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The chromaticity of unique white viewed in object mode and under dark adapted conditions was investigated for 3 luminance levels (200, 1000 and 2000 cd/m2) using two experimental methods: unique white setting and rating. The results of the two methods were found to agree well. Both showed quite large observer variation and an apparent shift of the average unique white (across observers) towards colder correlated color temperatures as the stimulus luminance was dropped from 2000 cd/m2 to 200 cd/m2, although no such trend was observable at the individual observer level. Unique white was shown to encompass a region in color space, mostly located below the blackbody locus at around 6000 K. The low and high color temperature ends of the CIE class A and B white regions tend to respectively over- and slightly underestimate the size of the chromaticity area perceived as white by the dark adapted average observer. However, the agreement along a direction approximately perpendicular to the blackbody locus was quite good. Finally, the unique white ratings were modeled by a bivariate Gaussian function, resulting in a simple empirical metric to predict the degree of neutrality of any object stimulus viewed under dark adapted conditions.
© 2014 Optical Society of America
1. Introduction
“White” is an important and widespread concept in lighting and color vision science. It is used to “describe physical properties of radiation, physical properties of surfaces and psychophysical properties of experience” [1]. However, often there is a considerable ambiguity as to what is actually meant by the term “white”.
For example, white light can refer to illumination with a wide variety of correlated color temperatures (CCT), the standard white points used by many color spaces and color appearance models can differ substantially (e.g. D65 for CIELAB and the equal-energy-white for CIECAM02), white point selection can also vary from application to application (e.g. D50 for graphic arts versus D65 for photography). As a specification of surface properties white usually denotes a non-selective and high spectral reflectance. Even here some vagueness remains, especially when considering the possible addition of fluorescent whitening agents to increase the perceived whiteness of the object.
In psychophysical research, white – designated by terms such as neutral white, pure white, achromatic color or unique white – often specifically refers to as color devoid of any hue sensation, i.e. neither red, nor green, nor yellow or blue. It is the point at which the r-g and y-b opponent channels are balanced (and the light from the stimulus is sufficiently intense to be perceived as white rather than gray or black). That unique white is thought to correspond to a baseline state of the chromatic part of the visual system has made it an important tool for investigating color constancy and chromatic adaptation. Despite this exact specification of the meaning of “white” – one that makes intuitive sense –, various differing values have been reported for its chromaticity. Based on data from 4 observers, Priest [2] reported an average white chromaticity (under dark surround conditions) near 5100 K. Helson and Michels [3] found an average (3 observers) dark adapted white chromaticity of approximately 15000 K. Hurvich and Jameson [1] determined limits for white lighting with chromaticity on the blackbody locus. For two out of their three observers they found that at 5500 K a luminance approximately 30 cd/m2 was required to elicit a white sensation. For the third observer, the white chromaticity was located around 7500 K. The average was 6200 K. For all observers, the range of color temperatures that were considered white increased with luminance. Honjyo and Nonaka [4] investigated the perception of white under dark adapted conditions with test stimulus luminance values between 2.5 and 16 cd/m2. Using the method of minimal changes, they reported a large scatter of white chromaticity values ranging from 5000 to 14000 K, mostly below the blackbody locus. However, in a separate constant-stimulus experiment they reported that the white point of 95% of their test subjects was located in the vicinity of CIE illuminant C. In experiments with 30 cd/m2 test field in dark surround, Valberg [5] also found large individual differences with correlated color temperatures ranging from 5600 to 11000 K. In a study investigating the possibility of using unique white to normalize the cone action spectra, Walraven and Werner [6] reported unique white settings with correlated color temperatures of approximately 4000 K and 7400 K for their two observers. While studying chromatic adaptation, Kuriki [7] reported values approaching the chromaticity of equal-energy-white (approx. 5500 K) for increasing test stimulus intensity, i.e. with the chromatic adaptation to the illuminant becoming negligible. Smet, Ryckaert, Pointer, Deconinck and Hanselaer [8] reported the (P,T)-chromaticity coordinates in IPT color space for neutral gray to be (−0.0193, −0.0217) which is equivalent to a CCT of approximately 7100 K. Recently Rea and Freyssinier [9] found a “line of whites” for lighting that lies above the blackbody locus at correlated temperatures (CCT) higher than 4000 K and below for lower CCTs. In a similar experiment, Ohno and Fein [10] found a line of whites that was located completely below the blackbody locus at a Duv of approximately −0.013. However, it should be noted that such a “line of whites” is most likely an experimental artifact [11], as in both experiments the chromaticity of the test illuminant was varied along loci of constant CCT and for each such locus observers were asked to identify the most white lighting. The line of whites was obtained by taking these whitest illuminant chromaticities at each investigated CCT. However, this approach does not take into account possible differences in perceived whiteness across different CCTs. A more general approach would be to have observers rate a random sequence of chromaticities taken from a uniform 2D grid spanning the blackbody locus. Finally, Chauhan, Perales, Xiao, Hird, Karatzas and Wuerger [12] reported average unique gray settings (on a monitor, with stimulus luminance intensities of 5, 20 and 50 cd/m2) near 8840 K, slightly above the blackbody locus.
Most of the above studies had a rather limited range of test stimulus luminance and have investigated unique white either in aperture or in illumination mode. Little or no data on the chromaticity of unique white (and its variation among individuals) is available for higher luminance values, nor when the test stimulus is presented explicitly as a real object. Although high luminance data is perhaps less applicable to many indoor lighting situations or to typical displays, they are nonetheless valuable for high dynamic range imaging, very bright displays [13] and from a color vision or color appearance modeling standpoint. In this study unique white has been investigated for test stimulus luminance values of 200, 1000 and 2000 cd/m2 under dark adapting conditions in a series of “unique white”- setting and -rating experiments.
2. Methods
2.1 Experimental setup
Stimuli were generated by illuminating a real 3D cube (8.5 cm x 8.5cm x 8.5 cm), with an approximately non-selective spectral reflectance (β ≈0.85), by a data projector in a specially designed viewing booth (width = 300 cm, depth = 120 cm, height = 265 cm; see Fig. 1). By only changing the pixels associated with the geometric projection of the 3D cube, the illusion was created that the cube itself changed color. As the change in color was attributed by the observers to a change in spectral reflectance of the cube, this specific setup ensured the stimuli were presented in an object color mode.
For this experiment the pixels associated with the background were set to black (cfr. baseline dark adaptation condition). The CIE 1976 u’v’ chromaticity and luminance of the black background were respectively, (u’10v’10) = (0.2759, 0.2344) and Y10 = 0.40 cd/m2.
The viewing booth was calibrated which allowed test subjects to adjust the chromaticity of the stimulus along 8 directions in the CIE 1976 u’v’ diagram using the keys of the numpad on a regular black keyboard. One key-press changed the chromaticity in the selected direction by 0.0006, by simultaneously pressing either the alt-, ctrl- or shift-key that step change was multiplied by a factor of respectively 5, 10 and 50. Ratings on a 0-10 scale could be made by using the F1-F11 keys on the keyboard.
The cube-observer distance was approximately 100 cm, providing a stimulus field of view (FOV) of 5.7°. As the FOV was larger than 4°, all chromaticity values were determined using the CIE 1964 observer from calibrated spectral measurements with an Ocean Optics QE65000 Pro spectrometer.
The 10° CIE 1976 u’,v’ chromaticity coordinates and luminance of the stimulus cube illumined with the data projector’s R(ed)G(reen)B(lue) primaries at maximum were: R = (0.4314, 0.5332, 1841 cd/m2), G = (0.1560, 0.5708, 6222 cd/m2) and B = (0.1336, 0.2250, 1141 cd/m2). To ensure a stable output the data projector was allowed a warm-up period of minimum 1 hour prior to starting the visual experiments.
2.2 Observers
Thirteen observers (7 male, 6 female) with normal color vision as determined by the Ishihara 24 plate test participated in the experiments. The average age of the observers was 31 ± 8.
2.3 Experimental procedure
Unique white was investigated in a series of experiments under dark adaptation conditions for 3 stimulus intensities: 200 cd/m2, 1000 cd/m2 and 2000 cd/m2. For each luminance level, the experiment consisted of two parts: a unique white-setting and a unique white-rating. Different luminance levels, as well as repeat experiments, to assess intra-observer variability, were performed on separate days. The unique white setting experiment was always done prior to the rating experiment to avoid influencing the observers by showing them possible whites.
It took observers on average approximately 45 minutes to complete one luminance level. The same group of observers was used for all three stimulus intensities, as preliminary experiments had shown the inter-observer variability to be quite large.
2.3.1 Unique white setting
In the first part observers were asked to adjust the chromaticity of the test stimulus along the axes of the CIE 1976 u’v’ diagram until it appeared neutral white, i.e. until it showed neither red, nor green, nor yellow, nor blue tint, nor could it be classified as either warm or cold white. They had to make 9 successive unique white settings, with the first two settings being trial settings to help observers get a feel for the experiment.
For each observer 7 random starting stimuli were generated, fulfilling two conditions: 1) excitation purity was within the projector gamut, but outside the CIE class A and B white regions [14]; 2) the dominant wavelengths of the 7 starting stimuli were uniformly distributed.
When observers were satisfied with their neutral white setting, it was spectrally measured and the 10° CIE 1976 u’v’ chromaticity coordinates were calculated. They were also asked to rate their final setting on a 0 – 10 scale: values below 5 signified hue was still clearly observable (with increasing hue for lower values) and values above or equal to 5 were whites that could be classified as either cold, warm or neutral (with increasing neutrality for higher values). Obviously the ratings were high as the goal of this experiment was to adjust the stimulus chromaticity until it appeared neutral. In the rating experiment described next, these values were used to identify the level above which a presented stimulus appeared neutral for each observer.
2.3.2 Unique white rating
In the second part of the experiment, the test stimulus was presented in 59 different chromaticities chosen at random from a uniformly spaced grid in CIE 1976 u’v’ space that enveloped the blackbody locus and extended slightly beyond the CIE class A and B white regions as illustrated in Fig. 2. Observers were asked to rate the presented stimulus chromaticity on the same 0 – 10 scale as in the adjustment experiment.
Fig. 2 Unique white rating grid (black circles). The blackbody locus, the CIE daylight locus and the CIE class A and B white regions are also shown.
3. Results and discussion
In the following subsections the results of each experimental method will be analyzed and discussed separately and will be followed by a statistical analysis of the joint results.
3.1. Experimental method 1: unique white setting
In the first experiment, observers had to adjust the color of the starting stimulus until it appeared neutral white. Three luminance levels were investigated. Figures 3(a)–3(c) show those results. The colored circles show the unique white settings of each individual observer. The colored ellipses are the observer 1-Standard Deviation ellipses and are a measure of the test subject’s intra-observer variability. The average 3-SD-ellipse (solid black line) – a measure for the average intra-observer variability – and the 3-SD-ellipse of the average observer unique settings (dashed black line) – a measure of the inter-observer variability – are also plotted. Note that the 3-Standard Deviation ellipses were plotted for clarity. The size of the major and minor axis, the center, the angle of rotation and the area (absolute and relative to luminance Y = 2000 cd/m2) of the 1-SD ellipses are given in Table 1.
Fig. 3 Unique whites obtained in the unique white setting experiment and the associated standard deviation ellipses for each observer (each color represents data of one observer): (a) 200 cd/m2, (b) 1000 cd/m2, (c) 2000 cd/m2 and (d) luminance invariance assumed. The average 3-SD-ellipse (solid black line) – a measure for the average intra-observer variability – and the 3-SD-ellipse of the average observer unique settings (dashed black line) – a measure of the inter-observer variability – are also plotted.
Table 1. Intra (Average) and Inter Observer Variability Ellipses for the Adjustment Method
From Fig. 3 and Table 1, it is clear that the intra- and inter-observer variations are quite large, which is consistent with results for unique white settings under dark adapted conditions reported in literature [4, 5, 15]. The intra-observer variability is also slightly larger than the inter-observer variability, as can be readily seen by comparing the size of the SD ellipses in Fig. 3 or Table 1. Finally, the major axis of the intra- and inter observer SD ellipses are directed approximately along the blackbody locus, which is consistent with the finding of Chauhan, Perales, Xiao, Hird, Karatzas and Wuerger [12].
In addition, but perhaps not immediately apparent from Fig. 3, the averaged results (over all observers) seemed to suggest a shift of unique white to higher correlated color temperatures as the luminance is decreased: 5256 K at 2000 cd/m2, 6126 K at 1000 cd/m2 and 6652 K at 200 cd/m2. The range of CCT at each luminance level shows the same general trend of increasing CCT with decreasing luminance (see Table 2). Although luminance dependent color appearance shifts are consistent with e.g. the nonlinear response of the yellow-blue opponent channel or by different states of adaptation, no such trend was apparent at the individual observer level, as can be readily seen from Fig. 4(a). This was confirmed by a series of repeated measures MANOVAs, one for each test subject, with luminance level as the within-subjects factor and u’, v’ as the DVs: no significant difference (Bonferroni corrected p < 0.004) could be established. Therefore, under the assumption of luminance-invariance of the unique white settings the raw settings of the different luminance levels were pooled and the 1-SD intra and inter-observer variability ellipses were also calculated. They are reported in Tables 1 and 2 under the header “luminance-invariance” and plotted in Fig. 3. The luminant-invariant average unique white setting had a CCT of 5963 K, which is, together with the luminance specific CCTs and observed ranges reported earlier, in good agreement with unique whites and their ranges reported in literature [1, 2, 4–7].
Table 2. Maximum and Minimum of the CCT and Duv Corresponding to the Centers of the Individual Observer SD-ellipses and the CCT and Duv (and Their Standard Errors, SE) for the Average Observer as Obtained in the Adjustment Experiment
Fig. 4 CCT (a) and Duv (b) versus luminance level. Colored solid lines: individual test subjects. Black dashed lines: ‘average’ observer.
A repeated measures ANOVA with CCT as DV also revealed no significant effect of luminance (F(2,24) = 1.695, p = 0.205, partial eta squared (𝞰2) = 0.124).
As for Duv – the distance above or below the Planckian locus in the CIE 1960 UCS color space – no individual or average trends were visible [see Fig. 4(b)], except for the fact that most observers had unique white settings with negative Duv values, in agreement with the results obtained by Ohno and Fein [10], but not with those from Rea and Freyssinier [9].
It should be noted that the disagreement with the latter could be due to differences in viewing context and adaptation state. In the study of Rea and Freyssinier [9] observers were looking into a matte-white tabletop cube illuminated at 300 lx with a light of specific CCT and Duv, thus effectively providing a fully immersive stimulus (no background and a field of view of nearly 180°) where peripheral effects and stimulus adaptation become important. In contrast, although the Ohno and Fein [10] study was also conducted at 300 lux with the observers fully immersed, the immersion was of a different, more natural kind. Observers were seated in a room filled with different kinds of colored objects and they were asked to rate the overall acceptability and naturalness of the chromaticity of the lighting in the room.
A repeated measures ANOVA showed no significant effect of luminance level on Duv (F(2,24) = 3.208, p = 0.090, partial eta squared (𝞰2) = 0.211). The degrees of freedom were corrected using the Greenhouse-Geisser approach as Mauchly’s test showed the assumption of sphericity was violated (p = 0.001).
Note that reported CCTs and Duvs, like the test stimuli chromaticities, were calculated with the CIE 10° observer.
3.2 Experimental method 1: unique white rating
In the rating experiment 59 uniformly spaced chromaticity points were rated for degree of neutrality by the same group of observers as in the unique white setting experiment.
First, the data were analyzed similarly as in the previous experiment, by limiting the analysis to the stimuli rated (near) neutral. In a second phase, the full data set of 59 ratings was taken into account and a model was developed to predict the degree of neutrality.
In the first phase, to obtain an equal sample size as before, for each observer only the 7 highest scored chromaticity points were retained in the analysis. These chromaticity points and the associated 1-SD variability ellipses are plotted in Fig. 5, which is the equivalent for the rating experiment of Fig. 3. The major and minor axis, the angle of rotation, size and location of these 1-SD ellipses are given in.
Fig. 5 Unique whites obtained in the rating experiment and the associated standard deviation ellipses for each observer (each color represents data of one observer): (a) 200 cd/m2, (b) 1000 cd/m2, (c) 2000 cd/m2 and (d) luminance invariance assumed. The average 3-SD-ellipse (solid black line) – a measure for the average intra-observer variability – and the 3-SD-ellipse of the average observer unique settings (dashed black line) – a measure of the inter-observer variability – are also plotted.
Again, it is clear that the intra-observer variability is larger than the inter-observer variability. Both of them are also smaller than those obtained using the unique white setting approach, suggestive of the rating method or being more accurate or being limited by the size of the grid of unique whites presented to the observers. As the grid extended beyond the CIE class A and B white boundaries and as almost no unique settings were made beyond these boundaries in the first experiment, the former explanation is more likely.
An analysis of the results in terms of CCT is, like with the unique white setting method, also suggestive of an increase in CCT as the luminance is decreased. As can be seen from Table 4 the CCT corresponding to the ‘average’ observer increase from 5755 K to 6342 K as the luminance is lowered from 2000 cd/m2 to 200 cd/m2. The range of observed CCT values tells a similar story. But again, no such trend is observable for the individual test subjects, as is clear from Fig. 6(a). Like before, data under the assumption of luminance-invariance are also reported in Tables 3 and 4.
Table 4. Maximum and Minimum of the CCT and Duv Corresponding to the Centers of the Individual Observer SD-ellipses and the CCT and Duv (and Their Standard Errors) for the Average Observer as Obtained in the Rating Experiment
Fig. 6 CCT (a) and Duv (b) versus luminance level. Colored solid lines: individual test subjects. Black dashed lines: ‘average’ observer.
Table 3. Intra (Average) and Inter Observer Variability Ellipses for the Rating Method
The luminant-invariant unique white was found to have a CCT 5989 K. Again, these unique whites and their ranges are in good agreement with those reported in literature [1, 2, 4–7].
A repeated measures ANOVA with CCT as DV showed no significant effect of luminance level (F(2,24) = 1.515, p = 0.240, partial eta squared (𝞰2) = 0.112), confirming the previous results of the adjustment experiments.
As for Duv, no individual trends were apparent [see Fig. 6(b)], except that they were all negative, confirming the earlier results of the adjustment experiment and those of Ohno and Fein. A repeated measures ANOVA did not indicate a significant effect of luminance level on Duv (F(2,24) = 2.029, p = 0.153, partial eta squared (𝞰2) = 0.145).
In the second phase of the analysis of the data of the rating experiment, the full data set was analyzed by taking into account the ratings of all 59 presented stimuli. First, an average observer was constructed by taking the median – to reduce the influence of potential outliers – of the ratings of all observers. The resulting distribution of raw median ratings is plotted in Fig. 7.
Fig. 7 Distribution of the neutrality scores for the ‘average’ observer. The 1-SD inter-observer variability ellipses of the unique white setting experiment and the rating experiment are plotted as a solid and dashed black line respectively. The dashed-dotted black line is the elliptical contour – at a Mahalanobis distance of 1 – of a bivariate Gaussian fit to the data. The centers of the three respective ellipses are marked with ‘ + ’, ‘x’, ‘o’.
From the figure it is clear that neutrality – cfr. high ratings – encompasses a (rather large) region in color space and is not confined to a line of whites as reported by Ohno or Rea. The degree of neutrality is also not equal for all CCTs or Duvs and as already established earlier, chromaticities slightly below the blackbody locus result in a higher perceived neutrality or whiteness. It can also be seen that the CIE class A and B white regions, although in quite good agreement with the neutral area – colored red in Fig. 7 – along a direction roughly perpendicular to the blackbody locus, are extended too far towards lower color temperatures and don’t extend far enough towards higher color temperatures. Furthermore, a comparison of the size, location and orientation of the rating and adjustment 1-SD inter-observer variability ellipses, plotted in Fig. 7 and given in Tables 2 and 3, indicates the two experimental methods result in similar unique whites. A more rigorous and statistical analysis of the influence of experimental method on the unique white results is reported on in the next subsection.
Secondly, for each luminance level the average observer scores were modeled with a bivariate Gaussian function (Eq. (1)):
with Sneutral the degree of neutrality, a1-6 fitting parameters (see Table 5) and u’v’ the CIE 1976 chromaticity coordinates of the stimulus. A plot of the bivariate Gaussian model is shown in Fig. 8 for each luminance level, as well for the luminance-invariant case. The elliptical contour – at a Mahalanobis distance of 1 – of the bivariate Gaussian model is also shown as a black dashed-dotted line in Fig. 7. The goodness-of-fit, quantified by the Standardized-Residual-Sum-of-Squares (STRESS) [16], of the four models was 0.19 (2000 cd/m2), 0.21 (1000 cd/m2), 0.19 (200 cd/m2) and 0.18 (luminance-invariance), indicating a satisfactory fit given the larger average inter-observer variability STRESS values of respectively 0.29, 0.29, 0.28 and 0.27. The good fit is also observable in the 3D model plots in Fig. 8.Table 5. Fitting Parameters of Bivariate Gaussian Fitted to the Neutrality Ratings of the Average Observer with the CCT and Duv Associated with the Center Also Given
Fig. 8 Bivariate Gaussian model of the neutrality score of an ‘average’ observer. The chromaticity points of the 59 presented stimuli are shown as black dots.
A comparison of the CCT and Duv given in Table 5 and Table 4 show that the former are well within the 95% confidence intervals of those obtained by taking only the 7 highest scored chromaticity points (cfr. Table 4) into account, indicating the practical equivalence of both approaches, as can also be seen from the close proximity of the centers of the elliptical contour of the bivariate Gaussian model (dash-dot black line, ‘o’) and the rating 1-SD inter-observer variability ellipse (dashed black line, ‘x’) in Fig. 7.
3.3 Global statistical analysis: influence of luminance level and experimental method
A doubly multivariate repeated measures MANOVA, with a three factor within-subjects design, was conducted with SPSS to investigate the influence of the luminance level on the unique white setting and the impact of the method used to determine it. The three factors (Independent Variables) were: IV1 = luminance level, IV2 = method, IV3 = repeats. The dependent variables (DV) were the CIE 1976 u’v’ coordinates of the unique whites obtained during the experiments. For the unique white adjustment experiments these were the 7 settings made by each observer under each luminance condition. The DV’s for the unique white rating experiments were obtained by taking the u’v’ coordinates values with the 7 highest scores.
The main assumptions for a doubly multivariate repeated measures MANOVA – multivariate normality and within-subject sphericity – were respectively checked with Mardia’s test on multivariate skewness and kurtosis [17] and Mauchly’s test of sphericity [18]. No significant (p < 0.05) violations were found for the main effects of method, luminance level and repeats.
The results of the statistical analysis were as follows. The effect of method was found to be non-significant (Wilk’s Lambda = 0.771, F(2,11) = 1.633, p = 0.239, partial eta squared (𝞰2) = 0.229), while the effect of luminance level was (Wilk’s Lambda = 0.197, F(4,9) = 10.302, p = 0.002, partial eta squared (𝞰2) = 0.821). Although the size of the interaction between luminance level and method was large (partial eta squared (𝞰2) = 0.506), it was not significant (Wilk’s Lambda = 0.494, F(4,9) = 2.304, p = 0.137). Finally, the repeats factor (cfr. random start positions) had a large effect size (partial eta squared (𝞰2) = 0.626) but was not significant (Wilk’s Lambda = 0.374, F(12,1) = 0.140, p = 0.980). No significant interactions with repeats were observed (p < 0.05).
Posthoc follow-up tests for the effect of luminance level on the chromaticity of the unique white showed that only the 2000 cd/m2 and 200 cd/m2 luminance levels differed significantly (Wilk’s Lambda = 0.448, F(2,11) = 6.790, p = 0.012, partial eta squared (𝞰2) = 0.552). However, a series of repeated measures MANOVAs, one for each observer and with luminance level and method as the within-subjects factors and u’, v’ as the DVs, showed a significant (p < 0.05) effect of luminance for only 3 of the 13 observers. Applying a Bonferroni correction, to account for the inflation of the type-I error due to the multiple MANOVAs, no significant (p < 0.004) effect remained.
Therefore, although luminance was found to have a significant effect in general, no such effect was established at the individual level. The latter is consistent with the findings of Walraven and Werner [6] and Hurvich and Jameson [1] who had investigated unique white at the individual observer level and found it to be luminance-invariant. In contrast, Chauhan, Perales, Xiao, Hird, Karatzas and Wuerger [12], who focused on unique white settings averaged across their test subjects, also reported a significant effect of luminance, which is consistent with the former.
4. Conclusion
Unique or neutral white under dark adapted conditions was examined using two experimental methods – adjustment and rating – at 3 luminance levels – 200, 1000 and 2000 cd/m2 – for a group of 13 color normal observers. Although high luminance data are perhaps less applicable to many indoor lighting situations or to typical displays, they are nonetheless valuable for high dynamic range imaging, very bright displays [13] and especially from a color vision or color appearance modeling standpoint [19]. It was found that both in terms of method and luminance level very similar average unique whites were found, all located below the blackbody locus and approximately centered around 6000 K. The results showed neutrality or unique white to encompass a region in color space rather than a line as reported by Rea and Freyssinier [9] and Ohno and Fein [10]. They also indicated that the low and high color temperature ends of the CIE class A and B white regions tend to respectively overestimate and slightly underestimate the size of the chromaticity area perceived as white by the dark adapted average observer. However, the agreement along a direction approximately perpendicular to the blackbody locus is quite good. Unique white, at least under dark viewing conditions, is a very subjective sensation as evidenced by the large inter-observer variation found in both experiments. Although the average unique whites (across observers) in each experiment seemed to shift towards colder color temperatures as the luminance level was decreased, no such systematic trend was observed at the individual level, which is in agreement with the invariance of unique white reported by Walraven and Werner [6] and Hurvich and Jameson [1]. The data were therefore also analyzed under the assumption luminance-invariance. For each luminance level, as well as for the luminance-invariant case, the unique white ratings could be modeled quite accurately with a bivariate Gaussian function, resulting in a simple empirical metric to predict the degree of neutrality of any stimulus viewed under dark adapted conditions by an average observer.
Acknowledgments
Author KS would like to thank the Research Foundation Flanders (FWO) for supporting this study through a Postdoctoral Fellowship (12B4913N).
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