# A Fast and Reliable Luma Control Scheme for High-Quality HDR/WCG Video
## 4 Simulations and Results
The performance difference between the best and the worst cases corresponds to only 0.12 dB on average (the average was calculated from the difference for each test sequence (i.e. the average of the biggest differences), not directly from the \"Average\" case of Table 2 (i.e., the difference of averages)), and the biggest difference is 0.33 dB from the  
\begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline
**seq. ** & \(a=1\), & \(a=2\), & \(a=3\), & \(a=4\), & \(a=5\), & \(a=6\), & \(a=7\), & \(a=8\), & \(a=9\), \\
**Name** & \(b=9\) & \(b=8\) & \(b=7\) & \(b=6\) & \(b=5\) & \(b=4\) & \(b=3\) & \(b=2\) & \(b=1\) \\ \hline \hline Freeater & 71.5844 & 71.5858 & 71.5870 & 71.5880 & 71.5887 & **71.5888** & 71.5883 & 71.5866 & 71.5826 \\ Market & 69.2396 & 69.27  
\"Market\" sequence. This limited change of the performance comes from the tightness of the derived bounds and enables us to use a fixed parameter just near the center point of the two bounds. Finally, we show an example of the subjective quality comparison among the tested luma control algorithms. As noted earlier in [5; 8; 9; 10], the artifacts introduced by the NCL Y'CbCr 4:2:0 format would appear as false contours around the object boundary and/or speckle noises in the smooth area. These artifacts become significant in a bright region of highly saturated colors and/or an edge region having large brightness changes. Hence, those artifacts can be easily seen from bright yellow, cyan, or magenta color regions rather than neutral color regions with low-to-medium brightness. Figure 5 shows such artifacts and the quality enhancement by luma control algorithms for the 108 th frame of the test sequence \"Carousel\", where we highlighted the differences in two parts (see green boxes) of the cropped image patch (i.e., as shown in Figure 5a) among different luma control algorithms. The subfigures b,c of the Figure 5 clearly show the subjective quality problem in the 4:2:0 media format of HDR/WCG video. We can observe that the texture inside the left green box became rougher and the bright pink dots in the right green box got dark after 4:2:0 conversion without luma control. Because of such big changes in brightness, the quality became only 26.65 dB in tPSNR-Y, as shown in Figure 5c. On the other hand, from the subfigures d-g of Figure 5, we can identify that the luma control schemes significantly ameliorate such quality problems and enhance the subjective quality. The rough texture and the dark pink dots disappeared in all luma control outputs, resulting in a better perception of the scene brightness. However, the problematic pink dots are observed to be not fully recovered and the rough textures look smoother than the original, illustrating that a video format with higher chroma resolution is desirable for better perception of HDR/WCG video. Figure 5: The visual effect comparison for the test sequence “Carousel” (108 th frame). The number in parentheses for each subfigure means the tPSNR-Y value of the image patch produced by each luma control algorithm. Although the tPSNR-Y values of the subfigures d-g are quite different (i.e., from the 42.04 dB of the \"Enhanced Fast Luma Control\" scheme in (e) to the 69.48 dB of the \"Iterative Luma Control\" scheme in (g)), it is hard to observe any subjective difference among the luma control schemes. In order to identify which part was attributed to such a big difference of tPSNR-Y values, we compared the luminance error defined in (1) for the outputs of the 108 th frame of \"Carousel\" sequence produced by the fast and the proposed luma control schemes. After subtracting the per-pixel error of the proposed output from the fast luma control error, we sorted the difference to find the pixel location having high error difference. Then, we marked top 0.1% location with \"Green\" pixels and cropped the same area as that which was compared in Figure 5. Figure 6 shows the area of the biggest quality difference between the two luma control schemes.