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Gamut Coverage Metric for Wide- Displays

Kenichiro Masaoka

For ultrahigh-definition television, a wide-gamut system ance spaces. It is herein proposed to measure display gamut colorimetry is specified in the International Telecommuni- sizes by employing the Rec. 2020 area-coverage ratio in the cation Union-Radiocommunication Sector (ITU-R) Rec- xy diagram. ommendation BT.2020 (Rec. 2020). Presently, ultrahigh- definition television (UHDTV) displays recognize the Rec. 2020 representation, but their inherent gamut sizes 1. Introduction vary, which necessitates a proper gamut size metric. A prac- A wide-gamut system colorimetry with the chromatici- tical metric used in the display industry involves compar- ties of the primary positioned on the spectral locus ing the area-size ratio or area-coverage ratio of the triangle is specified for UHDTV in Rec. 20201). For high-definition formed by connecting the RGB primaries of a display to television (HDTV), a system colorimetry based on the char- that of a standard in the International Commis- acteristics of cathode ray tube (CRT) phosphors is speci- sion on Illumination (CIE) 1931 xy diagram fied in ITU-R Recommendation BT.709 (Rec. 709)2). Fig- or CIE 1976 u′v′ chromaticity diagram. Based on color sci- ure 1 shows the chromaticity*1 coordinates of UHDTV and ence, however, the color gamut is defined as a solid volume HDTV primary colors in the xy and u′v′ chromaticity dia- in a perceptually uniform three-dimensional color appear-

ance space, rather than planimetric in a chromaticity dia- *1 The numerical value indicating the hue and saturation of a gram, although the calculation of the gamut shape and size color is called the chromaticity. The chromaticity diagrams is very complex. This report reveals high correlations be- specified by CIE include the xy and u’v’ diagrams. The u’v’ tween the Rec. 2020 area-coverage ratios in the xy diagram diagram is more suggestive of the perceptibility of color dif- ferences when luminance is constant. and the Rec. 2020 volume-coverage ratios in color appear-

Figure 1: Rec. 709 and Rec. 2020 RGB primaries.

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grams. The wide-gamut system colorimetry of UHDTV can display’s RGB triangle, and Adisp∩Astd the area of the po- reproduce highly saturated colors of objects that cannot be lygonal overlap region between the display and standard reproduced by HDTV3). RGB triangles, the relative gamut size of the display has

Presently, many consumer displays are compatible with been expressed as the area-coverage ratio (Adisp∩Astd)/Astd in the Rec. 2020 color representation, but their inherent gamut some cases and the area ratio Adisp/Astd in others. In addition, sizes vary. A practical metric used in the display industry both the xy chromaticity diagram and u′v′ chromaticity dia- involves a comparison of the area of the triangle formed by gram have been used in calculating either the area-coverage connecting the red (R), green (G), and blue (B) primaries ratio or area ratio. (RGB triangle) of a display to that of a standard color space Rec. 2020 is the most promising wide-gamut color space, in a chromaticity diagram. In contrast, the color gamut in in that its RGB color space covers the major standard color the field of color science is represented as a color solid in spaces and most real object colors, and it is also the standard the CIE L*a*b* (CIELAB) color space*2 commonly used as gamut for UHDTV, making it the most suitable target gamut a perceptually uniform*3 three-dimensional space, as shown for wide-gamut displays. From the point of view of source in Fig. 2. Here, however, factors such as the complexity of color reproduction accuracy, the gamut-coverage ratio rath- calculating the shape or volume and the difficulty of grasp- er than the gamut-size ratio is valid. ing the concept of a color solid have made a volume-based In this work, the use of the xy diagram rather than the metric unacceptable to the market. perceptually uniform u′v′ diagram to measure relative dis- At the same time, there are problems with metrics based play gamut sizes is validated by presenting a quantitative on area. Letting Astd denote the area of a standard RGB tri- analysis of gamut sizes. angle in a certain chromaticity diagram, Adisp the area of a

2. Simulations *2 A three-dimensional color space representing lightness L* and Figure 3 shows the sampled RGB primary coordinates color coordinates a* and b*. for a variety of wide-gamut displays, as shown by the red, *3 The condition under which distance is proportional to color green, and blue points in the u′v′ chromaticity diagram. difference in a three-dimensional color space representing Any RGB primary combination of the sampled primaries lightness, hue, and saturation is called “perceptually uni- form.” encloses the Rec. 709 gamut and therefore satisfies wide-

Figure 2: Rec. 709 and Rec. 2020 in three-dimensional color space.

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Figure 3: RGB primaries sampled to cover Rec. 709 color space.

Figure 4: Rec. 2020 area-coverage ratios in xy and u′v′ chromaticity diagrams.

Figure 5: Rec. 2020 area-coverage ratios and Rec. 2020 volume-coverage ratios (r in the figure denotes correlation coefficient).

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gamut-display conditions. Figure 4 shows Rec. 2020 area- 3. Standardization coverage ratios calculated in the xy and u′v′ chromaticity On the basis of the above simulation results, the Rec. diagrams for all of the sampled RGB primary sets. Here, 2020 area-coverage ratio in the xy chromaticity diagram the Rec. 2020 area-coverage ratio differs by a maximum was proposed to the Association of Radio Industries and of 18% in these chromaticity diagrams. Figure 5 shows the Businesses (ARIB) as a method of calculating a gamut-cov- relationships between Rec. 2020 area-coverage ratios calcu- erage ratio for displays used in UHDTV program produc- lated in the xy and u′v′ chromaticity diagrams and Rec. 2020 tion and formulated as the ARIB Technical Report TR-B367) volume-coverage ratios4) calculated in the CIELAB, CIE in 2015. This technical report recommends not only an area- *4 *5 L*u*v* (CIELUV) , and CIECAM02 JaCbC color spaces. coverage ratio for the entire Rec. 2020 RGB triangle but The results of this simulation show that the Rec. 2020 vol- also gamut-coverage ratios for different hues. ume-coverage ratios have high correlations with the Rec. As shown in Fig. 6, straight lines drawn from the white 2020 area-coverage ratios calculated in the xy chromatic- (W) chromaticity point in the Rec. 2020 RGB triangle to ity diagram. It can therefore be considered appropriate to each of the R, G, and B chromaticity points divide the tri- represent the relative gamut size of a wide-gamut display angle into the three areas of (AC), magenta (AM), and by the Rec. 2020 area-coverage ratio in the xy chromatic- yellow (AY). The area-coverage ratios of each area can now ity diagram. The appropriateness of using the xy chromatic- be computed as the Rec. 2020 gamut-coverage ratios by ity diagram in calculating the area-coverage ratio has also hue: (Adisp∩AC)/AC, (Adisp∩AM)/AM, and (Adisp∩AY)/AY. The been demonstrated for target gamuts such as Adobe RGB calculated gamut-coverage ratios describe the area-cover- (standard color space for photography and graphic arts) age ratios for the entire Rec. 2020 RGB triangle and each of and DCI-P3 (the gamut for a reference projector in digital the C, M, and Y areas rounded off to the first decimal place. cinema)5). Details on calculating the area-coverage ratio are The Rec. 2020 gamut-coverage ratio of the Rec. 709 gamut given in [6]. (Rec. 709 RGB triangle) is described below as an example. Rec. 2020 gamut-coverage ratio: 52.9% (C: 27.5%, M: 68.7%, Y: 60.1%) 4 CIELAB and CIELUV are color appearance models standard- * The gamut-coverage ratio of each of the three hue-spe- ized in 1976 by CIE. CIELUV was once dominant in the field of television but CIELAB is mainly used at present. cific areas provides a better understanding of the balance *5 The latest standardized , which is among the gamut sizes for different hues than does the total used mostly in scientific applications. gamut-coverage ratio.

Figure 6: Rec. 2020 RGB triangle divided into three regions in xy chromaticity diagram.

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4. Conclusions 2) Recommendation ITU-R BT.709-6, “Parameter Values for the In this study, we compared by simulation the Rec. 2020 HDTV Standards for Production and International Programme area-coverage ratios in xy and u′v′ chromaticity diagrams Exchange” (2015) with the Rec. 2020 volume-coverage ratios in three-dimen- 3) K. Masaoka, Y. Nishida, M. Sugawara and E. Nakasu: “De- sional color appearance spaces and showed that the Rec. sign of Primaries for a Wide-Gamut Television Colorimetry,” 2020 area-coverage ratio in the xy chromaticity diagram is IEEE Trans. Broadcast., Vol. 56, No. 4, pp. 452-457 (2010) appropriate as a metric for the gamut size of wide-gamut 4) K. Masaoka and Y. Nishida: “Metric of Color-Space Coverage displays. for Wide-Gamut Displays,” Opt. Express, Vol. 23, No. 6, pp. 7802-7808 (2015) This paper includes additions and revisions to the following 5) K. Masaoka: “Single Display Gamut Size Metric,” J. Soc. paper appearing in Optics Express: Info. Disp., Vol. 24, No. 7, pp. 419-423 (2016) K. Masaoka and Y. Nishida: “Metric of Color-Space Coverage 6) K. Masaoka: “Display Gamut Metrology Using Chromaticity for Wide-Gamut Displays,” Opt. Express, Vol. 23, No. 6, pp. Diagram,” IEEE Access, Vol. 4, pp. 3878-3886 (2016) 7802-7808 (2015) 7) ARIB TR-B36, “Metric of Color-Space Coverage of UHDTV Displays for Program Production” (2015)

References 1) Recommendation ITU-R BT.2020-2, “Parameter Values for Ultra-high Definition Television Systems for Production and International Programme Exchange” (2015)

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