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Abstract
A new method was developed to evaluate the perceived gamut of a display. A multispectral image of a white gypsum sphere was projected onto various highly chromatic lights, producing a series of images with distinct hue perceptions at the gamut boundary of displays. These images were subsequently used in a psychophysical experiment to examine the perceived color gamut. Afterwards, the visual results were further compared with the prediction results from various uniform color spaces (UCSs) and color appearance models (CAMs). The present results demonstrate that CAM16-UCS provides the most accurate prediction across the entire color gamut, whereas the cyan-to-blue region is more poorly predicted than the other hue regions for all CAMs and UCSs investigated.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Displays are widely used in our daily lives. For example, mobile displays act as a contact window between users and digital content. Although a variety of factors [1] should be considered when developing a display, the color gamut is without any doubt one of the most essential color rendering properties. The term, color gamut, is a frequently used word to describe the complete range of reproducible colors of a display, and a more general definition is given by CIE [2]: “a range of colors achievable on a given color reproduction medium (or present in an image on that medium) under a given set of viewing conditions – it is a volume in color space” . As stated in the definition, Color gamut is primarily influenced by three elements, i.e. the reproduction medium, the viewing condition, and the specific color space [3].The latter two components form a color appearance model [4]. As a result, a color gamut of a display, refers to the capability to reproduce a range of color stimuli under a given color appearance model.
People have the desire to develop a display with a larger color gamut over the years. In the 1950s, highly saturated primaries were recommended for the NTSC system to cover the gamut of real surface colors [5]. However, it is not strictly followed due to the difficulties in manufacturing phosphors with high saturation at that time. Later, more realistic primaries were chosen by the Rec. ITU-R BT.709 [6] for HDTV and sRGB [7], a de-facto standard for displays. However, primaries in these two proposals mainly consider the industrial technologies of cathode ray tube (CRT), resulting in an inherent constraint in the color gamut. With advancements in image technology, more non-CRT displays are becoming available, allowing for a broader color gamut. Liquid crystal display (LCD), organic light-emitting diode (OLED), Quantum Dot (QD) LCD display, and laser display are typical examples of these displays. They usually adopt monochromatic light sources as backlights [8], or non-monochromatic light sources with narrow-band color filters [9] to produce sharp emission spectra. More recently, there have been reports of displays with more than three primaries [10]. With these new technologies, restrictions on CRT display are no longer an issue, and a pretty wide gamut can now be produced. This has implications for the color reproduction capability of a display, as color gamut is one of the most important factors in dominating image quality. However, a single large gamut cannot guarantee increased image quality; without proper color rendering guidelines, color distortions such as oversaturation, hue shift, and lack of naturalness can occur when communicating colors between displays of different gamut sizes [11–13]. As a result, new standards or recommendations to provide rules on how to manage color rendering have been proposed, including DCI-P3 [14] for digital cinema reference projectors, Rec. 2020 [14] for ultra-high definition (UHD) TVs, and Rec. 2100 for high-dynamic-range (HDR) contents [15]. These new recommendations consider technical constraints when designing physical primaries, and set proper regularizations on color conversion between the device driving signals and the output tristimulus values, reducing color discrepancies between displays. Therefore, although a larger gamut is preferred, there still exists some constraints on the size and shape of the gamut for real display products.
It is widely assumed that more saturated primaries will result in a larger gamut. However, this remains a conundrum because there is no universally accepted technique for determining the size of the color gamut. Traditionally, gamut size is measured in a certain color space under a specific viewing condition. However, there is no consensus on which color space should be used. The two-dimensional (2D) chromaticity diagram is the easiest way to define the color gamut of a display. A trichromatic display is typically represented as a triangle formed by connecting the chromaticities of RGB primaries in the CIE1931 xy chromaticity diagram or in the CIE 1976 u'v’ chromaticity diagram. Any color within this triangle can be represented by a linear combination of the primaries under Grassmann's laws of additive color mixture [16]. The xy chromaticity diagram is often preferred due to its mathematical simplicity. However, its linear transformed version, the u'v’ chromaticity diagram, is designed to provide superior perceptual uniformity. As a result, it is preferable to compute the gamut size using the u'v’ chromaticity diagram rather than the xy chromaticity diagram. This is verified with MacAdam ellipses [17], which represent the just noticeable differences (JNDs) from the center to the ellipse boundary. This conclusion, however, is based solely on the chromaticity diagram, which ignores the luminance channel. Human perception, on the other hand, is three-dimensional and includes both chromaticity and luminance. As a result, it is questionable if this is still the case when luminance is taken into consideration. According to recent research [18], the gamut area in the xy diagram corresponds closer to the 3D gamut volume than the u'v’ diagram does.
Since a chromaticity diagram cannot accurately describe the color gamut, 3D color space is gaining popularity. Adding a lightness channel, such as xyY or u'v'Y [19], is a simple way to extend the 2D chromaticity diagram into 3D color space. Researchers found that the gamut area in the chromaticity diagram is proportional to the gamut volume only when the luminance is at a very low level [20,18]. However, this condition is hard to achieve because there is always dark current in real displays, therefore the luminance of the black level is always not zero.
Although a chromaticity diagram with a luminance channel can represent the color gamut to some extent, it is not perceptually uniform and is far from ideal. In this case, more complex UCSs are proposed, which can provide a more reasonable prediction of gamut size. The CIELAB, which was established by CIE in 1976 to quantify color differences of surface colors, is perhaps the most well-known UCS [21]. It has been widely adopted in practically all fields related to colors. The CIELUV is another CIE-recommended UCS established in the same time. Although they have outdated [22], both of them are still CIE recommendations. With a specific UCS, gamut volume can be determined and be regarded as an indicator to demonstrate the capability of a display to reproduce colors. However, the nominal JNDs in different color spaces range substantially, making it hard to determine how many discernible colors [23] can be reproduced in a given UCS. As a result, to estimate the number of discernible colors, gamut volume is sometimes divided by the threshold cell, whose side equals the JND [24]. Further, researchers argue that CIELAB does not correspond well to perceptual color differences, particularly for small color differences [25]. As a result, non-Euclidean color difference formulas, such as $\varDelta {E_{CMC}}$ [26], $\varDelta {E_{94}}$ [27], and $\varDelta {E_{00}}$ [28] are proposed. Despite the fact that these adjustments do not represent a true UCS, they can still be utilized to estimate the perceptible color differences when tied to the CIELAB. However, such estimation needs various assumptions that have not been thoroughly validated, therefore most studies continue to utilize the gamut volume to demonstrate the color rendering capability of a display.
Although a uniform color space such as CIELAB is useful for quantifying perceptual color differences, it does not account for viewing conditions. Color perception, on the other hand, is generally recognized to be greatly dependent on viewing conditions. As a result, CAMs are sometimes preferred to better reflect human perceptions. Color scientists use CAM to quantify the color attributes of a stimulus under a given viewing condition. Many color attributes exist, including relative color attributes like lightness, chroma, and hue, as well as absolute color attributes like brightness and colorfulness. Other attributes, such as vividness, depth, and clarity [29], have recently been reported to provide a better description of human perceptions and have been demonstrated to be effective [30,31]. The most well-known color appearance model should be CIECAM02 [4], and it has just been replaced by CIECAM16 [32] as the new CIE-recommended CAM. Both of them have the associated UCS, i.e., CAM02-UCS [4] and CAM16-UCS. The performance of these two models is quite similar, as CIECAM16 is only intended to solve unexpected computational failures that may occur in real-world applications.
It should be noted that all of the UCSs and CAMs discussed above were developed under standard dynamic range (SDR) conditions. None of them have taken the high dynamic range (HDR) content into consideration in the model design. To solve this problem, a variety of new UCSs and CAMs have been proposed to improve predictions for HDR and wide color gamut (WCG) content, including ICTCP by Dolby Vision [33], and Jzazbz by Safdar et al. [34], along with its color appearance model, ZCAM [35]. A key component, the Perceptual Quantizer (PQ) curve [36], is embedded in these models, allowing a large luminance range of 0.001 to 10, 000 cd/m2. And they are reported to give better predictions on HDR and WCG content than the SDR models in some way [37,38].
Figure 1 illustrates the DCI-P3 gamut in various UCSs. The gamut in the xy chromaticity diagram exhibit somewhat smaller than in the u'v’ chromaticity diagram, particularly in the green region. This is reasonable because gamut in the green region is thought to be overestimated in the xy diagram and is partially resolved in the u'v’ diagram. The xyY color space extends the original diagram by adding a luminance channel to form a 3D color space. Although each point in the xyY space is consisting of both chromaticity and luminance, it does not take the viewing condition into account and thus cannot represent human color perceptions. As a result, the gamut shape in the xyY color space differs significantly from that of a UCS. Moreover, there is still a difference in gamut shape between different UCSs. This is due in part to the fact that each UCS has its own unit, resulting in varying gamut sizes, and in part to the fact that they are not perfectly uniform, resulting in distortions in some parts of their space. It is clear that, the gamut in CEICAM16 is closer to that in the Jzazbz than that in the CIELAB, suggesting the former two UCSs perform similarly. It's worth noting that the aspect ratios in each diagram are all set to be the same.
Fig. 1. DCI-p3 gamut in a) the CIE1931 xy chromaticity diagram, b) the CIE 1976 u'v’ chromaticity diagram, c) the xyY color space, d) CIELAB UCS, e) CIECAM16, and f) Jzazbz UCS. The aspect ratio is set to be equal in each plot.
Although the difference in UCSs is clearly shown in Fig. 1, such a comparison is illustrative but not comprehensive. Masaoka [39] recently proposed an alternative method for converting a 3D gamut plot to a 2D one, allowing for the analysis of the gamut shape of all hue directions at once. This new technique is known as gamut ring, and it uses rings of gamut areas to represent gamut volume. The gamut ring is made up of multiple rings, each of which is dedicated to a specific lightness value. The ring's area represents the gamut volume from zero to a specified lightness, and the arc's area from center to border represents the gamut volume in that given direction (hue slice). The gamut ring of DCI-P3 in CIELAB is given in Fig. 2.
Fig. 2. The gamut ring of CDI-P3 in CIELAB color space. There are 10 rings in total, from lightness 10 to 100 with an interval of 10. Each of them represents the gamut volume from zero lightness to that specified lightness value.
Although color gamut can be well described in those uniform color spaces, it remains unclear which space best agrees with human perceptions. The majority of previous studies evaluated UCSs based on color difference merits. There is no doubt that color difference is a good indicator to demonstrate the uniformity of a UCS. However, it cannot directly reflect the gamut size of a space since none of those UCSs are perfectly uniform. Therefore, a method that can effectively measure the gamut size is highly preferred. In this study, a novel technique was developed to evaluate the gamut size of displays as well as the prediction performance of UCSs. It was divided into three stages. Initially, the image of a white gypsum sphere under D65 was captured and its corresponding reflectance image was estimated using a Pseudo-Inverse method [40]. This reflectance image was furthered rendered to generate the XYZ images under various LED lighting conditions, each of which was highly saturated and exhibited a specific tint. These lighting conditions were meticulously determined so that the reproduced white was precisely on the gamut boundary of each test display. Finally, all of the XYZ images representing the display gamut were reproduced on a master display, and a psychophysical experiment was performed to compare the perceived color gamut of these images. The present results demonstrate that CAM16-UCS provides the most accurate prediction across the entire color gamut, whereas the cyan-to-blue region is difficult to predict when compared to other hue directions for all CAMs and UCSs investigated. To sum up, the main contributions of this paper can be divided into two aspects,
- 1) to present a novel method to visualize the entire gamut of each hue direction.
- 2) to easily compare different gamut boundaries between those calculated results from different color spaces, leading to the conclusion that CAM16-UCS most closely matches human perceptions.
2. Preparation
2.1 Images
To fully describe the gamut size, images containing highly saturated colors should be obtained. The appearance of those colors on a display can well demonstrate the perceptual color gamut of human eyes. In this study, these images were generated using a gypsum sphere with a white surface under various highly chromatic LED illuminants. This is to say that those images will exhibit saturated and have colors near the gamut boundary. The setup is illustrated in Fig. 3. The gypsum sphere is shown fixed in the center of a lighting cabinet. An 18-channel LED lighting system is embedded in the ceiling, 12 of which are highly chromatic. Their spectral power distributions (SPDs) are depicted in Fig. 4 and their chromaticity are shown in Fig. 5(a). As demonstrated, they all have narrow full width at half maximum (FWHM), resulting in saturated chromaticities near the spectrum locus. Those LED lights are the most chromatic lights available in actual use, and more saturated lights, such as lasers, are not considered as real light sources since no one will use them in real daily life. As a result, images captured under those LED lights can serve as good representatives for demonstrating the true perceptual gamut boundary of images on displays.
Fig. 5. (a) Color distributions of the LED lights marked using diamonds. (b) The reproducible colors of the LED lighting system are enclosed by the extreme colors connected by the black dashed line. The display gamut is defined by the solid purple line. The center is set at D65 marked with a star. The gray dashed line represents the 12 chosen hue directions. They cross the display gamut, resulting in 12 extreme colors that are reproducible by both the display and the LED lighting system.
However, a direct image capture is not feasible in most of the cases. On the one hand, the images captured under those highly chromatic lights are typically outside of the camera's gamut, resulting in a cut off in the RGB space. On the other hand, even if all of the colors in a scene are within the gamut of a camera, the functions embedded in the Image Signal Processing (ISP) may introduce color distortion, either for inaccuracy in color formation or for the purpose of more preferred color reproduction. As a result, it is challenging to precisely control the chromaticity of the captured images. To avoid this problem, the simulation method was adopted in this study instead of real capture. The workflow is given in Fig. 6. Initially, an RGB image of the sphere was captured under illuminant D65, along with the X-Rite ColorChecker Classic Chart (MCCC). The latter was used to train a reflectance estimation algorithm, i.e., the conventional Pseudo-Inverse method [40], to estimate reflectance information from RGB values. Subsequently, the RGB image was converted into a hyper-spectral reflectance image using this newly trained Pseudo-Inverse model. Finally, any images under a specific illuminant can be simulated by integrating the spectral power distribution (SPD) with the hyper-spectral image and the CIE 1964 standard colorimetric observer. The model accuracy of the Pseudo-Inverse method was tested using the X-Rite ColorChecker Digital SG color checker and the average color difference was 1.56 ΔE00 units. It should be noted that the accuracy of reflectance estimation is not a significant issue in this study. What matters is the chromaticity coordinates reproduced by the reflectance image, which can be precisely controlled by selecting for a particular illuminant. The readers interested in reflectance estimation are recommended to refer to more recent proposed methods [41].
Once the reflectance image has been determined, the corresponding RGB images with specified chromaticity coordinates can be generated. This was accomplished by applying a proper SPD to the reflectance image. The reproducible colors are within the convex hull enclosed by the extreme points of the LED lights in the chromaticity diagram. This is illustrated in Fig. 5(b). Note that the chromaticity coordinates of the LEDs have been shifted a bit compared with Fig. 5(a) due to the introduction of surface white of the sphere. 12 different hues ranging from 0°to 360°with an interval of 30 °were tested in this study. They corresponded to 12 extreme colors and were determined by the intersections of the line from the center (D65) to the hue direction and the gamut boundary of the display. As a result, all the intersections are the most chromatic colors reproducible by both the display and the LED lighting system.
There are numerous recipes available to simulate those intersection colors. One simple method is to use its three nearest vertices. As shown in Fig. 5(b), point P can be surrounded by a triangle formed by LEDs 6, 7, and the center. As a result, point P can be thought of as a linear combination of them, and their coefficients can be easily calculated using basic matrix multiplication. According to Grassmann's laws of additive color mixture, these coefficients can also be applied to their SPDs to form the illuminant SPD. Another important factor to consider is the magnitude of the SPD, or say its luminance. It should be set below a certain level to avoid being out of display gamut. To determine the luminance level, XYZ values with the same chromaticity but different luminance levels were generated first. They were then processed using the reverse display characterization model to calculate their corresponding RGB values. In this step, colors out of gamut will be mapped onto the gamut boundary, which means their RGB values will be cropped to 0 or 255 for some channels. Afterwards, the forward display characterization model was applied to these RGB values in order to calculate the predictive XYZ values. Finally, the color difference between the original and predictive XYZ values was computed. In this study, colors with a color difference of less than one ΔE00 unit were considered to be reproducible.
Following all the steps described above, images with specific color chromaticity coordinates were finally generated and are illustrated in Fig. 7. Each image exhibits a continuous and smooth color shading. Comparing all images, the blue image appears to be the darkest. This is consistent with Fig. 1(c), in which the blue to purple region has low luminance levels. A window of colors was extracted to examine if these images had been generated correctly, as depicted in the top-left of Fig. 7. Those colors were firstly averaged in row, and then ten points were sampled from the top (brightest) to bottom (darkest), with the black level subtracted. Their chromaticity coordinates are plotted in Fig. 8(a) and L*Cab* in CIELAB color space in Fig. 8(b). It can be seen that all of those colors are within the expected colour shifts, which verified the effectiveness of the proposed method. It was found that some points were outside the display gamut. This is due in part to the removal of the black level and in part to the fact that those colors were taken from the XYZ image rather than the RGB image. They will be mapped into the display gamut when processed with a reverse display model.
Fig. 7. All the generated images under saturated LED lights. Their hue directions are defined in the $u'v'$ diagram from 0°to 360° with an interval of 30°. A consistent lightness transition can be observed in the sphere from top to bottom.
Fig. 8. Ten points from bright to dark are extracted from the generated images with black removed. (Left) the color chromaticity coordinates are marked using colored dots. (Right) the color distribution in the CIELAB Lightness-Chroma diagram.
The benefits of including the sphere images instead of simple color patches can be divided into three aspects,
- 1) It offers a more natural appearance to the observers than merely using color patches or color ramps, like to view a colored ball illuminated by a white light, i.e., the surface of the sphere covering colors of gamut boundary with a smooth transition.
- 2) It provides a whole gamut of each hue within a single image. Color patches can only represent a single color at a time and particular images cannot convey the entire gamut of each hue within a single image. With this novel setup, observers can see the whole gamut boundary of each hue at once and make accurate judgments on the perceived gamut.
- 3) It provides a more realistic environment than just viewing color patches. Image content is never simply color patches in the real world. As a result, the use of sphere images can better represent the real viewing condition, like viewing a real colored ball, and thus provide more accurate and stable results.
2.2 Displays
In section 2.1, images were generated using colors on the display gamut boundary. This implies that the display should be predetermined. In this study, a NEC PA311D display was adopted. The white point of the NEC display was set at D65 and its highest luminance can reach 345 cd/m2. The GOG model [42] was applied to perform display characterization and the model accuracy was found to be 0.7 CIEDE2000 color difference units when tested using the MCCC colors. The color ramps of each channel from dark to bright, with a 15-unit interval for each channel, served as the training samples. The MCCC colors were chosen as the testing samples. Their trichromatic values were predicted using the newly derived GOG model and then compared with the real measured values. Note all colors on the display were measured by a JETI Spectrobo 1211 tele-spectroradiometer.
It is acknowledged that a full colorimetric display model consists of both colorimetric values of the primaries and an Electro-Optical Transfer Function (EOTF), known as the gamma function. This means that any displays can be simulated by altering the primaries or the EOTF function, as long as the simulated display is within the gamut of the original display. In this study, the EOTF as defined in the sRGB standard was adopted and the primaries were modified to generate five imagery displays. As shown in Fig. 9, the largest gamut, which covers the majority of the DCI-P3 gamut, can be provided by Display 5 (full gamut of the NEC display). The smallest gamut was found on Display 1. Its red and green primaries are set the same as sRGB while its blue primary shifts a bit towards the positive direction of x-axis. Other displays (Displays 2 to 4) were linearly interpolated between Display 1 and Display 5. For each display, three luminance levels, i.e., 100, 200 and 300 cd/m2 were included. Consequently, there are 15 virtual displays (5 gamut areas ${\times} $ 3 luminance levels) investigated in total.
Note that only one display was chosen and those real-measured display primaries were not used. The reasons are two-fold. Firstly, different displays have different primaries, due to various peak wavelengths. When viewing those intensely saturated colors, observers may experience significant observer metamerism [43] and the extent varies for different display peaks. Secondly, it is challenging to locate a master display with a wide gamut that encompasses all the primaries of other displays. As a result, only one real display was used, and other imagery displays were simulated by restricting primaries in the display characterization model.
3. Psychophysical experiment
A psychophysical experiment was conducted to investigate the color gamuts of the displays described in Section 2. The whole experiment was conducted on a master display, namely the NEC PA311D, in a darkened room. The interface background was set to middle gray (L*a*b* = [48, 0, 0] under the display white) to ensure a consistent white adaption. The experimental interface was given in Fig. 10.
Twenty observers (11 males and 5 females) participated in this experiment. They were all students, ranging in age from 20 to 30 years, with an average of 24 years and a standard deviation of 2.7 years. They all had experience of participating psychophysical in experiments and had knowledge in color science. As a result, they understand the basic terms to describe display properties. Moreover, all those participants were asked if they understood the meaning of display gamut, and none of them was confused about what he/she was doing. All observers passed the Ishihara Color Vision Test. As shown in Fig. 10, two reproductions corresponding to two distinct displays were simulated using the master display. Observers were asked to view the images following a random sequence and judged which image appeared to have larger color gamut. Once a session is finished, another pair of images will show. In total, 23400 judgments were made, i.e., $C_{15}^2$ image pairs (display pairs) ${\times} $ 13 images (one repeated) ${\times} $ 16 observers.
4. Result and data analysis
4.1 Inter- and intra-observer variability
Initially, the experimental results were analyzed to ascertain observer variability. The Wrong Decision (WD) metric [44] represents intra- and inter-observer variability. They indicate the concordance of each observer's results with his or her own and, respectively, with the mean scores. For intra-observer variation, we define WD as a repeated evaluation that differs from the initial decision and calculate it by dividing the total number of incorrect decisions by the total number of decisions multiplied by 100. For inter-observer variation, WD is defined as the probability of making an incorrect decision, i.e., the number of minority responses divided by the total number of responses multiplied by 100. The intra-observer and inter-observer variations are presented in Table 1.
Table 1. The WDs representing the intra-observer and inter-observer variability
The mean intra-observer and inter-observer variations are both 28. This value was comparable with [31] using a similar experimental setup but slightly higher than [30], which has a reference image in the middle of the experimental interface. In this experiment, observers were asked to judge which image had a larger perceived gamut. And we had two different modifications to the test images, i.e., to increase the luminance level or to enlarge the gamut area. As a result, observers had to determine which factor has a larger impact on the perceived gamut. Larger variations mean larger discrepancies on their influences. In this sense, this higher variability can be considered reasonable since individual preference on the luminance direction or the chroma direction varies. However, it is a reasonable agreement amongst all observers.
4.2 Result of the psychophysical experiment
Results accumulated from the psychophysical experiment were converted into an interval scale following the Law of Comparative Judgement [45]. They were reported in terms of z-scores (unit normal deviates) by referring to the area under the normal distribution curve. A higher z-score value means a larger perceived color gamut. A 95% confidence interval on the scale values was also obtained. It was calculated in terms of the scale unit. One unit on the interval scale equals $\sqrt 2 \delta $. Hence, the standard deviation $\delta $, was fixed at a value of $\frac{1}{{\sqrt 2 }}$, and the 95% confidence interval (CI) was then calculated as
Figure 11 illustrates the overall results in terms of perceived color gamut (combining all the 12 tested hues) on the tested displays. As expected, the perceived gamut increases with the increase of luminance levels and gamut area. In addition, it is observed that, G5 does not have a clear superiority over G4. This seems to suggest that people do not have high sensitivity to judge saturated colors. This implies that using u’v’ diagram to design displays could result in nonuniformity in the highly chromatic region.
Fig. 11. The overall experimental results. G means gamut. The display gamut area increases from G1 (smallest, similar to sRGB) to G5 (largest).
The combined psychophysical results were then compared with the gamut volume predictions from different UCSs and CAMs. Table 2 shows the results in terms of the Pearson product-moment correlation coefficient (r) [46]. As is shown, all of the models performed well for predicting the perceived color gamut of displays. CAM16-UCS, ZCAM-JCh, and ZCAM-QMh had the best performance. To find out if these models are significantly different, a statistical test was performed using the Hittner et al. ‘s z-test [47]. The results of the test are shown in Table 3. The larger the number between a pair of colour models indicate they are more significantly different. The underlined number means the hypothetical normality is rejected (p < 0.05). As can be seen, ZCAM-JCh and ZCAM-QMh gave the similar performance, and they exhibited a significant improvement compared with all the other models tested (except for CAM16-UCS). This situation is similar for CAM16-UCS, outperforming most of the other models. However, the performance of ICtCp was not so well as expected. This could be due to the experimental setup that the luminance range is within the standard dynamic range (SDR), whereas it was developed for HDR contents. ZCAM based UCSs for HDR applications also gave the similar performance as CAM16-UCS.
Table 2. Correlation Coefficients between visual results and gamut volume predictions from different models
Table 3. The results of the statistical test (Hittner ‘s z-test) to determine if there is a significant difference between models. Numbers that represent a significant difference (p < 0.05) are marked in bold and underlined
Using the gamut ring, we can obtain not only the total volume of each display's gamut, but also the volume of each hue on its own. The results are summarized in Table 4 and examples of the model performance are illustrated in Fig. 12. Notably, the hue directions in Table 4 were derived from CIE 1976 u'v’ chromaticity diagram as described in Fig. 5(b). When performing a comparison between various UCSs or CAMs, the hues were recalculated in that specific space using white as the origin, and the corresponding gamut volume in that hue direction was obtained following the method provided in gamut ring [39]. More illustrations are available in Dataset 1 (Ref. [48]).
Fig. 12. Examples of the model performance in the hues of 120° and 240°. They align with the correlation coefficients in Table 4. The dot, cross, and star symbols represent the data of displays having a peak luminance of 100, 200, and 300 cd/m2, respectively. Within each group, displays G1 to G5 are arranged following an ascending order.
Table 4. The correlation coefficients between the psychophysical results with the predictions of different UCSs or CAMs in each hue directiona
It is clear that all the UCSs or CAMs had a reasonably good correlation coefficient to predict the perceived color gamut of displays. CAM16-UCS had the best performance, indicating that it provides the most accurate prediction of color perception across the entire gamut. Interestingly, despite the fact that neither xyY nor u'v'Y can provide a good uniformity when compared to others, they are still both good indicators of the perceived gamut in each hue direction. And ICtCp did not perform so well as expected in this test, primarily as a result of its inaccurate prediction in the cyan to blue region.
When examining each hue direction, it can be seen that most of the UCSs or CAMs performed poorer in the 150° to 240° hue direction (cyan to blue in u'v’ diagram, see Fig. 5(b)) than the other hues. This is a typical problem especially for highly chromatic color [34]. And despite the fact that the overall performance of ICtCp is not as expected, it still delivers accurate predictions for the majority of hues. CAM16-UCS performed significantly better than most of the spaces, giving an overall first ranking in the most of hues. This implies that it is the most promising UCS for calculating the color gamut volume of a display.
5. Discussion
Although this study provides a unique approach to estimate the perceived gamut of a display, some issues should be discussed before drawing a final conclusion.
Firstly, the key feature of the proposed gamut estimation technique is the inclusion of a white sphere. The goal of this study is to develop a method that can perform a direct visual comparison of two displays in terms of their color gamuts. A 3D sphere was proposed to give a natural representation of the real object and to be easier for visual comparison than to view color patches or digital images. The gradual changes in surface coolers of a 3D sphere accurately simulate a real surface being illuminated by a tinted light. As a result, the color gamut volume can then be well represented as a colored sphere. Moreover, this new set-up can provide the whole gamut of different hues within a single image, offering a more realistic environment than the conventional color patches or images.
Secondly, the tested hue directions were chosen from the CIE 1976 u'v’ chromaticity diagram. Some readers may question whether or not these images have a consistent hue perception. It must be acknowledged that the optimal way to select these colors is along the consistent hue loci [37]. However, such a large dataset covering the entire color gamut investigated in this study does not exist. Moreover, each of the generated images has been thoroughly examined to ensure that there is no discernible hue shift among those colors via a visual judgment by 4 observers. This is confirmed by the fact that none of the observers who participated in this experiment complained about the hue shift.
Thirdly, in this novel approach, the gamut boundary colours located in the curve converge at zero black point for each hue (Fig. 8 (right)), approximating the sphere seen in real lighting conditions. Note that the colors present in the generated images form only the lower boundary of the hue slice. In other words, colors between the cusp (the most chromatic point in the hue slice) and the white were omitted from the image. This is in consistence with real lighting conditions and those colors (between the cusp and the white) do not represent the real objects illuminated by the saturated colored lights. And from the feedback of participants, the color perceptions were primarily influenced by the cusp, indicating that the absence of white does not make a significant difference.
Finally, the background of the interface was set to grey in this study. An alternative is to set to black. However, a black background would not be able to achieve neutral adaptation. In addition, a black background would make the bottom of the sphere to be grey, to appear unnatural. As a result, a gray background is preferred.
6. Conclusion
In this study, a novel method for evaluating the perceived gamut of a display is proposed, and it is then tested in a psychophysical experiment to determine the prediction performance of various CAMs and UCSs. The CAM16-UCS is capable of providing the most accurate predictions of perceived gamut across all hue directions. And it is discovered that the cyan-to-blue region is hard to predict compared with other hue directions for all the CAMs and UCSs investigated.
Funding
Scientific Research Fund of Zhejiang Provincial Education Department (Y202249304); Fundamental Research Funds for the Provincial Universities of Zhejiang (GK219909299001-019); National Natural Science Foundation of China (501100001809).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available in Dataset 1 Ref. [48].
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