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Abstract
Color matching experiments were conducted for 11 pairs of displays, using 7 displays with different spectral characteristics. The color matching results between the LCD display and displays that have a narrowband spectrum, such as a laser projector, QLED, or OLED, demonstrated a significant color difference between two matched colors. The maximum difference was 18.52 ΔE00, which indicates the white color difference between the LCD and laser projector. There was also a clear observer variability of 2.27 ΔE00. The new cone fundamental function derived from 757 metameric pairs showed good performance compared to CIE standard observers reducing the display color mismatching significantly. This function also demonstrated a better performance when evaluating color matching in color chart image.
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1. Introduction
With the development of wide color gamut display technologies having the narrowband spectrum, producing more saturated colors than conventional displays is now possible. However, when two different displays use the same CIE 1931 tristimulus values to produce the same colors, a color mismatch with different color appearances can be observed. Similarly, two colors with the same appearance on different displays were found to have different tristimulus values [1–15]. Such a color mismatch problem indicates that the CIE standard observer does not represent the real average observer.
Issues related to color mismatch have recently become critically important. Therefore, several color matching experiments have been conducted using displays with various spectral characteristics. These experiments were conducted to demonstrate the occurrence of color mismatch and observer variability when using CIE standard color matching functions (CMF).
For instance, 50 observers adjusted six test colors in the CIE u’v’ color space using one LCD and four OLEDs for a field size of view (FOV) of 4.77° in a study by Wu et al. [1]. The results showed that the color difference between the reference and matched colors was 0.0042 Δ u’v’, and there were 0.0059 Δ u’v’ inter-observer variations. Huang et al. conducted a color matching experiment by adjusting the intensities of one or two primaries using LED panels at an FOV of 5.7° with 70 observers [2]. The color difference between the reference and matched colors was 0.0123 Δu’v’ and 0.0059 Δu’v’ for inter-observer variations. In a study by Shi and Luo, 20 observers adjusted colors in the CIELAB color space using three LCDs and two OLEDs at 4° of FOV [3]. The results showed that the color difference between the reference and matched color was 4.93 ΔE00, and there was a 2.58 ΔE00 of inter-observer variations. Bodner et al. performed a color matching experiment with an OLED and a CRT display with a 1° FOV [4]. The 16 observers adjusted the CIELAB a*b*, chroma, and lightness, and the results showed that the color difference between the reference and matched color was 2.7 ΔE00. Fan et al. conducted an experiment where 35 observers adjusted colors by manipulating the correlated color temperature and CIELAB a*b* using two LCD displays at an FOV of 4° [5]. In this experiment, there were 5.5 ΔE00 inter-observer variations.
These studies clearly demonstrated that color mismatch and the observer variability cannot be ignored when using the CIE standard color matching function. Although observers performed color matching to have the same color appearance in two displays with different spectral characteristics, the two colors actually had different CIE 1931 tristimulus values. There were also differences in color matching for each individual. Therefore, a new color matching function is required to complement the CIE metameric failure and observer variability and to reflect the characteristics of various displays, including the narrowband spectrum [16,17].
In this study, color matching experiments were performed using seven displays with different spectral characteristics, including recently developed narrowband spectrum displays such as laser projectors, QLED, and OLED. The results of the color matching experiment were used to derive new cone fundamentals using Asano’s individual colorimetric observer model [16]. The performance of the new cone fundamental functions was validated by evaluating color matching in the color chart image.
2. Display color matching experiment
2.1 Apparatus and setup
Two displays with different spectral characteristics were placed side by side. Two types of experimental settings were used depending on the FOV of the stimulus. In the experimental setting A, 2° and 4° stimuli were used, whereas full-sized stimuli were used in setting B.
Figure 1(a) demonstrates the experimental setting A. The stimuli were shown in a size of 9.1 cm x 9.1 cm; excluding these parts, the remaining display was covered with a black paper. The distance between the two stimuli was set at 15 cm. The distance between the observer and the displays was set at 270 cm for a 2° viewing angle and 130 cm for a 4° viewing angle.
Figure 1(b) demonstrates the experimental setting B. The size of the stimuli was set to fit the smaller display size between the two displays, and the remaining part of the larger display was covered with a black paper. The distance between the observer and the displays was set at 200 cm.
2.2 Test displays
Seven test displays, including three RGB LCDs with different spectral characteristics (RGB LCD1, RGB LCD2, and RGB LCD3), QLED, RGB OLED, WRGB OLED, and a laser projector, were used in the experiment. Figure 2 displays the spectral power distribution (SPD) of the test displays. Note that WRGB OLED uses RGB and white sub-pixels while other displays use RGB only.
2.3 Experimental procedures
Before the experiment, all the test displays were warmed up for at least 30 min. The experiment was conducted in a dark room. The observers were located at the center of the two displays.
The experiment was conducted by manipulating the color of the test displays to have the same color appearance as the reference display. When the observers were making a judgement, they were allowed to freely move their eyes and postures but were guided to focus the center of the two displays to minimize the effect of color change by display non-uniformity.
Each test display was characterized using a gain-offset-gamma model [18], and the color was controlled in the CIELAB color space. The observer adjusted the brightness (L*), redness-greenness (a*), and yellowness-blueness (b*) of the color on the test display using a keyboard. The changed CIELAB value was then converted to XYZ, which was subsequently converted to the corresponding RGB value and the color was observed by the observers watching the test display.
Before the main experiment, the observers performed a training session to familiarize themselves with the color control method. When color matching was performed, the color in the test display began with the color having the same luminance and different chromaticity as the reference stimulus. The observer performed the color matching without a time limit. Immediately after each color matching, the spectral data of the stimuli on the reference and test displays were measured using a spectroradiometer (Konica Minolta CS-2000). The observer was asked to press the enter key to move to the next stimulus. The same procedure was followed for each experimental session, and each experiment lasted 30 min to 90 min. The experimental protocols and procedures were approved by the Institutional Review Board of the Ulsan National Institute of Science and Technology.
2.4 Experimental session and test stimuli
Table 1 lists the experimental sessions that were conducted, which demonstrates the type of displays used, FOV, experimental setting, number of test stimuli, number of observers, and number of repetitions. Experimental session 1 was conducted using the same RGB LCD1 display to test the sufficiency of individuals in matching the colors. Experimental session 3-2 were conducted twice with different observers (6 and 7) on different days but the data were combined for further analysis. In the case of Setting B, as explained in Section 2.1, FOV was adjusted to fit the smaller display. Therefore, Laser projector’s screen size was adjusted as 26° for Session 8 following RGB LCD2 size and 15° for Session10 following RGB LCD3 size.
Table 1. Color Matching Experimental Session
All the test stimuli were located within the color gamut of the reference and test displays. Because white has the largest metamerism [16], it was included as a test color in all the experimental sets. Only the white color was used in the experimental sessions in which only one stimulus was tested; nine sessions belonged to this case. In the remaining seven types of experiments, color matching was performed on the white color and various colors with different hues and colorfulness, which included red, green, blue, cyan, magenta, and yellow. The CIE u’10v’10 chromaticities of the test stimuli for each experimental session are shown in Fig. 3.
Fig. 3. Color chromaticities for test stimulus of each experimental session: (a) sessions 1, 2, 3, 4, 5-1, 6-1 (only white color), (b) sessions 5-2, 6-2, 7, (c) sessions 8, 9, 10, 11.
2.5 Observers
Nine observers (eight females and one male) with an average age of 28 years participated in this experiment. Each observer participated in a minimum of 3 and a maximum of 11 experimental sessions. All of them had normal color vision, as tested using the Ishihara color vision test.
2.6 Data analysis method
The X10Y10Z10 were calculated for the reference and matched spectra. From the tristimulus values, u’10v’10 values were calculated to represent the colors on the chromaticity coordinates and CIELAB values to calculate the color difference. The reference white for the calculation of CIELAB values was the white of RGB LCD2, and its tristimulus value is [97.62, 103.36, 111.43]. Using the CIELAB values for the reference and the matched color, the CIEDE2000 color difference, ΔE00, was calculated.
The color matching results were analyzed in terms of ‘Observer Metamerism Magnitude (OMM)’ and ‘Observer Variability (OV)’ [2,15]. The OMM indicates the average color difference between the reference and individual matching colors, as demonstrated in Eq. (1). The OV calculates the average color difference between the average matching color and the individual matching colors, as demonstrated in Eq. (2). The term i represents the observer, from 1 to N, and N represents the number of observers per experimental session.
2.7 Results
2.7.1 Color matching accuracy test
To evaluate the color matching accuracy, color matching was first conducted on the same RGB LCD1 display. When the color matching experiment was performed using the same display, observers should generate the same color as the reference color. The average ± standard deviation of OMM was determined to be 0.98 ± 0.68 ΔE00 and the OV was 0.22 ± 0.15 ΔE00, indicating that the observers can match colors fairly well.
2.7.2 FOV effect on color matching
Experimental sessions 3 (RGB LCD1 and RGB LCD2) and 4 (RGB LCD1 and RGB OLED) were conducted using both 2° and 4° FOV.
Table 2 summarizes the color matching results between the 2° and 4° FOV. The results show that as the FOV increased, both the OMM and OV slightly decreased, but t-test showed that they were not significantly different (p > .05). This trend was also observed in the u’10v’10 chromaticity diagram.
Table 2. Color Matching results between 2° and 4° of FOV
Figure 4 displays the white color matching results of Session 3 (RGB LCD1 and RGB LCD2), and Fig. 5 shows the results of Session 4 (RGB LCD1 and RGB OLED). The arrow direction represents the individual color matching result from the reference color coordinates. The red arrow indicates the result at 2°, and the blue arrow indicates the result at 4°. The results show that there was no significant difference between the 2° and 4° FOV of the color matching results.
2.7.3 Relationship between the observer metamerism magnitude and observer variability
Table 3 summarizes the color matching results in terms of the OMM and OV. The maximum average OMM was 18.52 ΔE00, which indicates the white color difference between the RGB LCD2 and laser projector. Our experimental data also confirms the significant color mismatches in wide-gamut displays having the narrowband spectrums as found in the previous studies.
Table 3. Color matching results based on the OMM and OV
Figure 6 presents the relationship between OMM and OV using the white color matching experimental data. The x-axis represents the experimental session.
Note, for OMM, the laser projector demonstrates the largest color difference, followed by the WRGB OLED and QLED when color matching was performed with the RGB LCDs. Compared to the OMM, there was a relatively smaller difference between the display pairs for OV. The average OV was 2.27 ± 1.81 ΔE00 for the entire experiment. For instance, when Exp8 (RGB LCD2 and laser projector) and Exp3 (RGB LCD1 and RGB LCD2) are compared for the white test color, the OMMs are 18.52 and 3.16 ΔE00, respectively, while the OVs are 4.39 and 3.22 ΔE00, respectively, showing relatively similar results.
This result indicates that the OV is not significantly affected by the type of display, while there can be a significant color mismatch between the LCD and new types of displays, such as a laser projector when the colorimetric matching was performed using the CIE XYZ values. Additionally, when comparing the results of color matching of only white to those of matching various colors including white, color mismatch is demonstrated to be more significant for the white color.
The color matching data were further analyzed using the u’10v’10 chromaticity diagram. Figure 7 shows the white color matching result of Session 8 (RGB LCD2 and Laser projector) in the u’10v’10 color space. The blue arrow direction represents the reference color (CIE standard observer) to the individual matching result (each observer) indicating OMM. On the other hand, red arrow connects the average matching data point with the individual matching data indicating the variability within the observers in this study (OV).
The results show that although deviations of individual matchings exist, the chromaticities of all the matched colors on the laser projector are generally located in the + u’10-v’10 direction from that of the reference color on RGB LCD2. This indicates that when the RGB LCD2 and laser projector were set to have the same u’10v’10 coordinates, all the observers perceived the laser projector to appear greener than the LCD display, although there were slight differences in the color perception.
3. New LMS cone fundamentals derivation
A total of 829 metameric pairs were collected through the color matching experiment, and the color matching data using RGB channels are used for new LMS cone fundamentals derivation excluding WRGB OLED (Session 7) matching data. Using these 757 color matching data, the LMS cone fundamentals were derived by optimizing the parameters based on an individual colorimetric observer model by Asano [16,19,20]. The Asano model is based on the CIE 2006 cone fundamentals. This model proposes cone fundamentals while considering individual variability. To propose the cone fundamentals, the following 10 parameters were optimized: age (a), field size (v), deviation from the average lens density (dlens), deviation from the average macula density (dmacula), deviation from the average LMS cone density (dL, dM, dS), and deviation from the average LMS cone shift (sL, sM, sS). Among the 10 parameters, age and field size were obtained from the CIE 2006 model, and the remaining eight physiological parameters were obtained from the Asano model.
3.1 LMS cone fundamentals parameter optimization process
The overall process of the LMS cone fundamentals parameter optimization is as follows.
First, the tristimulus LMS value of the reference stimulus was calculated by multiplying the reference stimulus spectral data of the (n × 1) matrix and the test cone fundamentals (test CMF) of the (n × 3) matrix. In this case, n is 79, which is 390 nm to 780 nm with a 5 nm step. The initial parameters for the test CMF were 38 for age, 2° for field size, and 0 for the remaining.
Second, the predicted spectrum, which has the same LMS tristimulus values on the test display as the reference display, was calculated using Eq. (1). The input values were reference LMS tristimulus values of the (3 × 1) matrix obtained from the first step, the test display maximum RGB primary spectrum of the (n × 3) matrix, and the test CMF of the (n × 3) matrix.
Fourth, using the tristimulus values, the u’10v’10 values of the matched and predicted colors were calculated; the color difference between them was calculated using Δu’10v’10. The 10 parameters were optimized using an unconstrained nonlinear minimization method, such that the average Δu’10v’10 was minimized. During the parameter optimization process, the age was limited to 20-80 years, the field size was limited to 1°-10°, and the remaining parameters were optimized without any restrictions.
To derive the new cone fundamentals, 757 metameric pairs were grouped into 26 training datasets such as using the data from each experimental session only, each observer’s data and using all the data etc. For instance, when obtaining the cone fundamentals of each experimental session, 10 parameters were optimized using all the observer data of each experimental session as the input values.
3.2 New cone fundamentals performance test results
The performance test was conducted to determine the sufficiency of the new cone fundamentals in explaining our datasets. It was analyzed using the color difference, ΔE00, between the matched colors from the actual color matching data and the predicted colors using optimized cone fundamentals in each experimental session. The performance of the CIE 1931 2°, CIE 1964 10°, CIE 2006 2° color matching functions, 3-by-3 matrix correction method, and 10 categorical observers by Asano [16] as well as the 26 new LMS cone fundamentals were tested. The 3-by-3 matrix correction method means applying 3 × 3 matrix to X10Y10Z10 values of the test display color to correct the color mismatch [3,4]. In this study, the optimized 3 × 3 matrix was obtained by minimizing the Δu’10v’10 values between the references and predicted colors.
The results are summarized in Table 4 showing the average data without distinguishing white and other colors for Sessions 5-11. The new LMS cone fundamentals were numbered from 1 to 26 in order of good performance. Then, those 26 functions were grouped into 9 categories showing the similar performances.
Table 4. LMS cone fundamentals performance test
The best-performing method was the cone fundamentals function, CMF1, derived using all the experimental data. The performance of the CIE CMFs was good in the order of CIE 1964 10°, CIE 2006 2°, and CIE 1931 2°, on average. In the case of Asano’s categorical observer, Category2 observer showed the better performance than CIE CMFs. For the color matching experiments with broadband displays, the CIE CMF, Asano categorical observers, and new cone fundamentals presented a similar performance; however, for experimental sessions 8 and 10, which included the narrowband display, new cone fundamentals outperform the others.
It is notable that the performance of 3 × 3 matrix correction method is fairly good indicating that applying 3 × 3 matrix to current CIE XYZ values can be an easy and practical solution to reduce the display color mismatch. However, applying the same 3 × 3 matrix to all types of display will cause the errors when applied to the display that CIE colorimetry should work such as Session 1. The average observer function that works well both for broadband and narrowband spectrums are needed to solve the display color mismatching problem.
4. New LMS cone fundamentals verification
A new cone fundamentals evaluation experiment was conducted to determine whether the new cone fundamentals work sufficiently with color chart images.
4.1 Apparatus and setup
The experimental setting was the same as that displayed in Fig. 1(b) of the color matching experiment. The image size was set based on a smaller display. A larger display presents as black on the remaining part and an additional black paper is used to prevent light observed from the oversized area.
4.2 Test displays and test stimuli
Two test displays were used, an RGB LCD2 and a laser projector. The test stimuli were represented by a color chart, as displayed in Fig. 8. The color chart consisted of 15 colors, including two white, one black, six low chromatic, and six high chromatic colors. All the colors were located within the color gamut of the reference and test displays. Figure 9 demonstrates the actual experimental scene.
4.3 Test color matching function
From Table 4 in the previous section, 10 test color matching functions were selected, including CIE 1931 2°, and CIE 2006 2° color matching functions. A representative function from each category was chosen as the test color matching function to have various chromaticity coordinates when predicting colors using them.
Figure 10 presents the white color prediction results using ten test color matching functions in RGB LCD2 and a laser projector. Each circle indicates the chromaticity of the color predicted by each color matching function. Note that CMF7 is from Category1 showing the good performance on average and CMF8 is from Category2 showing the good performance for Session 8 (RGB LCD2-Laser projector) experiment.
In the experiment, a laser projector was used as the reference display, and RGB LCD2 was used as the test display. The stimuli for the experiment were designed to have the same LMS tristimulus values on the two test displays according to each color matching function. In this case, the color difference between the actual measured color and the target color of the RGB LCD2 stimulus was set to less than 1 ΔE00.
4.4 Observers
Fourteen observers (ten females and four males) with an average age of 27 years participated in this experiment. Seven of them also participated in the color matching experiment. All observers had normal color vision, as tested using the Ishihara color vision test.
4.5 Experimental procedures
Before the experiment, all test displays were warmed up for at least 30 min. The experiment was conducted in a dark room. The observers were seated in the center of the two displays and were guided to focus the center of the two displays. The experiment was conducted using two-interval forced-choice method. The stimulus was set to appear on the entire screen, and arrow keys were used to alternately present two stimuli. The observers selected one of the two stimuli that looked more similar to the stimulus on the reference display. They were instructed to not just look at one color, but look at a whole color during their selection. The observers started the experiment after clearly setting their own selection criteria through the training session and were able to see two stimuli as many times as they wanted in each trial. Following the selection, the next stimuli were presented in a random order when the enter key was pressed. For each trial, 45 pairs were evaluated, three repetitions were performed, and the experiment lasted for approximately 40 min.
4.6 Data analysis method
Assuming Thurstone's Case V model [21], the z-score of the test color matching functions was calculated from the pair-comparison data. In the calculation process, proportion 0 was converted to 0.01, and proportion 1 was converted to 0.99. A higher z-score indicates a color matching function that the observer chooses is similar to a reference stimulus, whereas a lower z-score indicates a color matching function that looks different from the reference stimulus.
4.7 Results
Figure 11 demonstrates the results of the pair-comparison with 10 test color matching functions. The x-axis represents the test color matching functions, and the y-axis represents the z-score. When seven observers who participated in the previous color matching experiment were marked as experienced and the remaining seven observers were marked as naïve, t-test result showed that the difference between the two groups was insignificant (p > .05). The results indicate that CMF10 shows the best performance followed by CMF7 and CMF8.
The pair-comparison data were further analyzed using the u’10v’10 chromaticity diagram, as illustrated in Fig. 10. The arrow direction represents the individual color matching result from the reference color coordinates. As indicated in the color matching experiment, the chromaticities of all the matched colors on the laser projector were generally located in the + u’10-v’10 direction from that of the reference color on RGB LCD2. It is notable that the color prediction results by the best performance CMFs, CMF10, 7 and 8 are also located in the same direction as the individual matching results. However, CMF8 showing the best performance for the color matching data for white color was not the best CMF for the chart image experiment.
5. Proposed LMS function
The results of our two experiments demonstrated that the optimal LMS function, CMF7, obtained from the color matching experiment performed well, even in images containing various colors. In other words, two different experiments, which are color matching experiment and new cone fundamentals verification experiment, presented similar results with a high performance in the same LMS cone fundamentals. The optimal LMS function obtained in this study is depicted in Fig. 12 and tabulated in Table 5 to be used for evaluation in the future studies.
6. Conclusion
A color matching experiment was designed to collect 829 metameric pairs using seven displays with different spectral characteristics, including displays with a narrowband spectrum. The results demonstrated that the color matching accuracy was reliable, and there was no significant difference between the 2° and 4° FOV. The OMM was the highest for the laser projector, a display having the narrowest spectrum among all the test displays. A significant OV that cannot be ignored always appeared, which was 2.27ΔE00 on average. The color matching results indicate that the CIE standard observer fails to explain the color matching results, requiring more accurate color matching functions.
Based on the 757 color matching data and the individual colorimetric observer model by Asano, the parameters of cone fundamentals were optimized and new cone fundamentals were derived. The performance differed depending on the training datasets used. For color matching with broadband displays, both CIE CMFs and new cone fundamentals demonstrated a good performance. However, when narrowband displays such as laser projector were used, the performance was more than three times better in the new cone fundamentals.
As a result of the new cone fundamentals verification experiment using a color chart stimulus, the response of the observers indicated that the new cone fundamentals are similar to the reference stimulus compared to the existing CIE 1931 2° and CIE 2006 2° color matching functions. The cone fundamentals with high z-scores predict the color in the direction of the actual individual matching results. Additionally, although individual differences existed for each observer, it was possible that an observer was satisfied to a certain extent despite using the same color matching function without using different color matching functions for each observer. Therefore, the experimental results indicated that the optimal LMS demonstrated a good performance, even in images with various colors, and it is likely to explain the observations of several individuals using one common color matching function – the real average observer.
In this study, the necessity and possibility for a “new average colorimetric observer function” was presented. The new LMS cone fundamentals could solve the display color mismatch problem caused by current CIE standard observers. Further intensive and global cooperative researches are required to obtain new standard average observer. The proposed LMS functions obtained in this study are based on limited number of Korean observers and the limited number of metameric color pairs obtained from display color matching experiment. More diverse observers’ data covering wide range of ages, gender and ethnic groups should be obtained using more diverse experimental methods and setting including the size effect, color patch vs. natural images etc. Also, more researches are needed for the colorimetric observer models.
Appendix: information of proposed LMS cone fundamentals
Table 5. Cone sensitivities of Proposed LMS cone fundamentals
Funding
Samsung Electronics Co. Ltd.; National Research Foundation of Korea (NRF-2021R1A2C1013610).
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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