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Abstract
It is a challenge to determine the RGB primaries when designing a display. A big issue is to estimate the colorimetric performance of the display. In this paper, a systematic method was proposed to determine the best RGB primaries for a display. Nine testing metrics were implemented and they were divided into two groups (the gamut metrics and the colour related metrics). They were adopted to evaluate the performance of 52 displays having different RGB primary combinations. The results verified the proposed method. Some of the testing metrics gave similar results and it should be sufficient to choose some of them to reveal the overall performance of a display.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
It is widely acknowledged that primaries are of vital importance for displays to render a pleasing and realistic appearance in terms of colour image quality [1]. Traditionally, sRGB [2] is the de facto standard in the imaging industry, which is also defined in ITU-R BT.709 [3]. This was suitable when the CRT display devices were prevalent and there were little choices for the display primaries. However, with the rapid development of imaging industry, various display technologies [4,5] are emerging, such as OLED, QD-LCD and laser displays, with a variety of primaries to select from, which often leads to a larger colour gamut. Therefore, image signals adopting the conventional sRGB primaries are no longer suitable for these new devices. In other words, the mismatch between their colour gamuts will lead to colour distortions including oversaturation, hue shift and lack of naturalness [6–8]. The typical approach to solve this problem is gamut mapping, and plenty of algorithms are available in the literature. The interested reader is recommended to refer to a well-written book by Morovic [9]. We also proposed gamut compression and gamut extension algorithms [10,11] to ensure a faithful or preferred colour reproduction among displays. However, such algorithms always need extra supports from an operation system and is not easy to accomplish. Hence, it has not been considered in the design of a display.
New standards or recommendations were proposed to provide guidelines to render display colours, including DCI-P3 [12] for the reference projector for digital cinema, Rec. 2020 [13] for ultra-high definition (UHD) TVs and Adobe RGB [14], as a de facto standard in the professional colour processing. Their primaries are specified. So, the primaries-related problems can be resolved to some extent by applying these new standards. However, display manufacturers do not use the exact same primaries defined in the standards or recommendations due to the consideration of its cost, durability, emission efficiency or other limitations. Hence, there is a need to develop standard methods to evaluate the display rendering performance, or say the colour image quality, when adopting a set of commercially designed primaries.
Colour image quality is the most important property for a display and is largely affected by the selection of display primaries. Many researchers endeavored to understand how to control it. Our earlier work by Tian et al. [15] developed a model to evaluate the image quality for an OLED TV. Eight image attributes were investigated, including “peak brightness”, “blackness”, “colourfulness”, “contrast”, “reality”, “sharpness”, “texture details” and “overall image quality”. It is concluded that the overall colour image quality is mainly affected by three major factors, i.e., 1) colour quality, which is defined as the quality of an image by comparing it with an imaginary image that have perfect colour quality; 2) black level, which is defined as the amount of light from the darkest region in the image; and 3) brightness, which is defined as the amount of light from the brightest region in the image. The colour quality was associated with “colourfulness” and “reality”, which can be interpreted as gamut volume [16,17] and colour accuracy. Meanwhile, a lower black level and a higher brightness also led to a larger gamut volume [18]. Hence, we can deduce that gamut volume and colour accuracy are the two main factors contributing to the colour image quality. Choi et al. conducted a large-scale psychophysical experiment on a large size display and established a model to correlate the image appearance attributes with the image quality [19]. They found that colourfulness, contrast, and naturalness were the key attributes. In accordance with Tian’s work, it can be concluded that colourfulness and contrast are closely associated with gamut volume and naturalness is highly associated with colour accuracy. From the above two studies, we can infer that gamut volume and colour accuracy have a large impact on image quality. This is in line with some other findings to improve the colour image quality using some treatments on images or displays, e.g., to add some colourfulness to the original image to extend the image gamut volume [20] or to preserve skin colours via a content-based analysis to increase colour accuracy [8]. Even for multi-channel displays, the luminance and the colour consistency of a display, which referred to gamut volume and colour accuracy respectively, were also regarded as the two main factors affecting the perceived colour image quality [21–23]. All the factors discussed above are influenced by the display primaries.
This paper is aimed to define a “good” set of primaries to give satisfactory colour perception. In this paper, a systematic evaluation of the colorimetry of a display was conducted. Firstly, a large database of RGB primaries were collected. They were all in practical use and offered by display manufacturers. Subsequently, they were combined to form different primary sets and each of them was regarded as a real RGB display. Afterwards, different metrics were implemented to evaluate these displays by assuming they were all well-behaved additive colour colorimetry systems [1,24–26]. Finally, analysis was conducted to evaluate the display performance using these metrics.
2. Methods
All the colour specification of primary sets was provided by the display manufacturer and the data were obtained by real measurements using a Konica Minolta CS2000 tele-spectral radiometer. There were 14, 23 and 6 primaries for red, green and blue channels respectively. Figure 1 shows their chromaticity coordinates together with triangles corresponding to standard primaries, i.e., NTSC [27], sRGB and DCI-P3. It can be seen that the red and blue primary groups were located around that of sRGB and the green group was close to that of DCI-P3. Note that, although 1932 (14 reds by 23 greens by 6 blues) sets of displays can be generated in total, only 52 sets of them were included in this study and others were abandoned due to their relatively low peak luminance. The goal of this study is to find a best set of primaries that could be used for real mobile phones. Hence, the peak luminance of a white should not be too low, or problems will occur in an outdoor condition. Although not all the combinations were investigated in this study, the evaluation procedure should be appliable to evaluate any primary set.
Fig. 1. The distributions of the primaries studied in CIE 1976 u'v’ chromaticity diagram together with the boundaries of sRGB, DCI-P3 and NTSC gamuts. a) all the primaries tested, b) red primaries, c) green primaries and d) blue primaries
Each primary set was regarded as an imagery display. The peak white for all displays was set at 480 cd/m2 and D75, having xy coordinates of [0.299, 0.315]. The white has a slightly higher correlated colour temperature (CCT) compared with that of sRGB and DCI-P3. However, this is the real situation for mobile displays in Asia and people tend to prefer a blueish white. The peak white was the same for all the displays, indicating a consistent white adaptation. However, the maximum luminance of each channel for each display was different. If the chromaticity coordinates of red, green, and blue primaries were defined as (${x_R},{y_R}$), (${x_G},{y_G}$) and (${x_B},{y_B}$), their corresponding XYZ values could then be obtained with their channel luminance according to basic colorimetry [28,29]. And the maximum luminance of each channel is determined from Eq. (1). In Eq. (1), [$\; {X_{white}},{Y_{white}},{Z_{white}}$] represents the peak white of the display. [$\; {X_C},{Y_C},{Z_C}$] represents the relative XYZ values of each channel. ${Y_R}$, ${Y_G}$ and ${Y_B}$ are fixed at unity. ${L_{C,max}}$ represents the maximum luminance of each channel. Hence, [$\; {Y_{R,max}},{Y_{G,max}},{Y_{B,max}}$] can be easily acquired using simple matrix operations.
A full colorimetric display model consists of both colorimetric values and an Electro-Optical Transfer Function (EOTF) [30], known as the gamma function. The EOTF was used to define the luminance factor of ${L_{C,{d_{c}}}}$ for a digital input ${d_C}$ for each channel. A maximum digital input of 255 for an 8-bit display, will lead to the maximum luminance factor of unity. In this study, the EOTF as defined in the sRGB standard was adopted and was given in Eq. (3). It should be noted that an EOTF that differs from the sRGB standard will also make a difference to the performance of a display [31–33]. Hence, a simple colorimetric display model was developed using Eq. (2).
3. Test metrics
There has never been a widely accepted standard to test displays. Inspired from the earlier works [1,24–27,34,35], nine testing metrics were designed. They were aimed to give an in-depth investigation of the display in terms of its colour rendering performance. In this section, a brief account will be given. These metrics can be divided into 2 groups, i.e., the gamut metrics and the colour related metrics. The former metrics are dealing with the colour rendering capability, i.e., how many “colours” that can be produced by a display and the latter metrics are emphasizing colour perceptions, like colour fidelity, colour accuracy or colour preference.
3.1 Gamut metrics
Four different gamut metrics were implemented, i.e., gamut area ratio, NTSC gamut coverage, gamut volume ratio and the coverage of real surface colours. Gamut area is a commonly adopted metric to show the colour rendering capability of a display. It is defined as the area of the RGB primary triangle in CIE 1976 u'v’ chromaticity diagram. For simplicity, gamut area was calculated by performing an operation of division between the display gamut area and sRGB gamut area. It is well known that the chromaticity of primary is independent from its luminance. Hence, the area in a chromaticity diagram does not manifest a volumetric difference caused by the change of luminance level [36].
NTSC was the analog television standard in Northern America and a few countries in Asia. While no longer used for its original purposes, it is still used by the market as a reference to describe the colour rendering capability of a display. In this study, the NTSC coverage was also included. Note that, the NTSC coverage was calculated as the overlapping area divided by the area of NTSC gamut. This was slightly different from the calculation of gamut area ratio.
Gamut volume is another commonly used metric to quantify the number of colours that can be produced by a display. In this study, it was calculated in CIELAB uniform colour space and reported using the ratio to that of sRGB gamut as well. CIELAB has been widely used in the imaging industry for its simplicity. Besides, it was also adopted in most of the relevant studies [1,35]. To be compatible with them, CIELAB was finally adopted in this study.
In addition to the traditional gamut area and gamut volume indicators, the real surface colours were also included to investigate a display’s colour rendering capability for realistic colours. Real surface colours mean surface colours of real objects. To the best of our knowledge, there are three available datasets, i.e., the Pointer’s gamut [37], the Standard object colour spectra (SOCS) database [38] and the Leeds dataset [39]. The Pointer’s gamut consists of 576 colours representing the maximum gamut of real surface colours provided under illuminant C. The SOCS database consists of 53,361 spectral reflectance/transmittance samples. It is also included in the Leeds data to form a largest real surface colour gamut. The Leeds data has a total number of 102,801 colours and all of them are expressed using reflectance functions specified from 360 to 780 nm at an interval of 10 nm. Since the Leeds dataset is the most comprehensive collection to date and comprises the other two datasets, it was finally adopted in this study. A comparison between the real surface colour gamut and sRGB gamut was illustrated in Fig. 2. It can be clearly seen that, a large amount of real surface colours is out of the sRGB gamut. This indicates that more colourful primaries are desired to cover all the real surface colours. Like NTSC coverage, the coverage of real surface colours was also calculated as the overlapping volume divided by that of the real surface colour gamut.
Fig. 2. Gamut comparison between sRGB (dashed) and real surface colours (solid) in the CIELAB colour space. The top-left is a projection on the a*b* plane and others are the hue slices at different hues.
It is expected that all the testing metrics were calculated using a single uniform colour space. However, in order to make a fair comparison with earlier studies, the calculations follow the conventional procedures as used in other studies [1,24–27,31,32].
3.2 Colour related metrics
In addition to the gamut metrics, the colour related metrics were also included to test different displays. They can be divided into three major subsets, i.e., colour compatibility, colour deviation and hue linearity. Colour compatibility was defined as the severity of colour shift for a stimulus when displaying from a standard display to a test one and is calculated as the colour difference between them. Colour deviation was particularly developed using memory colours [40]. They represent colours of familiar objects in our daily life and have a great influence on the performance of a display. Hue linearity was evaluated using colours having a unitary hue [41]. It served as a good indicator to show the degree of hue shift. In these tests, the reference standard display was set as an sRGB display. However, it can be replaced using other standard displays in compliance with the real needs.
3.2.1 Colour compatibility
Colour compatibility is calculated as the colour difference between a standard and a test display when displaying the same image signals. As discussed in Section 1, change of display primaries will introduce colour distortions, i.e., colours perceived from the new device are different from that of a standard display. Hence, colour shift can be adopted as an indicator to test the new display. Two test datasets were selected in this study. One was XRite ColorChecker Chart (MCCC) consisting of 24 colours and the other one was a RGB cube consisting of 18*18*18 colours, all of which were equally spaced in the RGB colour space. Colour difference was calculated to represent the colour compatibility between a sRGB display and each tested display. The MCCC was adopted to evaluate colours that were commonly used and the RGB cube was to test the overall compatibility between these two colorimetric systems. Since their white points were different, the CAT02 [42] was performed when calculating their perceived colour difference. In this test, a larger colour difference means a poor compatibility and preprocesses should be implemented before images displayed in a new display.
3.2.2 Colour deviation
In addition to the objective metrics, a psychophysical dataset, i.e., memory colours [40] was also introduced in this study. Memory colours can be understood as a phenomenon where, in our minds, a particular object has a particular colour associated to it [43]. That is to say, our mind is quite familiar with these colours and when rendering images containing those familiar objects, they should be as close to our memory as possible. All the test objects are illustrated in Fig. 3. As is shown, they can be divided into two categories: 1) vegetable and fruit colours, and 2) natural colours such as skin, sky blue and green grass. These samples were selected in consideration of familiarity, colour distribution, and importance in applications. All of them are familiar in our daily life and observers can easily recognize the change of colour. Colour difference in CIELAB unit was again used to represent the display performance for this type of test dataset.
3.2.3 Hue linearity
It is well known that human vision is sensitive to hue change. Hence, efforts were made to maintain the original hues in many colour manipulations. For all colours to have the same hue perception, they should lie in a straight line in a uniform colour space. So, it is necessary to investigate their hue shift when transferred from a standard display to a new one. In this study, two datasets were included, i.e., const hue loci [1] and unique hue data [41].
An easy and quick method to avoid hue shift is to put the new primaries on the constant hue loci [1] of the primaries of standards. A constant hue locus is a line having different chroma appearance but identical hue perception. Figure 4 illustrates the constant hue loci of each sRGB primary in CIE 1976 u'v’ chromaticity diagram. As is shown, all the primary set candidates were scattered around each locus. In this study, the distance from the constant hue loci to the new primary was adopted as a metric to represent the hue shift. A zero distance means a perfect agreement. This concept is like duv used in the lighting industry [44], which is defined as the distance from the Planckian locus. The result was represented by the sum of deviations for each of the RGB primaries to their corresponding constant hue loci.
Fig. 4. The constant hue loci for the sRGB standards, illustrated using white dashed lines in CIE 1976 u'v’ chromaticity diagram.
Unique hue data [41] are also quite important for image processing applications. As illustrated in Fig. 5, the dataset adopted is consisting of pure colours having a unitary hue, forming a straight line in a uniform colour space. This means all the colours lying in the same line will have a same hue perception. Four unitary colours, i.e., pure red, pure green, pure yellow and pure blue, were included. All the colours were derived from psychophysical experiments for hue matching and had different luminance values. Thus, it can be seen that not all of them aligned well as a straight line in CIE 1976 u'v’ chromaticity diagram, indicating this colour space was not uniform in hue.
Fig. 5. The unique hue data shown in the CIE 1976 u'v’ chromaticity diagram. Some colours are adjacent, indicating they have different luminance levels.
It also should be noticed that the constant hue loci data are different from the unique hue data since they have different perceived hues. The former dataset is tied to a standard display and changeable when using different standards. However, the latter dataset is universal to all displays and more sensitive to human perceptions.
It is of course preferred to adopt a unified unit for these two tests. However, calculations for the constant hue loci were performed in the CIE 1976 u'v’ chromaticity diagram in conformity with former studies [1,35]. For the unique hue data, calculations were performed in the CIELAB uniform colour space and only hue composition, i.e., $\Delta H$. from the CIELAB colour difference equation, was used. This is because only the hue shift was considered for this type of dataset and the inclusion of CIELAB colour space should offer a more accurate colour difference prediction than the CIE 1976 u'v’ chromaticity diagram.
4. Results and discussion
To obtain a best RGB primary set, the results from the above tests were ranked to clearly show the merit of the 52 displays tested. Afterwards, all the ranks corresponding to each test were summed up to represent the final result. A lower sum indicates a better rendering performance. The final result was illustrated in Fig. 6, where bars in red represent colour related metrics and bars in grey represent gamut metrics. A longer bar means a worse performance. Meanwhile, primaries of the best five displays were picked out and shown in Fig. 7 with their exact chromaticity coordinates summarized in Table 1. The best display was superior in the gamut metrics. The fifth-best display outperformed the others for the colour related metrics, and the results for the other three displays were balanced between the gamut metrics and the colour related metrics. It was also found that, although the gamut metrics and the colour related metrics are always trade-off, a display can perform well in one group while gives a not bad performance in the other group.
Fig. 6. The testing results of all the displays studied. The CC_MCCC means using the MCCC dataset to test colour compatibility, and the CC_Cube using 18*18*18 colours. The HS_RGB means using the deviations of RGB primaries from the const hue loci to test hue shift and the HS_UniqueHue using unique hue dataset. The CD_MemoryColour means using the memory colour dataset to test colour deviation. GA and GV mean gamut area and gamut volume, respectively.
Fig. 7. The chromaticity coordinates of the best five displays. It is clear that their red primaries were near that of sRGB and green primaries were near that of DCI-P3.
Table 1. The exact chromaticity coordinates of the best five displays.
Correlations for the gamut metrics were incorporated in Table 2 using the Spearman’s correlation coefficients. The Pearson’s correlation was not included here because the testing results were reported in different units and a rank correlation was more appropriate. A high correlation coefficient of 0.90 means a good agreement between gamut volume and gamut area metrics. The real surface colour coverage was moderately different from the above two tests. This was caused by the shape of display gamut to be different from that of the real surface colour gamut. This also implies that some colours within the display gamut are synthetic and cannot be found in the real world. It was not surprising to see that the NTSC coverage do not give a good agreement with gamut volume and gamut area. However, it related somewhat better with the real surface colour coverage, implying NTSC coverage can be taken as a rough estimation for the rendering capability of the real surface colours of a display to some extent.
Table 2. The Spearman’s correlation coefficients for gamut metrics.
Correlation coefficients for the colour related tests were also calculated and summarized in Table 3. The CC_Cube results and the CC_MCCC results matched well, indicating the MCCC dataset is a good representative of the overall RGB colour space. Further, the MCCC dataset was also found to give a best agreement with the memory colour datasets. This is expected because MCCC contains some natural familiar colours, like skin, sky, and grass.
Table 3. The Spearman’s correlation coefficients for colour-related tests.
The result showed that the unique hue data do not give the highest correlation with the HS_RGB results. This might be attributed to their different hue angles. The unique hue data is consisting of pure colours, i.e., pure red, pure green, pure yellow and pure blue. However, the primaries are not pure colours, e.g., the red primary may appear to contain either yellow or blue. Hence, even if all the primaries lied in the const hue loci, the unitary colours in a standard display will not guarantee a constant perceived hue when transformed to another display.
5. Conclusion
This paper investigated the colour rendering performance of displays in terms of colorimetry by considering their RGB primaries. A systematic method was proposed to find the best RGB primary combination. It consists of nine test metrics in two groups, i.e., the gamut metrics and the colour related metrics. Its performance has been verified using 52 sets of displays.
Comparing different colour related metrics, the result from the MCCC dataset was found to agree well with that from the RGB cube dataset. This implies that the former was a good representative of the overall RGB colour space. However, the result from the unique hue dataset did not give the highest correlation with that from the const hue loci dataset. This is due to their different hue angles.
Comparing different gamut metrics, a good agreement was found between the gamut volume and gamut area metrics. This indicates that both types can accurately evaluate the rendering capability of a display. In addition, although a reasonable agreement was found between the real surface colour gamut and other gamut metrics, it is still cannot be concluded that the real surface colour coverage can be fully represented by other gamut metrics. This is attributed to the different gamut shapes between the gamut of real surface colours and that of a display. Also, this indicates displays with more chromatic primaries are preferred to produce more colourful and brighter images.
Funding
National Natural Science Foundation of China (61775190); OPPO Guangdong Mobile Communications Co. Ltd.
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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