A method for optimising settings of colour primaries for wide colour gamut displays

Optik 154 (2018) 216–225

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Optik journal homepage: www.elsevier.de/ijleo

Original research article

A method for optimising settings of colour primaries for wide colour gamut displays Rui Gong a,∗ , Xiandou Zhang b , Xuan Li a , Xiaopeng Shao a a b

School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071, China School of Media and Design, Hangzhou Dianzi University, Hangzhou 310018, China

a r t i c l e

i n f o

Article history: Received 6 June 2017 Accepted 18 September 2017 Keywords: Colour reproduction Colour rendering Colour gamut Displays

a b s t r a c t Recently, wide colour gamut displays which adopt highly saturated primaries of red, green, blue have been rapidly applied. These displays can evoke more vivid and more pleasing effects for images. However, images shown on these newly developing wide gamut devices cannot achieve preferred quality under the control of conventional signal standards that are developed based on smaller colour gamut. To achieve the preferred display effects on wide gamut devices in digital image reproduction, a whole procedure to optimise gamut settings of colour primaries were proposed, in which particular algorithms were designed to render images from signal standard such as sRGB via simulating various gamut settings on the given display. Thus, the optimum specifications of colour primaries can be determined by calculations of the proposed preference index. Furthermore, a psychophysical experiment along with a detailed discussion were carried out as a verification, in which the consistence between the preference index calculation and the visual data could certify the effectiveness of the proposed procedure and algorithms. This study may help display researchers and manufactories by supporting some recommendations to determine the primaries of wide gamut devices in applications. © 2017 Elsevier GmbH. All rights reserved.

1. Introduction Wide colour gamut is an advantage to evoke more vivid and more pleasing images for different displays including desktop monitors, TVs (televisions), tablet computers, and smart phones [1]. Recently, various display technologies [2,3] have been raised to produce highly saturated primaries of red, green, blue. However, the conventional broadcasting standards such as PAL (phase alteration line) and NTSC (National Television Standards Committee) are based on smaller colour gamut, as well as the sRGB (it means standard red green blue colour space) system [4] widely used in the display industry. Consequently, when images are displayed on wide gamut devices according to these standard signals without additional processing, the mismatch of their gamut would cause unavoidable colour distortions by introducing oversaturated, unpleasant effects [5]. The reason is that, both naturalness and colourfulness are key factors to influence the perceptual quality in image colour reproduction, but they show contradictions in some situations [6,7]. The perceptual image quality will firstly be improved gradually with the increase of colourfulness and then be suffered from the over-colourful situation, which is due to poor effect of naturalness in that case [8,9]. Though wider gamut is acceptable or even preferable for representing outdoor scene images to show more colourful sky, flowers, grass, but it may fail for reproducing some familiar colours such as skin [10,11].

∗ Corresponding author. E-mail address: [email protected] (R. Gong). http://dx.doi.org/10.1016/j.ijleo.2017.09.072 0030-4026/© 2017 Elsevier GmbH. All rights reserved.

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Fig. 1. Procedure of optimising settings of colour primaries for a wide colour gamut display. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

In pace with the spread uses of wide gamut devices, a series of researches were concentrated on discussing the correlations between gamut features and image effects [12,13], and revealing how to calculate gamut parameters such as size and boundaries [14–16], which built a good foundation in this field. Therefrom, some approaches should be put forward to deal with the mismatch between wide gamut displays and current standards. At present, new signal standards based on wider colour gamut appears accordingly, such as the ITU-R (International Telecommunications Union-Radiocommunications Sector) BT. 2020 and the SMPTE (Society of Motion Picture and Television Engineers) for highly developed TVs [17,18]. New signal standards can solve the problem in some degree. However, there are various display technologies, which make different displays from such a many manufactories show large diversities on their colour gamut features, so that employing one universal standard to suit those different displays will still cause image distortions. To resolve the problem in terms of principles, quite a few scholars endeavored in introducing some treatments on images or displays, which were aimed to achieve preferred image quality under the control of existed signal standards. For pretreatment process of images, some researchers made efforts on improving image reproduction effects for specific colour contents, e.g. a procedure to protect skin colours via a content-based analysis on wide gamut displays [19]. Considering content-based algorithms might be complicated and unstable in applications, more studies were focused on designing colour conversion schemes with pertinence for different wide gamut devices rather than for image contents, e.g. based on multi-channel technology which supported a way of enlarging colour gamut. For multi-channel displays with several pixel combinations such as RGBY (red, green, blue, yellow), RGBCY (red, green, blue, cyan, yellow), RGBCW (red, green, blue, cyan, white), RGBW (red, green, blue, white), the algorithms for converting traditional RGB (red, green, blue) signals were proposed accordingly [20–22], whereas similar works were carried out on TVs with RGB primaries [23]. Also, methods of determining gamut boundary or optimising between brightness and gamut were deeply discussed [24,25]. In the field of pretreatment procedure on displays, this study concentrated on optimising settings of colour primary specifications on wide gamut devices, in which an image rendering procedure was designed and a psychophysical experiment was then conducted. Finally the optimum colour primaries was determined to produce preferred colour reproduction for sRGB images. This work may support some recommendations to determine the primaries of wide gamut devices for display researchers and manufactories as an example of application. 2. Procedure and algorithms 2.1. Strategy for optimising settings of colour primaries For a given wide gamut display, a procedure for optimising settings of its colour primaries is designed, which can supply a strategy of seeking appropriate gamut settings for different displays. The proposed work flow is described step by step as shown in Fig. 1. For this wide gamut display, different gamut settings can be obtained within the sRGB gamut and the display maximum gamut by adjusting the positions of its three primaries (red, green, blue) in the CIE1976UCS diagram [26]. To test these new gamut settings, a series of algorithms is put forward to simulate their image display effects on the same display, so that the performances of these gamut settings can be judged by two approaches, i.e. the visual evaluation from psychophysical experiment, and a proposed preference index with particular calculations. Therefore, the optimum gamut settings can be determined based on considering results of the visual evaluation and the preference index. The process and algorithms for simulating the image display effects for individual gamut settings on this given display are depicted in detail in the following. 2.2. Image simulation of different gamut settings An image processing procedure is established to search for the optimum chromaticity coordinates of the three primaries by adjusting their positions in the CIE1976UCS diagram. For each determined gamut setting, we assume that it can be regarded

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Table 1 Scaling factors for the three primaries.

ˇR ˇG ˇB

t1 ≤ 1, t2 ≤ 1

t2 ≤ t1 , t1 >1

t1 ≤ t2 , t2 >1

t1 t2 1

1 t2 /t1 1/t1

t1 /t2 1 1/t2

as an “imaginative” device, and Fig. 1 shows the methods of accurately simulating the visual effect for each “imaginative” device on the same display with the same setting. When images are shown on the “imaginative” device, the visual effect for each pixel can be simulated based on the physical and colorimetric settings of the display, such as peak luminance and chromaticity coordinates of three primaries. For the test gamut setting of this “imaginative” device, the CIE1976UCS u’v’ coordinates of red, green, blue primaries are denoted as (u’R , v’R ), (u’G , v’G ), (u’B , v’B ). Whereas for the display maximum gamut, the u’v’ coordinates of three primaries are marked as (u’R0 , v’R0 ), (u’G0 , v’G0 ), (u’B0 , v’B0 ), and their peak luminance values are YR0 , YG0 , YB0 , respectively. According to the basic colorimetry [26,27], the coordinates (u’R , v’R ), (u’G , v’G ), (u’B , v’B ) are transformed to corresponding tristimulus values, i.e. (XRT , YRT , ZRT ), (XGT , YGT , ZGT ), (XBT , YBT , ZBT ), and Eq. (1) shows the calculation of obtaining tristimulus values for the three primaries, where J = R, G, B.

⎧ X = 9YJT · u J /4v J ⎪ ⎨ JT ⎪ ⎩

YJT = YJ0





(1)

ZJT = 9YJT /v J − XJT − 15YJT /3

For different settings of the display, the CCT (correlated colour temperature) parameter is fixed with definitized u’v’ coordinates (u’CCT , v’CCT ), such as 6500 K. To maintain the same CCT for different gamut settings, the white point (XW , YW , ZW ) as the sum of the tristimulus values of three primaries should be in accord with the (u’CCT , v’CCT ) [26], and calculations of getting (u’CCT , v’CCT ) from (XW , YW , ZW ) are expressed in Eqs. (2) and (3).

⎧ X = XRT +XGT +XBT ⎪ ⎨ W ⎪ ⎩

YW = YRT +YGT +YBT

(2)

ZW = ZRT +ZGT +ZBT

⎧ ⎪ ⎨ u CCT = ⎪ ⎩ v CCT =

4XW XW + 15YW + 3ZW 9YW XW + 15YW + 3ZW

(3)

Afterwards, by solving Eqs. (1)–(3), three coefficients of t1 , t2 , and t3 are given, as depicted in Eqs. (4)–(6), which are employed to develop the corresponding scaling factors of modulating the current luminance values of the three primaries, i.e. YRT , YGT , YBT .

⎧ a = 4XRT − u CCT · (XRT + 15YRT + 3ZRT ) ⎪ ⎨ 1 ⎪ ⎩

a2 = 4XGT − u CCT · (XGT + 15YGT + 3ZGT )

a3 =

u

CCT

(4)

· (−3XBT + 15YBT + 3ZBT )

⎧ b = 9YRT − v CCT · (XRT + 15YRT + 3ZRT ) ⎪ ⎨ 1 ⎪ ⎩

b2 = 9YGT − v CCT · (XGT + 15YGT + 3ZGT ) b3 =

v

CCT

(5)

· (XBT + 6YBT + 3ZBT )

⎧ t = (a3 · b1 − a1 · b3 ) / (a2 · b1 − a1 · b2 ) ⎪ ⎨ 1 ⎪ ⎩

t2 = (a3 · b2 − a2 · b3 ) / (a1 · b2 − a2 · b1 )

(6)

t3 = 1

Considering the solved luminance values YRT , YGT , YBT may exceed the display’s peak luminance values YR0 , YG0 , YB0 for each primary, which will cause display aberration in applications. Therefore, new scaling factors ˇR , ˇG , ˇB are proposed from the coefficients of t1 , t2 , and t3 for three primaries, which are listed in Table 1, in order to get suitable luminance values

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YR , YG , YB in practice. And Eq. (7) shows the process to obtain the tristimulus values of three primaries on the “imaginative” device, i.e. (XR , YR , ZR ), (XG , YG , ZG ), and (XB , YB , ZB ), where K = X, Y, Z.

⎧ K = ˇR · KRT ⎪ ⎨ R ⎪ ⎩

KG = ˇG · KGT

(7)

KB = ˇB · KBT

Based on the colorimetric parameters of the “imaginative” device, the device-independent information of each pixel can be transformed to the device-dependent RGB space. As shown in Fig. 1, for any digital inputs (ro , go , bo ), their corresponding tristimulus values (Xc , Yc , Zc ) can be calculated via the forward chromatic characterization [28]. The typical chromatic characterization methods include the GOG (gain-offset-gamma) model, the PLCC (piecewise linear interpolation assuming constant chromaticity coordinates) model, and the PLVC (piecewise linear interpolation assuming variable chromaticity coordinates) model, etc [28–30]. For most displays with good performance on channel independence, the prediction from (ro , go , bo ) to (Xc , Yc , Zc ) are shown in Eqs. (8) and (9), where Qc is the forward transformation matrix derived from the given gamut setting, and X(0,0,0) , Y(0,0,0) , Z(0,0,0) stand for the tristimulus values when all the primaries of the display are off. In addition, for displays with poor channel independence, particular chromatic characterization methods will be employed [31]. The relationships between the intermediate variables LR (ro ), LG (go ), LB (bo ) and (ro , go , bo ) could be fitted by different expressions, and Eq. (10) gives an example of GOG model [29], in which  R ,  G ,  B , ␣R , ␣G , ␣B ,  R ,  G ,  B are device-dependent parameters determined by the u’v’ coordinates and the peak luminance of three primaries with one given gamut setting, and N is the number of bits for each primary to record colour information, usually N = 8.

⎡

⎤

XR

XG

XB

QC = ⎣ YR

YG

YB ⎦

ZR

ZG

ZB

⎢

⎡

XC

⎤

⎡

⎥

LR (rO )

(8)

⎤ ⎡

X (0, 0, 0)

⎤

⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ YC ⎦ = QC ⎣ LG (gO ) ⎦ + ⎣ Y(0, 0, 0) ⎦ LB (bO )

ZC

Z(0, 0, 0)

⎧  R rO ⎪ LR (rO ) = R ( N ) + ˛R ⎪ ⎪ 2 −1 ⎪ ⎪ ⎪ ⎨  G ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩

LG (gO ) = LB (bO ) =

G (

gO ) + ˛G 2N − 1

B (

bO ) + ˛B 2N − 1



(9)

(10)

B

The tristimulus values (Xc , Yc , Zc ) can be transformed to colour appearance parameters of lightness Jc , chroma Cc , and hue hc according to the CIE (Commission Internationale de L’Eclairage) recommended CIECAM02 model [32,33], which has the advantage of involving the observation condition such as surround, background, and observer adaptation state. According to Hunt’s reproduction objective of “equivalent” reproduction [7,34], the original and reproduction should have the same appearance under their respective viewing conditions, which is no longer measured physically but needs to be judged psychovisually. Hence, the to-be-displayed colour appearance coordinates (Jm , Cm , hm ) should be the same or be close to the colour appearance coordinates (Jc , Cc , hc ). Afterwards, the (Jm , Cm , hm ) could be transformed to tristimulus values (Xm , Ym , Zm ) by considering its observation condition, and then the final digital inputs (rm , gm , bm ) are calculated via the inverse chromatic characterization with the transformation matrix Hm , in which the colorimetric parameters of the actually used gamut setting (usually it is the display maximum gamut setting) are employed. Similar to the forward chromatic characterization, Eqs. (11)–(13) depict the corresponding calculations to derive the digital inputs (rm , gm , bm ), which are reversible operations of Eqs. (8)–(10).

⎡

⎤−1

XR0

XG0

XB0

Hm = ⎣ YR0

YG0

YB0 ⎦

ZG0

ZB0

⎢

ZR0

⎡

LR

⎤

⎡

⎥

Xm − X(0,0,0)

(11)

⎤

⎢ ⎥ ⎢ ⎥ ⎣ LG ⎦ = H m ⎣ Ym − Y(0,0,0) ⎦ LB

Zm − Z(0,0,0)

(12)

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Fig. 2. Process of obtaining preference index for a given gamut setting of three primaries.

Table 2 The employed samples containing both memory colours and high-saturated colours. samples

digital inputs

samples

digital inputs

1 2 3 4 5 6

(170, 120, 96) (192, 154, 129) (199, 156, 135) (210, 162, 149) (3, 73, 171) (96, 139, 216)

7 8 9 10 11 12

(26, 59, 21) (58, 89, 62) (99, 132, 63) (129, 148, 61) (144, 0, 9) (178, 19, 2)

⎧     rm = 2N − 1 · LR 1/R − ˛R /R ⎪ ⎪ ⎨     gm = 2N − 1 · LG 1/G − ˛G /G ⎪ ⎪     ⎩ b = 2N − 1 · L 1/B − ˛ / m

B

B

(13)

B

By adopting the above calculations, for each original image, its derivative versions for any given gamut setting under any viewing environment can be accurately simulated on the display with the display maximum gamut setting under one given viewing environment.

2.3. Calculation of preference index Based on different derivative versions of one original image, various gamut settings can be judged by a proposed expression, i.e. the preference index, thus these gamut settings can be compared by the results of preference index prediction. The procedure of calculating image preference index is demonstrated in Fig. 2, in which for some appointed pixels, their colour appearance parameters calculated from the current gamut setting are compared with those calculated from the sRGB gamut. Not all the colours are involved in the preference index, the appointed colour samples in this process consider both vivid scenes and natural objects, such as skin, sky, grass, vegetables, and fruits [8,10,34,35]. A series of colour samples is extracted from several typical images, and their digital inputs (rAi , gAi , bAi ) are shown in Table 2. The selected samples contain some typical memory colours and high-saturated colours that are close to three primaries and their mixtures (cyan, magenta, and yellow), i.e. located near the display gamut boundaries. These 18 samples supply a general recommendation, e.g. skin (sample 1–4), sky (sample 5–6), grass (sample 7–10), vegetables and fruits (sample 9–14), ocean (sample 15–16), and flowers (sample 17–18). In addition, the selection of colour samples may vary in some situations when it is need to put emphasis on particular colours for displays. In Fig. 2, for digital inputs (rAi , gAi , bAi ) of each colour sample, the corresponding tristimulus values (Xsi , Ysi , Zsi ) according to the sRGB standard are predicted by the IEC (International Electrotechnical Commission) 61966-2-1 standard [4], where i = 1, 2, . . ., 18. The transformation algorithms are specified and explicit as in Eqs. (14) and (15), according to the rule of sRGB

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Table 3 Physical parameters of the test display. Basic parameters

Settings of the three colour primaries 24 inch (51.7 cm × 32.3 cm) 1920 × 1200 16 million (256 steps per primary) 200 cd/m2

Size Pixel resolution Colour resolution Peak luminance

CCT CIE 1976 u’v’ chromaticity coordinates

Red Green Blue

6500 K (0.5315, 0.5177) (0.0733, 0.5778) (0.1929, 0.1106)

standard. Then, the colour appearance parameters (Jsi , Csi , hsi ) for (rAi , gAi , bAi ) under the given environment are calculated from (Xsi , Ysi , Zsi ) along with the parameters of observation condition via the CIECAM02 model.

⎧  r 2.4 ⎪ Ai ⎪ ⎪ LR (rAi ) = ( 255 + 0.055)/1.055 ⎪ ⎪ ⎪ ⎪ ⎨  2.4 gAi

+ 0.055)/1.055

(14)

⎤ ⎡ LR (r ) · 80 ⎤ Ai ⎢ ⎥ ⎣ ⎥ ⎢ ⎣ YSi ⎦ = 0.2126 0.7152 0.0722 ⎦ ⎣ LG (gAi ) · 80 ⎦

(15)

L (g ) =

(

G Ai 255 ⎪ ⎪ ⎪ ⎪ ⎪  2.4 ⎪ ⎪ ⎩ LB (bAi ) = ( bAi + 0.055)/1.055

⎡

XSi

⎤

255

⎡

ZSi

0.4124

0.3576

0.1805

0.0193

0.1192

0.9505

LB (b Ai ) · 80

Besides, for each colour sample, the tristimulus values (Xmi , Ymi , Zmi ) and the colour appearance parameters (Jmi , Cmi , hmi ) under the current test gamut settings are obtained from (rAi , gAi , bAi ) by calculations of Eqs. (8)–(13). Afterwards, for all the samples, the preference index can be derived from comparing the colour appearance parameters between the sRGB gamut and the current test gamut setting. The design of the algorithm is on account of some literature results and our previous studies [6–10,35], e.g. hue is the most important factor in memory colour evaluation, and for most colours including memory colours such as trees, sky, and grass, their visual effects in one gamut setting will be preferred by observers when they are exhibited more saturated and more vivid than the effects under the sRGB specification. However, extremely saturated colours may cause uncomfortable feelings especially for skin colours, thus their visual effects should not be oversaturated, that is to say, the reproduction close to the original colour appearance will be preferable. Therefore, two criteria are followed in predicting preference index based on the appearance differences between the sRGB gamut and the current gamut. Firstly, the hue deviation for all colour samples (samples 1–18) and the chroma deviation for skin colour samples (samples 1–4) will cause a decrease of preference index. Secondly, the higher values of lightness Jmi for all colour samples and the higher values of chroma Cmi for the colour samples except skin colours (samples 5–18) may result in a rise of preference index. The method of representing the preference index “PI” is shown in Eq. (16), here, in applications the recommended values are Q = 120, 1 = 0.228, 2 = 0.394, 3 = 0.148, and 4 = 0.076, which are gained from multiple linear regression of experimental data. PI = Q − 1

18 

|hmi − hsi | − 2

i=1

4  i=1

|Cmi − Csi | + 3

18  i=1

(Jmi − Jsi ) + 4

18 

(Cmi − Csi )

(16)

i=5

3. Psychophysical experiment Visual evaluation is another approach to compare the performances of different gamut settings, which should be in accord with the results of calculating the preference index. To test the effectiveness of the above process and to supply more information of optimising the values of Q, 1 , 2 , 3 , and 4 in Eq. (16), a wide gamut display was employed in a psychophysical experiment, so that the display effects for different gamut settings could be evaluated and compared with the proposed preference index by analyzing the visual data. 3.1. Test display and image preparation A 24 inch wide gamut LCD (liquid crystal display) with LED (light emitting diode) backlight was adopted, which has a gamut to cover sRGB, Adobe RGB, etc. Its physical parameters are listed in Table 3, including the settings of peak luminance, CCT, and the u’v’ coordinates of three primaries, as well as some basic parameters such as size and resolution. The physical measurement of the display was conducted using a Konica-Minolta CS-2000 tele-spectroradiometer according to IEC 619664 standard [36]. Fig. 3 illustrates the gamut visualization for the display with comparison to some image standards, in 2D (two dimensional) form of CIE1976UCS diagram and in 3D (three dimensional) form of CIELAB colour space respectively. The sRGB gamut has lower lightness values than the display gamut since they adopted the same white point when being

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Fig. 3. Visualization of the wide gamut display with comparison to some standards: (a) 2D gamut for the positions of the three primaries in CIE1976UCS diagram; (b) 3D gamut in the CIELAB colour space.

Fig. 4. The u’v’ coordinates for the adjusted positions of the three primaries in CIE1976 UCS diagram: (a) in global view; (b) red primary in partial view; (c) green primary in partial view; (d) blue primary in partial view. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

converted to CIEL* a* b* values. Clearly shown in Fig. 3, the display exhibits its significantly wide gamut, stating it is competent for simulating various gamut settings in a free range. On the basis of the large gamut of this display, the new positions of three primaries could be adjusted within the region between sRGB gamut and the display maximum gamut in the CIE1976UCS diagram. Thus, for each primary, different amount of u’v’ coordinates (Nr , Ng , Nb for red, green, blue primaries respectively) were chosen as new specifications, resulting in a total of Nr × Ng × Nb gamut settings. Based on the consideration that too small variations between two neighboring gamut settings may not be visually distinguishable, Nr × Ng × Nb was set as 8 × 5 × 4 in the experiment. The selection of u’v’ coordinates for each channel adhered to two principles. Firstly, these plots should cover a certain range of variations from the sRGB gamut to the test display gamut boundaries. Secondly, they should be located in a well-distributed spread. Fig. 4 depicts the adjusted positions for the three primaries respectively. To judge the image reproduction effects of each gamut setting, the source images containing all the 18 colour samples in Table 2 were regarded as original test images. Then their corresponding images were generated to simulate the display effects on each “imaginative” device with the given gamut setting, according to the process of “Section 2.2”. In the image simulation process, the GOG model was adopted which achieved high accuracies of 0.49 and 0.56 E00 units [37] in the forward and the inverse colorimetric characterization respectively (using 100 colours with random digital inputs as test samples), so that the outputs of the display could be accurately controlled. By implementing the procedure, 30 primary specifications from the 8 × 5 × 4 combinations were determined by a pilot visual assessment. Therefore, 30 rendered versions were prepared

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for each original test image. These gamut settings also included the display maximum gamut and the sRGB gamut, so the other 28 gamut settings could be compared with these two special References 3.2. Psychophysical procedure A psychophysical experiment was put into practice to verify which gamut settings could produce the preferred colour reproduction for images from sRGB standard. The visual experiment was conducted in a dark room, and a panel of 10 observers (5 male and 5 female) participated. All the images were resized to the same resolution of 960 × 600 pixels, and the remaining part of the screen was set as neutral gray with 18% peak luminance. Thereby, the viewing angle was 18.4◦ × 11.5◦ at a distance of 80 cm, and the observers focused their attentions on the display perpendicularly. Since the visual effect was a major consideration for consumers in the display industry, the attribute of image preference was taken into account, which was defined as the extent of the image quality being preferred by observers [6,9]. This attribute was assessed via the psychophysical scaling method of categorical judgment [35,38], since this technique has the advantage of allowing direct responses of the observer to variations in the stimulus. In this method, a seven-point scale was adopted to describe perceptual feelings in grades, where grade “7” corresponded to the “highest imaginable preference”, and grade “1” to the “least imaginable preference”. The procedure of the psychophysical experiment is as follows, and then massive visual judgments were obtained. To test whether the observer has normal colour vision. To show the observer a detailed instruction, both in English and in Chinese, to help him/her to understand the visual task. To perform two-minute dark adaptation and one-minute light adaptation. To present one version of one original image on the display to the observer and record his/her judgment via a software interface controlled by a specially designed program. e) To repeat the step d) with another version of the same image until all its 30 versions were evaluated. The sequence of these versions shown to observers was randomly generated. f) To change to another original test image, and repeat the steps d) and e). The sequence of the 8 original images shown on the display was also random. When the evaluations of all the images were finished, one session was completed for one observer. g) To repeat the above sessions for all the observers.

a) b) c) d)

4. Results and discussions 4.1. Deriving equal-interval scale values The raw experimental data assigned by observers are not equal-interval scale values (equal-interval scale means equal distances anywhere along the scale represent the same significance) but just category names. Hence, these raw category names were converted to equal-interval scale values by adopting Case V of Thurstone’s law on comparative judgment. Firstly, the raw category grades were converted to a frequency matrix, denoting the amount of individual category grade judged by the observers, then its cumulative frequency matrix could be obtained by calculating the cumulative sum of the above frequency values. Afterward, a cumulative probability matrix was calculated from the cumulative frequency matrix via being divided by the number of total judgments, so that it was converted to a z-score matrix according to the inverse function of standard normal cumulative distribution [39]. Finally, the ultimate equal-interval scale values from categorical judgment method could be derived from a difference matrix and a matrix of category boundary estimates, which were both calculated from the z-score matrix. Therefore, for each evaluated image version, its categorical grades judged by all the observers were converted to an equal-interval scale value. The derived equal-interval scale values could be used to determine which colour gamut could produce preferred colour reproduction effect for images from sRGB standard, by which the 30 evaluated gamut settings can be analyzed and compared. Herewith, Table 4 lists the equal-interval scale values of each primary specifications (according to the descend order), along with the u’v’ coordinates for each colour primary. The parameter “gamut area ratio to sRGB gamut” as an indicator of gamut size was calculated by performing an operation of division, i.e. the triangle area of the current gamut divided by the triangle area of the sRGB gamut in the CIE1976UCS diagram. 4.2. Analyzing the visual data To deeply analyze the data in Table 4, a comparison is implemented involving the gamut ratio and the preference index which are calculated from the current gamut setting, and Fig. 5 exhibits the tendency of the gamut ratio and the preference index with variation of equal-interval scale values. It can be clearly seen from Fig. 5, the more preferred gamut settings with higher equal-interval scale values do not have high values of gamut ratio, and there are no consistence between the gamut size and the performance of gamut settings, the low Pearson correlation coefficient r value of −0.1043 implies that expanding the gamut tenaciously for display devices is not an advisable way to achieve pleasing visual effects, instead, appropriate settings of primary specifications are more

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Table 4 The equal-interval scale values and primary information for the 30 evaluated gamut settings. Equal-interval scale values

Red primary u’v’ coordinates

Green primary u’v’ coordinates

Blue primary u’v’ coordinates

Gamut area ratio to sRGB

Comments

2.3838 2.2932 2.2154 2.2148 2.1690 2.1598 2.1476 2.1340 2.1279 2.1075 2.1045 2.0800 2.0620 2.0466 1.9626 1.9446 1.9424 1.8691 1.7847 1.6762 1.6570 1.5785 1.5389 1.3978 1.3936 1.3712 1.3400 1.3087 1.2748 1.1495

(0.4776, 0.5212) (0.4776, 0.5212) (0.4756, 0.5125) (0.4712, 0.5053) (0.4507, 0.5229) (0.4507, 0.5229) (0.4756, 0.5125) 0.4712, 0.5053) (0.4507, 0.5229) (0.4712, 0.5053) (0.4507, 0.5229) (0.4756, 0.5125) (0.4756, 0.5125) (0.4712, 0.5053) (0.4776, 0.5212) (0.4712, 0.5053) (0.5005, 0.5021) (0.4756, 0.5125) (0.5046, 0.5194) (0.4917, 0.4878) (0.5315, 0.5177) (0.4507, 0.5229) (0.5046, 0.5194) (0.5005, 0.5021) (0.4712, 0.5053) (0.4776, 0.5212) (0.4756, 0.5125) (0.4917, 0.4878) (0.4507, 0.5229) (0.4507, 0.5229)

(0.1031, 0.5467) (0.0981, 0.5604) (0.0991, 0.5701) (0.0981, 0.5604) (0.1031, 0.5467) (0.0981, 0.5604) (0.0981, 0.5604) (0.0991, 0.5701) (0.0991, 0.5701) (0.0981, 0.5604) (0.1031, 0.5467) (0.0981, 0.5604) (0.1031, 0.5467) (0.0991, 0.5701) (0.1031, 0.5467) (0.1031, 0.5467) (0.0733, 0.5778) (0.1031, 0.5467) (0.0733, 0.5778) (0.0733, 0.5778) (0.0733, 0.5778) (0.0981, 0.5604) (0.1031, 0.5467) (0.0981, 0.5604) (0.0733, 0.5778) (0.0733, 0.5778) (0.0733, 0.5778) (0.0981, 0.5604) (0.1250, 0.5625) (0.1250, 0.5625)

(0.1862, 0.1369) (0.1862, 0.1369) (0.1862, 0.1369) (0.1929, 0.1106) (0.1974, 0.1419) (0.1929, 0.1106) (0.1929, 0.1106) (0.1862, 0.1369) (0.1929, 0.1106) (0.1795, 0.1632) (0.1862, 0.1369) (0.1795, 0.1632) (0.1862, 0.1369) (0.1929, 0.1106) (0.1795, 0.1632) (0.1862, 0.1369) (0.1929, 0.1106) (0.1974, 0.1419) (0.1929, 0.1106) (0.1862, 0.1369) (0.1929, 0.1106) (0.1795, 0.1632) (0.1862, 0.1369) (0.1862, 0.1369) (0.1862, 0.1369) (0.1862, 0.1369) (0.1862, 0.1369) (0.1795, 0.1632) (0.1795, 0.1632) (0.1929, 0.1106)

118.34% 122.98% 123.60% 127.15% 108.25% 121.24% 129.23% 121.62% 122.87% 112.37% 109.82% 114.19% 117.12% 128.94% 110.77% 115.25% 148.98% 115.36% 152.09% 136.29% 161.77% 107.12% 126.85% 129.23% 130.78% 134.39% 132.93% 117.61% 100.00% 112.99%

1st 2nd 3rd

maximum

sRGB

Fig. 5. The preference index and the gamut ratio compared with the equal-interval scale values.

significant and functional. As for the preference index, it can be seen that, there is obvious linear dependence between the results of psychophysical evaluation and the preference index prediction, the high value of Pearson correlation coefficient r 0.8319 states the reasonableness of the proposed procedure and algorithms for image simulation. Moreover, the accuracy of Eq. (16) is verified. Hence, in the display industry, the settings of colour primaries can be optimised for wide colour gamut displays via the realization of the image simulation and the preference index calculation. 5. Conclusions In this study, a whole procedure for optimising settings of colour primaries was presented for wide gamut displays, in order to achieve visually preferred appearance for images from the signal standards such as sRGB. An image processing procedure was developed to simulate image display effects for different gamut settings with specified colour coordinates of the three primaries. Then the visual effects of different gamut settings were predicted and compared by calculation of the preference index, thus the preferred gamut settings for optimum image reproduction could be determined. Moreover, a wide gamut display was employed as an experimental verification, by which the results of the preference index for 30 gamut settings were compared with their corresponding data of visual assessments. The consistence between the preference index calculation and the data derived from psychophysical experiment certified the effectiveness of the proposed procedure and its accessary algorithms. In conclusion, the preferred gamut settings are not close to the maximum gamut of the display, whereas suitable colour appearance parameters are more important for obtaining preferred colour reproduction effects

R. Gong et al. / Optik 154 (2018) 216–225

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for wide gamut displays. Our further studies may focus on investigating methods to adjust images from different signal standards adaptively, aiming to show a preferred visual effect on wide gamut displays with given primary specifications. Acknowledgments This work was supported by the National Natural Science Foundation of China (NSFC) (61505156 and 61675060). The author sincerely thanks to Prof. Xu of Zhejiang University for his conscientious guidance all the way through, and thanks to the fellows of Zhejiang University for their kind supports. References [1] H. Tanizoe, Development of the wide gamut display, J. Imaging Soc. Jpn. 43 (2) (2004) 75. [2] F. Aieta, P. Moroviˇc, J. Moroviˇc, M. Fiorentino, C. Santori, D. Fattal, Large color gamut displays with diffraction gratings, J. Opt. Soc. Am. A 33 (6) (2016) 1133. [3] Q. Hong, K.C. Lee, Z. Luo, S.T. Wu, High-efficiency quantum dot remote phosphor film, Appl. Opt. 54 (15) (2015) 4617. 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