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Abstract
In this study, the settings of the display white points were investigated, which presented the color appearance matched with a neutral surface as observed in the state of mixed chromatic adaptation. A psychophysical experiment was conducted under 20 illumination and viewing conditions via successive binocular color matching. It is discovered that the metameric light sources have generally equivalent effects on the observers’ adaptation states and the resulting white points. The correlated color temperature (CCT) of the illumination and the adapting luminance, both with a significant influence on the mixed chromatic adaptation, exhibit a positive and a negative relation to the white point CCT, respectively. The immersive illumination affects the white point through the adaptation ratio and the baseline illuminant. Finally, the experimental results were verified to be predictable with an amended mixed chromatic adaptation model, which produced a mean chromaticity error of only 0.0027 units of CIE 1976 u′v′.
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1. Introduction
In the cross-media color reproduction, it is desired to achieve an appearance matching between the real object and its softcopy displayed on a monitor [1]. The white point, as a fundamental parameter for color display, plays an important role in this sort of applications. Since the observer perceives colors differently under varying illumination or viewing conditions, the white point should change accordingly [2–7] to maintain its appearance matched with a neutral surface (defined as a surface with a non-selective spectral reflectance in this paper). Therefore, in previous studies, it was necessary to carry out preliminary experiments to determine appropriate white points under their respective conditions [8–11]. However, these existing studies were only concerning on the overall results of the color appearance reproduction, whereas the display white points have never been analyzed systematically.
The mixed chromatic adaptation frequently occurred in the white point determination experiments [8,10,11], whereby the observers compared the color appearance of the display stimuli and the neutral surface under a specified illumination using successive binocular observations, with the adaptation state being jointly affected by the illumination and the display stimuli [5,12–17]. There have been attempts to establish models for this particular adaptation mechanism, e.g., the framework recommended by International Commission on Illumination (CIE) [16] which combines CAT02 [18,19] with S-LMS [20]. However, the performance of the mixed chromatic adaptation model has not been verified on display white point prediction under various conditions.
Noting that, in some experiments, the observers were instructed to set the display white point only according to their own memories [2–5,21], which is more like the implementation of the color preference reproduction owing to the absence of surface color references, with different purposes from that of the color appearance reproduction discussed in this study.
This paper provides a new insight into the display white point settings based on the theory of mixed chromatic adaptation. A psychophysical experiment was carried out to collect visual data under various conditions (Section 2.), from which the display white points were derived through a data analysis (Section 3.). Therewith, systematical discussions were made on the chromaticity variations of the white points across different illumination and viewing conditions (Section 4.). Since the various types of color devices (e.g., displays, scanners and digital cameras) characterize colors in different ways, the experiment in this study is basically applicable to assessing the white points for displays and may not work for other cases.
2. Experiment
2.1 Illumination and viewing conditions
As listed in Table 1, the experiment was comprised of 20 sessions with various illumination and viewing conditions, which were divided into two categories, namely, the light booth conditions and the immersive conditions. The light booth conditions were commonly adopted in the reported experiments of color appearance reproduction [8,10,22,23], and thus were emphasized in this study.
Table 1. The experiment sessions with different illumination and viewing conditions.
2.1.1 Light booth conditions
A JIAYI JY-3000 light booth and an X-Rite Spectralight QC light booth were adopted to provide 16 different localized illuminations involving 6 typical light sources (i.e., A, D65, U30, TL84, CWF and the LED) and 5 levels of adapting luminance (i.e., the absolute luminance of the neutral reference denoted by $L_\text {Ai}$, approximately 24, 47, 70, 96 and 152 cd/m2). The spectral power distribution (SPD) of each light source was measured by a Konica Minolta CS-2000 tele-spectroradiometer . As listed in Table 1, the color fidelity index (Rf) was calculated from the measured SPD according to the lasted guideline proposed by Illuminating Engineering Society of North America (IES) [24]. Meanwhile, the illumination chromaticity was also derived from the SPD based on CIE 1964 10$^{\circ }$ color matching function. Noting that, U30 and A light sources used in this experiment had distinct SPDs but shared an almost identical chromaticity, as depicted in Figs. 1(a) and 1(b). Therefore, these two light sources were regarded as metameric light sources. Similarly, TL84, CWF and the LED made up another group of metameric light sources, whose chromaticity points and SPDs are plotted in Figs. 1(c) and 1(d).
Fig. 1. The chromaticity points (plotted in CIE 1976 u’v’ diagram) and the SPDs of the metameric light sources. (a) Chromaticity points of U30 and A, together with the blackbody locus (dashed line) and a 1-step MacAdam ellipse (solid line). (b) SPDs of U30 and A. (c) Chromaticity points of TL84, CWF and the LED, together with the daylight locus (dashed line) and a 3-step MacAdam ellipse (solid line). (d) SPDs of TL84, CWF and the LED.
The experiment sessions under the light booth conditions were carried out in a dark room, as illustrated in Fig. 2(a). A 30 cm $\times$ 50 cm gray board with the color of Munsell N5 was installed inside the light booth, acting as both the neutral reference and the adapting field of the illumination. There was a 7 cm $\times$ 7 cm black frame drawn at the center of the board to help observers focus their eyes on it. An EIZO CG241W professional desktop monitor mounted with a hood was placed adjacent to the light booth to present the full-screen color stimuli with the same dimensions as the neutral reference, as well as a similar black frame at the screen center. The luminance of the stimuli was maintained at 70 cd/m2 in all the sessions.
During the experiment, the observers sat in front of the light booth and the monitor. The localized illumination of the light booth occupied a field of view (FOV) of about 80° $\times$ 60°. The viewing distances to both the neutral reference and the screen were about 1 m, resulting in a 20° $\times$ 30°view angle for both media, and a 4° $\times$ 4°view angle for the centered black frames. The observers were allowed to shift their gaze back and forth between the two media freely and rapidly.
2.1.2 Immersive condition
The experiment sessions under the immersive conditions were conducted in a room with a multi-channel LED lighting system being equipped on the ceiling [25], which was controlled to generate 4 specified illuminations at the adapting luminance of 96 cd/m2 with the chromaticity of A, TL84, D65 and the 10400K daylight, respectively. The relative positions of the neutral reference, the monitor and the observers were kept the same with those under the light booth condition, as illustrated in Fig. 2(b). During the experiment, the observers were immersed in the LED illumination and viewed the two media with the same way as described in Section 2.1.1.
2.2 Stimulus chromaticity
Under each of the experiment sessions listed in Table 1, a series of 98 chromaticity points was selected for assessment, consisting of 14 correlated color temperatures (CCTs) and 7 levels of deviations from the blackbody locus (Duv). The interval of the adjacent points was around 0.0066 units of $u'v'$, and the center point was determined by a preliminary experiment via chromaticity adjustment. For example, in the experimental session 9, the chromaticity points of the display stimuli are uniformly distributed in CIE 1976 u’v’ diagram as shown in Fig. 3. The CCTs of stimuli range from 2955K to 7088K and the Duv values are between $\pm$0.0198. For the other sessions, the stimulus chromaticity points are distributed similarly with those for session 9. The monitor was chromatically characterized using the gain-offset-gamma model [26] based on CIE 1964 10$^{\circ }$ color matching function before the experiment.
Fig. 3. The chromaticity distribution of the display stimuli in experimental session 9 (under the TL84 illumination at a luminance level of 70 cd/m2)
2.3 Observers and procedure
A panel of 15 observers participated in the experiment, including 7 females and 8 males, with the ages ranging from 22 to 32. They all had normal color vision, as tested using the Ishihara pseudo-isochromatic plates. A training session was inserted to familiarize the observers with the experimental procedure beforehand. During the experiment, the 20 sessions listed in Table 1 were conducted with a random sequence, together with two repeated sessions for reliability verification under the light booth conditions at 96 cd/m2 with TL84 and U30 light sources, respectively.
At the beginning of each session, a 2-min dark adaptation and a 1-min background adaptation to the illumination were performed. Then the 98 stimuli (as determined in Section 2.2) were displayed on the monitor randomly. For each trial of assessment, the monitor first showed a stimulus for 1.5 s, and then blacked out to prevent the observer from fully adapting to it. The observer was instructed to compare the displayed stimulus with the neutral reference using successive binocular observations, and rate the appearance similarity by pressing one of the number keys on a keyboard, from 1 (totally different) to 5 (exactly matching), at any time after the stimulus was shown. Once the assessment had been made, another stimulus was shown after a 0.5 s delay of black-out. To sum up, 32340 assessments were collected during the experiment, i.e., 15 observers $\times$ 22 sessions (20 sessions with different conditions plus 2 repeated sessions) $\times$ 98 stimuli.
The experiment process was recorded as videos to confirm that the observers viewed both the media before rating. The viewing time is nearly equal across the observers, with an average of 1.4 s for the display stimulus and 1.5 s for the neutral reference, respectively. Despite the short viewing time, both the media inevitably have a partial effect on the observer’s color perception, due to the capability of the rapid adaptation of the visual system [27]. Therefore, the observers were in the state of mixed chromatic adaptation to both the illumination and the display stimuli.
3. Data analysis and results
3.1 Observer variation
The inter-observer variation of the assessment results is represented as the mean chromaticity difference from the mean (MCDM), derived from the chromaticity differences (defined by Euclidean distances among chromaticity points in CIE 1976 $u'v'$ diagram) of the exactly matching stimuli rated by each single observer and an average observer. The details of the calculation procedure of MCDM can be referred to [2]. In this study, the MCDM was calculated separately for each experimental session, having an average of 0.0111 and ranging from 0.0042 to 0.0177. The underlying causes of the inter-observer variation are probably the observer metamerism [28,29] and different speed of chromatic adaptation among observers [30], resulting in various visual perceptions to an identical stimulus.
The intra-observer variation is quantified by the chromaticity difference between the exactly matching stimuli assessed by the same observer in the repeated sessions, which has an average of 0.0022 over all observers and ranges from 0.0008 to 0.0130.
The inter- and intra-observer variations are comparable with those in the previous studies [2,3,5], indicating the reliability of the results of this experiment.
3.2 Display white point and standard deviation
For each session, the observers’ ratings are converted to interval scale values according to a law of categorical judgment [31], which are then taken as the weights of the corresponding stimuli. Thereby, the display white point is derived from a weighted sum of the stimulus chromaticity, and the standard deviation error is calculated from the weighted covariance as well.
Figure 4 plots the chromaticity points of the illuminations and the display white points located at the center of the one-standard-deviation error ellipses. Obviously, both the illumination chromaticity points and the white points are distributed along the black body locus. The white point CCT appears to change concurrently with different illumination and viewing conditions, whereas the Duv value only fluctuates within a small range. The one-standard-deviation error ellipses have analogous sizes and orientations to those obtained in the reported experiments without neutral references [4,5,21,32], manifesting that the existence of the reference does not affect the precision of the experimental results.
Fig. 4. The one-standard-deviation error ellipses of the display white point chromaticities under various illumination and viewing conditions. The chromaticity points of the illumination are also plotted with triangle marks. The ellipses and chromaticity points of different types of light sources are distinguished by symbol colors.
4. Discussion
4.1 Influence of metameric light sources
From Fig. 4 it can be observed that the sizes of the one-standard-deviation error ellipses vary under different light sources. For example, in Fig. 4(b) the ellipse for U30 is larger than that for illuminant A. The ellipse size reflects the variability of observers’ assessment on the display stimuli. Although the U30 and the A light sources used in this experiment share almost identical chromaticity, they have distinct SPDs, which may induce the observers to make different judgements in the visual assessment.
It is also discovered that the metameric light sources would not significantly affect the center of the one-standard-deviation error ellipses, i.e., the chromaticity of the display white points. The MCDMs of the white points under metameric light sources, together with those in repeated sessions, are listed in Table 2. It is obvious that the chromaticity differences resulted from the change of metameric light sources are roughly equal to the variations of repeated assessments. Moreover, one-way multivariate analyses of variance (MANOVAs) were applied to the white point chromaticity under the metameric light sources. First, the variance inflation factors of the chromaticity coordinates were computed to confirm that the visual data comply with the underlying assumption of MANOVA so that there is no multicollinearity among the dependent variables [33–36]. Then the p-values were calculated to represent the significance of the chromaticity difference of the white points, which are also listed in Table 2. The MANOVA confirms that there is no difference among the white point chromaticities under the metameric light sources at a significant level of 0.05, indicating an insignificant impact of the light source SPDs on the white point assessment.
Table 2. The MCDMs (with p-values in the brackets) among display white points under the metameric light sources and in the repeated sessions. The chromaticity differences among light sources are compensated for in the calculations.
4.2 Influence of illumination CCT
Figures 5(a) and 5(b) plot the white point CCTs and DDuv values (denoting the differences of the Duv values between the illumination chromaticity and the corresponding display white point) against the illumination CCTs, respectively. Figure 5(a) reflects a significant relation between the CCTs of the white points and the illuminations under either the light booth or the immersive conditions, with the Spearman correlation coefficients of 0.9999 (p = 2.3E-3) and 0.9975 (p = 2.5E-3), respectively. Specifically, under the illuminations at low CCTs, the white points deviate to higher CCT than those of the illuminations, while the deviation reduces gradually as the illumination CCT rises, exhibiting a positive relation with a slope lower than 1. Under the immersive conditions, the white point CCT converges to that of the illumination at around 9000K and then shifts to the opposite direction. The inconstancy of the white point indicates that the observer may never fully adapt to the illumination and that the mixed chromatic adaptation state varies substantially across different conditions. This trend agrees with the findings in the previous studies [2,5,37].
Fig. 5. Display white point chromaticity changing with the illuminations. (a) Display white point CCT changing with illumination CCT. (b) Display white point DDuv changing with illumination CCT. (c) Display white point CCT changing with adapting luminance. (d) Display white point DDuv changing with adapting luminance. The error bars represent the standard deviations.
Figure 5(b) shows that, there is no clear trend between DDuv values and the illumination CCTs. Although DDuv takes negative values (i.e., the Duv values of the white points are lower than those of the illuminations) under most conditions, the trend is not considerable according to the Student’s t-test on the null hypothesis of DDuv = 0, with the p-values being larger than 0.84.
4.3 Influence of immersive illumination
Figure 5(a) unfolds a clear comparison between the white points under light booth and immersive conditions corresponding to the same illumination CCT. A one-way repeated measures analysis of variance (ANOVA) was performed with the factor of the two categories of conditions on the white point CCT, which gave a p-value of 1.2E-2, revealing that, with a constant illumination chromaticity, the white point CCT under the immersive condition is considerably lower than that under the light booth condition. Given that the different SPDs of the LED system and the light booth have similar visual effect (according to Section 4.1), the main cause of the difference in white points is probably the immersion in the ambient illumination. Under the immersive condition, the illuminated surroundings always provide cues of illumination chromaticity when the display stimuli are being viewed, inducing the mixed chromatic adaptation state to be more susceptible to the illumination. Whereas, under the light booth condition, the monitor is viewed in dark surroundings, so the adaptation state is more likely to be affected by the display stimuli and so the resulting display white point has a larger deviation from the illumination chromaticity. In the mixed chromatic adaptation model, the adaptation ratio represents the weight of the influence of the display stimulus on the adaptation state. Obviously, under the light booth condition, the adaptation ratio is higher than that under the immersive condition.
According to the findings by Zhai et al. [5], the illuminant that has the identical chromaticity with the display white point obtained under it can be referred to as the baseline illuminant, which represents a baseline for calculating the degree of incomplete adaptation for the specified category of conditions. Figure 5(a) also implies that the baseline illuminant under the light booth condition has a higher CCT than that (around 9000K) under the immersive condition. The change of the baseline state of the adaptation is probably attributed to different mechanisms enabled under the immersive and the localized illumination. For example, the ambient illumination under the immersive condition occupying a larger FOV than that of the light booth is thus more likely to stimulate the non-visual photosensitive cells implicated in color perception and adaptation, as suggested by recent studies [38–40].
4.4 Influence of adapting luminance
Figures 5(c) and 5(d) plot the CCTs and DDuv values of the display white points against the adapting luminance, respectively. It is evident from Fig. 5(c) that the white point CCT varies inversely with the adapting luminance, with the Spearman correlation coefficients of −0.8919 (p = 1.6E-2) and −0.9813 (p = 1.8E-2) for U30 and TL84, respectively. A feasible explanation for this trend is that the effect of the adapting luminance is twofold. On the one hand, the higher luminance yields a more complete adaptation to the illumination, as the adaptation degree is positively related to the luminance in the chromatic adaptation like CAT02 [19]. On the other hand, the illumination with a higher adapting luminance than the display stimuli dominates the mixed chromatic adaptation and is highly influential on the observer’s color perception. With this factor the adaptation ratio is modulated by the luminance of both media in the mixed chromatic model recommended by CIE [16]. As a result, the observer tends to appreciate the display white points with their chromaticities close to the illuminations under high adapting luminance conditions.
For the conditions involved in Fig. 5(d), the p-value of a Student’s t-test with the null hypothesis of DDuv = 0 is larger than 0.86, indicating that the subtle differences of Duv values between the illuminations and white points are statistically insignificant.
4.5 Prediction of mixed chromatic adaptation model
In this section, the mixed chromatic adaptation model recommended by CIE [16] would be applied to predict the chromaticity of the display white points, with amendments being made based on the conditions of this study. Thereby, a comparison would be made between the perceived white points from the experiment and the corresponding predictions by the model.
4.5.1 Application of mixed chromatic adaptation model on display white point prediction
The calculation of the mixed chromatic adaptation model is based on the cone responses of the neutral reference (with the same chromaticity as the illumination) as well as the display white point, denoted by $[ L_\text {i} \ M_\text {i} \ S_\text {i} ]$ and $[ L_\text {d} \ M_\text {d} \ S_\text {d} ]$, respectively. $[ L_\text {i} \ M_\text {i} \ S_\text {i} ]$ can be transformed from the instrumentally measured tristimulus values using the matrix in CAT02 ($M_\text {CAT02}$) or the matrix in CAT16 ($M_\text {CAT16}$), and $[ L_\text {d} \ M_\text {d} \ S_\text {d} ]$ are unknown variables. The cone responses of incompletely adapting whites, $[ L'_\text {i} \ M'_\text {i} \ S'_\text {i} ]$ and $[ L'_\text {d} \ M'_\text {d} \ S'_\text {d} ]$, are calculated according to the recommendation by CIE [16]. For example, the L cone responses are given by Eq. (1).
$D_\text {i}$ and $D_\text {d}$ represent the degrees of adaptation to the illumination and the display stimulus, respectively. As recommended by CIE, the adaptation degree can be calculated by a function of the adapting luminance ($L_\text {A}$) and the surrounding factor ($F$) in CAT02, denoted by $D_\text {CAT02}(L_\text {A},\; F)$. However, recent studies suggested that the illumination with a low CCT or a large Duv value would induce a decline in the adaptation degree [3,5,42]. Peng et al. [2] proposed an empirical formula of the adaptation degree changing with varying illumination chromaticities, denoted by $D_\text {Peng}(u',\; v')$ . In this paper, the adaption degree is assumed as the CAT02 function modulated by the illumination chromaticity effect, which is expressed as
When the observer is viewing the display, both media partially affect the adaption state. In CIE recommended model framework, the cone responses of the adapting white $[ L''_\text {d} \ M''_\text {d} \ S''_\text {d} ]$ are expressed as a weighted sum of $[ L'_\text {i} \ M'_\text {i} \ S'_\text {i} ]$ and $[ L'_\text {d} \ M'_\text {d} \ S'_\text {d} ]$, as given by substituting Ep. (3) to Eq. (4).
The Newton’s method can be adopted to the solve Eq. (5) to obtain $[ L_\text {d} \ M_\text {d} \ S_\text {d} ]$, which are then transformed to tristimulus values using the inverse matrix in CAT02.
4.5.2 Comparison between experimental results and model predictions
The display white points predicted by the mixed chromatic adaptation model were compared with those obtained from this visual experiment. Three models were applied in the comparison, with different parameters as listed in Table 3. Model I is recommended by CIE, but is not always appropriate for practical applications [3,5,17,41–43]. And Model II and Model III embodied Eq. (2) as the function of adaptation degree, and the 9000K daylight was set as the baseline illuminant under the immersive condition. Additionally, the transformation matrix in Model III is changed from $M_\text {CAT02}$ to $M_\text {CAT16}$.
Table 3. The parameters for the mixed chromatic adaptation models, together with the mean prediction errors corresponding to the two categories of conditions.
For Model II and Model III, the interior point method [44] was performed to derive optimized $R_\text {abp}$ and the CCT of the baseline illuminant under the light booth condition, to minimize the average chromaticity difference between the predicted white points and the visual data. The optimized values of $R_\text {abp}$ are listed in Table 3. The larger $R_\text {adp}$ under the light booth condition implies that the observer is less affected by the light booth illumination when viewing the displayed stimulus. The optimized baseline illuminant CCTs under the light booth condition are 12500K and 11765K for Model II and Model III, respectively, much higher than that under the immersive condition. This phenomenon agrees with the discussions in Section 4.3.
The prediction errors of model are reported by calculating the mean chromaticity difference from the visual data. As seen in Table 3, the white point variation across the illumination and viewing conditions in this experiment is well described by the amended mixed chromatic adaptation models. The average prediction error over all conditions is roughly 0.0027 units of $u'v'$ for both Model II and Model III, which is smaller than the inter-observer variations and the diameters of one-standard-deviation error ellipse, indicating that the amended models achieve a reasonable accuracy when being applied to display white point prediction. Furthermore, the prediction errors under the immersive condition are smaller than those under the light booth condition, because the CIE recommended model and the modification on adaptation degree function were both derived from the experimental results under immersive conditions. Model II and Model III present comparable performance in white point prediction, which indicates that both $M_\text {CAT02}$ and $M_\text {CAT16}$ are applicable to the mixed chromatic adaptation model.
Further studies could develop a comprehensive mixed chromatic adaptation model for display white point prediction, in which, for example, a degree of adaptation model proposed by Ma et al. involving the impact of the field of view [45] is desired to be embodied.
5. Conclusion
This study focuses on the display white point settings for the cross-media color reproduction applications, which is perceived to be matched with a neutral reference in the state of mixed chromatic adaptation. A psychophysical experiment was carried out, obtaining the visual data of display white points under 20 illumination and viewing conditions from the 2 categories, namely the light booth conditions and the immersive conditions.
It is discovered that the metameric light sources have generally equivalent effects on the observers’ adaptation states as well as the resulting display white points. The illumination CCT and adapting luminance are both highly influential factors of mixed chromatic adaptation, with a positive and a negative relation to the display white point CCT, respectively. For the immersive and the light booth viewing condition, the adaptation ratio takes the values of 0.682 and 0.728, respectively, meanwhile the baseline illuminant has CCTs of 9000K and 12500K, respectively.
Finally, an amended mixed chromatic adaptation model based on the CIE recommended framework was applied to predicting the display white points under various conditions, which embodies an optimized adaptation ratio, a custom baseline illuminant and a modified adaptation degree function. The model predications are in good agreement with the experimental results in this study, with an average error of 0.0027 units of $u'v'$. The findings in this study would provide a new insight into the display white point settings based on the theory of mixed chromatic adaptation, and would be a useful reference for the related researches and applications.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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