color appearance, memory colors and preferred colors—respectively the colors we remember or would like objects to have—have been and still are of great interest to many areas of color research, such as color reproduction [2–9] and color rendering [10–13].
For example, in case of the evaluation of the color rendition properties of a light source, which usually involves a comparison of object color appearance under a test source with that under a reference illuminant, one could replace the latter with the colour appearance as stored in memory as long as the test objects are very familiar objects. The assumption is that light sources which render the colors of familiar objects similar to their memory (or preferred) colors will result in high color rendition quality in general. The advantage of this approach is that it doesn’t require any optimal reference illuminant. Indeed, it has been shown that the reference illuminants proposed by the Commission International d’Eclairage (CIE) for the calculation of the CIE color rendering index (CRI) —a blackbody radiator or daylight phase of the same correlated color temperature (CCT) as the test source for CCTs respectively below or above 5000 K—, and which have also been implemented in several other color rendition metrics [15–19], are not optimal with respect to subjective aspects of color rendition such as visual appreciation, preference and naturalness .
Despite their potential and obvious advantages, memory colors or preferred colors have so far only been implemented in four color rendition metrics: Sanders’ preferred color index Rp , Judd’s flattery index Rf , Thornton’s color preference index CPI  and Smet’s memory color rendition index Rm [12, 21]. Note that Sanders’ Rp and Smet’s Rm are the only two metrics that have explicitly implemented memory or preferred colors as references, as both Judd’s Rf and Thornon’s CPI use a preferred shift—calculated based on memory and preferred color data obtained from literature—to adjust the chromaticity of a set of Munsell test samples illuminated by the typical CIE reference illuminant. For a detailed analysis and discussion of the predictive performance of these metrics with respect to psychophysical data on visual appreciation and naturalness, the reader is kindly referred to Smet et al. .
A key question to answer when using memory colors, or even specific illuminants for that matter, as a reference in any sort of metric that assesses color appearance, is whether the chosen reference are region-dependent or culture-dependent. In a recent study, involving laboratories from seven different geographic regions, the memory colors of a set of eleven familiar objects were investigated . Although, a statistical analysis had shown a significant effect of geographical region, the effect size was found to be of the same order as or smaller than the inter-observer variability within a single geographical region, suggesting the effect is of little or no practical relevance.
The current paper specifically investigates the impact of the observed geographic differences of memory colors of some familiar objects on the evaluation of color rendition. First, seven regional and one global memory color rendition metric are developed, similar to Smet’s Rm, based on the regional color appearance rating data. Second, the impact of geographic region is investigated using two approaches. A first approach examines the impact on the regional memory color index values of a database of 401 light sources, while a second one focuses on the impact on the predictive performance—i.e. correlation with visually obtained color rendition data—of the various regional memory color rendition metrics.
2. Regional Memory Color Rendition Indices, Rm,reg
The following subsections describe the design of the regional memory color rendition indices, Rm,reg. Each regional memory color rendition index is composed of three key components: the similarity functions describing the normalized observer response with respect to the memory color (section 2.1), the spectral reflectance of each of the familiar objects (section 2.2) for the calculation of the objects’ appearance under the light source and its corresponding memory color similarity (section 2.3) and a rescaling function to obtain a more familiar CRI-like scale (section 2.4).
2.1 Similarity functions
In a recent study of Smet et al. , the memory colors of eleven familiar objects (Green Apple, Ripe Banana, Ripe Lemon, CAuliflower, ORange, StrawBerry, TOmato, Dried Lavender, SMurf®, Caucasian Skin and Asian Skin) were investigated in seven different geographic regions: BElgium, HUngary, BRazil, COlombia, ChiNa, TaiWan and Iran. At each location, identical experiments were conducted in which each familiar object was presented on a calibrated display in a large number (average 165) of different colors to a panel of test subjects. The subjects were asked to rate the similarity of the presented object color with respect to what they remember the object to look like. The adaptation state of the observers was controlled presenting the object surrounded by a white background (CIE illuminant D65 with Y10 = 200 cd/m2). Worldwide over 210 000 ratings were obtained, on average 30 000 per region and 2700 per region per object. For each geographic region reg (reg = BE, HU, BR, CO, TW, CN and IR) and each object i a region average observer was calculated by taking the arithmetic mean of the observer ratings. The region average observers were then modeled with bivariate Gaussian surfaces:
with fitting parameters;the Mahalanobis distance—which defines an elliptical contour of equal ratings —and the rating at the chromaticity coordinate. The subscript ‘10’ denotes the use of the CIE 1964 (10°) observer in the calculation of the chromaticity coordinates. The memory color is determined by the center of the bivariate rating function, while determine its size, shape and orientation. The parameters determine the scale range of the ratings for each object. As an example, the rating functions for a ‘ripe banana’ for each of the regions is illustrated in Fig. 1.
The bivariate rating functions for a global average observer (reg = GL) were obtained by modeling the pooled region average observers ratings of all geographic regions for each object. Full details and model parameters can be found in .
Although the rating functions could be used in a memory color rendition metric, it is however more appropriate to use the same scale for each familiar object to ensure each object contributes equally to the average score. Therefore, similarity functions, , were obtained that describe the degree of similarity of objects colors (chromaticity only) with their memory color on a zero-to-one scale by setting the model parameters a6 and a7 in Eq. (1)b to respectively one and zero.
2.2. Spectral reflectance
The spectral reflectance of most of the familiar objects were determined from spectral radiance measurements of the objects and of a standard white tile with known spectral reflectance. For each object, several measurements were made and the results were averaged. The spectral reflectance for dried lavender was taken to be the one used in Smet’s memory color rendition index as no dried lavender was available at the time of measurement. The spectral reflectance for the Caucasian and Asian Skin were taken as the average of the spectral reflectance functions of two skin databases, i.e. the OULU  and RIT  sets. The spectral reflectance of the eleven familiar objects, as adopted in the regional MCRIs, are illustrated in Fig. 2.
2.3 Calculation of the general similarity indicator, Sa,reg
A regional MCRI general indicator value, Sa,reg of a light source for region reg—indicative of the source’s overall color rendition quality for the region average observer—is calculated as follows.
First, the tristimulus values of the eleven familiar objects are calculated from their spectral reflectance, the spectral radiance of the light source and the CIE 1964 colour matching functions. These values are than transformed to their corresponding colours under the CIE illuminant D65 (i.e. the adaptation white point during the psychophysical experiments) using the CAT02 chromatic adaptation transform. The degree of adaptation is either calculated from the adapting field luminance or set to 0.9 in case the former is unknown. A value of 0.9 is advised as chromatic adaptation is rarely complete, especially for light sources with a less than neutral appearance. Secondly, the corresponding tristimulus values are transformed to the CIE 1976 u’v’ chromaticity coordinates. Thirdly, for each object i specific similarity indicators Si,reg are calculated by using the appropriate—i.e. the ones corresponding to the region in question—model parameters. A general similarity indicator, Sa,reg is then obtained by taking the geometric mean of the specific similarity indicator values Si,reg of all objects.
2.4 Rescaling the Sa,reg indicator to the Rm,reg index
Finally, the general similarity indicator Sa,reg, is transformed to a general memory color rendition index, Rm,reg, with a CIE-CRI-like scale using a specific scaling function.
In the MCRI published by Smet, et al.  a psychometric scaling function was used with the parameters chosen to ensure indicator values below 0.5 result in index values of 0 ànd CIE illuminants D65 and F4 have index values of respectively 90 and 50. However, using a similar scaling function whereby the scaling parameters are optimized for each of the geographic regions, would automatically result in nearly region independent index values. Since the main goal of this paper is to investigate the impact of cross-geographical differences on color rendition evaluation, this is not an appropriate approach as the rescaling might have a masking effect. Therefore, a simple linear rescaling has been applied for now, i.e. f(x) = 100 - a*(1-x), whereby the coefficient a has been set to 50. This results in a CIE-CRI-like scale whereby the mean Rm,reg for the global average observer of the CIE illuminants F1-F12 approximately equals their mean CIE Ra value. This is a common rescaling approach for color rendition metrics, as this way metrics are assumed to operate on approximately comparable scales . The global average observer was chosen as reference, to specifically investigate the possibility of proposing a single memory color rendition metric with worldwide validity.
3. Results & Discussion
The impact of geographic differences of memory colors on the evaluation of the color rendition properties of white light sources has been investigated in two ways. A first one examines the impact on the Rm,reg index values and a second one the impact on the predictive performance of the different regional memory color rendition metrics. For the former, respectively the latter, a database of 401 light sources—composed of commercially available sources, CIE illuminants, LED spectra, fluorescent spectra, etc.—  and a database of psychophysical data on subjective aspects—visual appreciation and naturalness—of color rendition were used.
3.1 Impact of geographic differences on Rm,reg index values
The impact on the Rm,reg index values was evaluated by comparing the regional values with those of the global index for 401 light source spectra. Agreement was assessed by means of the coefficient of determination R2, the Spearman rank correlation coefficient rS, the Mean-Absolute-Error and the STRESS measure. The results are given in Table 1 The agreement is also graphically illustrated in Fig. 3.
From the very high R2 and rS (resp. ≥ 93% and ≥96%, with the exception for BRazil) and very low STRESS values (≤ 2%) in Table 1, as well as the near 45° slopes observable in Fig. 3, it is clear that generally the regional metrics are highly correlated to the global metric. The near 45° slopes indicate that differences in visual color rendition are very similar across geographic regions, suggesting that the different metrics are likely to predict similar light source rank order, as was also confirmed by the high values of the Spearman rank correlation coefficient. However, as is also clear from Fig. 3, some index values do show, an albeit small, offset from the 45° line. This indicates, that although color rendition differences might be the same, their absolute level is not. These differences in absolute level were assessed by the MAE. From Table 1, it is clear that they are rather small, with the exception perhaps of that of TaiWan and IRan which show MAE values slightly larger than 5 units. It is commonly accepted that a 5 unit difference on a CIE-CRI-like scale corresponds to a just visible effect. Therefore, the results suggest that a single, i.e. the global, index can be used when relative light source rank order is the only parameter of interest, while it will result in small errors in predicted absolute color rendition level for some geographic regions. Although these small absolute differences could in principle be used to fine-tune the spectral design of light sources to specific geographic regions, the practical importance of these small errors can be questioned, as individual color appearance rating has been found to have a within-region variability of the same order or larger than the between-region variability .
3.2 Impact of geographic differences on Rm,reg predictive performance
The impact on the predictive performance of the Rm,reg metrics was investigated using a meta-correlation analysis identical to the one described by Smet et al. . In that analysis, the Spearman rank correlation coefficients between the metric values of several light source sets and their observer ratings obtained in psychophysical experiments were calculated. Metric performance was assessed as the weighted average correlation coefficient corrected for sampling error and study artefacts according to the method of Hunter-Schmidt . The following artefacts were corrected: study heterogeneity, range restriction/enhancement, inter-rater idiosyncrasy and sample correlation bias. The performance was investigated in terms of two subjective aspects of color rendition: visual appreciation (preference) and naturalness. Visual data were obtained for these two aspects from respectively twenty-one [27–41] and fifteen [27, 28, 30–34, 36, 37, 41–43] psychophysical experiments described in literature.
For visual appreciation, the different regional metrics have a good predictive performance (<rS> ≥ 80% for all metrics with the exception of HUngary and BRazil, median <rS> = 85%). However, the performance is slightly lower than that of the Smet’s Rm. This could be due to differences in the experimental setup. The visual rating data on which the regional Rm,reg metrics are based were obtained on monitors, while the Rm is based on data obtained using real objects. It is known that visual perception on self-luminous displays is different from that using real objects [44, 45], causes being, among others, a reduced adaptation of the visual system to the former [45, 46] and the influence of surface texture, shading, motion parallax and binocular disparity on similarity ratings  and on colour constancy [48, 49].
For naturalness, the correlation is lower but still moderate (median <rS> = 72%) and of approximately the same level as the regular MCRI. For a detailed discussion on reasons for the differences in performance for visual appreciation and naturalness, the reader is referred to .
From Fig. 4 it is clear that the regional Rm,reg metrics have a comparable performance for both subjective aspects of color rendition, with the exception of HUngary and BRazil, which have a slighly lower correlation.
To determine the statistical significance of these differences, the confidence-interval-method of Zou  for dependent overlapping correlations was applied under the null hypothesis of equal corrected average correlations, H0: (whereby i and j run over all metrics). A typical significance level of α = 0.05 was selected a priori. The method tests whether the 100 × (1- α)%-confidence interval (CI) contains zero, in which case H0 cannot be rejected. The CI-bounds closest to zero, henceforth referred to as CI0 of the confidence interval tests, are summarized in Table 3. When there is a statistically significant difference, the CI0 has been underlined and marked in red.
From Table 3 it can be seen that all memory color rendition metrics had significantly higher correlation coefficients than the CIE Ra index for visual appreciation. For naturalness, no significant differences were observed with the CIE Ra index.
For visual appreciation, the global Rm,reg index was only significantly different from the index for HUngary and BRazil. The latter two were also significantly different from one another, although only barely as can be seen from the small magnitude of CI0. Other, although small significant differences, were between (CN,BE), (CN,BR), (CN,IR) and (TW,IR).
For naturalness, the following small, but significant, differences were found: (IR, GL), (IR, TW), (CN, CO), (TW,BR), (TW,BE), (IR,CN), (TW,HU) and (CO, GL).
Overall, and in agreement with the earlier conclusion about metric value differences being approximately independent of geographic region, the results show that for most cross-comparisons the impact of geographic region on the predictive performance is not or only barely significant.
Note that, again, the same remark can be made about the significance of the results of the region average observer for those to be expected for an individual observer.
In a recent study , the effect of cross-regional variation on color appearance rating and memory colors of eleven familiar objects was investigated in seven different geographic regions: Belgium, Hungary, Brazil, Colombia, Taiwan, China and Iran.
Based on the bivariate Gaussian models of the observer rating data obtained by Smet et al. , seven regional and one global memory color rendition metric have been created. Using the latter, the impact of cross-regional differences in color appearance rating on color rendition evaluation was examined.
In a first analysis, the regional Rm,reg index values for a database of 401 light sources have been compared with those obtained using the global metric. The results indicate that the regional metrics are highly correlated with the global one. In addition, plots of the regional index values versus the global index values all have slopes close to 45°, indicating that color rendition differences between light sources are approximately preserved across regional metrics. However, the plots do show an offset indicating that absolute level is not preserved, although the Mean-Absolute-Errors between the regional and the global index values were small for most geographic regions. With the exception of TaiWan and IRan, all differences were smaller than 5 scale units. It is commonly accepted that a 5 unit difference on a “CIE CRI”-like scale corresponds to a just visible effect. Therefore, the results suggest that a single global index can be used when relative light source rank order is the only parameter of interest, while it will likely result in small errors in predicted absolute color rendition level for some geographic regions.
A second analysis examined the impact of cross-regional differences on the predictive performance of the regional memory color rendition metrics. Performance was assessed as the artefact corrected weighted average Spearman correlation—calculated according the method of Hunter-Schmidt—between metric predictions and psychophysical data published in literature. Predictive performance with respect to two subjective aspects of color rendition was investigated: visual appreciation (preference) and naturalness. Data of respectively twenty-one and fifteen experiments from seventeen studies were used. The results showed that most of the regional memory color rendition metrics had a high and comparable performance (median <rS> = 85%) for visual appreciation. Compared to the Smet’s MCRI Rm, which is based on color appearance rating data obtained using real objects, the performance is lower. However, this is likely due to differences in perception between real object presentation and presentation on self-luminous displays, for example due to reduced adaptation to the latter or due to the differences in surface texture, shading, motion parallax and binocular disparity, all of which are known to have an effect on similarity ratings and color constancy. For naturalness, the regional memory colour rendition metrics had a moderate, but comparable performance (median <rS> = 72%). A cross-comparison of the metric performance using the confidence interval method of Zou showed that for most of them the impact of geographic region on the predictive performance is not or only barely significant (p < 0.05).
Note that the conclusions listed above are applicable when dealing with color rendition, as expressed by the concept of an average observer. As was shown by Smet et al. , individual memory color based color appearance ratings have a within-region variability of the same order or larger than the between-region variability. Therefore, within-region differences—between individual observers and that of the region average observer—in color rendition evaluation are expected to be of similar magnitude as the ones reported above.
To conclude, the analyses indicates that a single, globally valid memory color rendition metric can be proposed which predicts light source rank order well and which results in only minor errors—of the same magnitude as those induced by inter-observer variability—in the absolute level of the predicted color rendition for some geographic regions.
In addition, as the global and Belgian Rm,reg metrics are very comparable, Smet’s Rm , obtained using Belgian test subjects (but different from the ones that participated in the experiments described in ), would be a good approximation to that globally valid metric, while ensuring a higher predictive performance due to the more representative (for color rendition evaluation) object presentation adopted during its development.
Such a globally valid metric—use Smet’s Rm for best performance—cannot only be applied to evaluate the color rendition properties of existing light sources but can also be implemented in the spectral optimization of new light sources that have a good overall (globally) lighting quality (visual appreciation). And although region-specific fine-tuning of light source spectra could in principle be done using the similarity function published in , the size of the cross-regional differences, comparable to the typical within-region observer variability, suggest that such spectral optimization might be of little practical value. Furthermore, lighting designers should bare in mind that those similarity functions were derived for objects presented on a monitor, resulting in a lower predictive performance than Smet’s Rm.
Author KS would like to thank the Research Foundation Flanders (FWO) for supporting this study through a Postdoctoral Fellowship (12B4913N).
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