# A Fast and Reliable Luma Control Scheme for High-Quality HDR/WCG Video
## 4 Simulations and Results  
To evaluate the performance of the proposed algorithm, an extensive comparison study was conducted using the previous luma control schemes explained in Section 2. The comparison is based on the pre-encoding and post-decoding processes defined in [12], with the downsampling filter, \(f_{0}\), having the filter coefficients of (1/8, 6/8, 1/8). Tested video sequences are shown in Figure 3, where the first three (denoted by \"Fireeater\", \"Market\", and \"Tibul\") are the BT.709 HDR video sequences used before in MPEG [15] and the last five sequences (denoted by \"Beerfest\", \"Carousel\", \"Cars\", \"Fireplace\", and \"Showgirl\") are the BT.2020 HDR sequences chosen from [16]. In contrast to the MPEG sequences, some of the chosen BT.2020 sequences have multiple shots of a scene with too many frames (more than 2000) for simulation. Thus, we further selected a representative 200-400-frames-long portion of each sequence for the performed simulations. Detailed information on these selections and the characteristics of each test sequence are summarized in Table 1.  
All the test videos were of the same 1920 \(\times\) 1080 resolution, maximum luminance of 4000 cd/m\({}^{2}\), and large amount of highly saturated colors. The color saturation was the most prominent property for the test sequences \"Market\", \"Beerfest\", and \"Carousel\", which had highly saturated colors around all three color gamut boundaries, while the others had one or two. The sequences \"Fireeater\" and \"Fireplace\" were low-key scenes (filmed in low-key) with flames covering a wide range of color temperatures. The \"Cars\" sequence showed directional sunlight on a black car, resulting in glare on the car bonnet and windows, with dark shades under the car. Finally, the \"Tibul\" and \"Showgirl\" sequences contained object(s) exposed to the maximum luminance, resulting in extremely high-contrast images. The characteristics of the test sequences described here are also summarized in Table 1.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Original File Name** & **Frames** & **Characteristics** \\ \hline Fireeater & Fireeater2 Clip4000 rr1_1920x1080p25_hf_709_444_xxxxx.ex  
As an objective measure for the performance comparison of luma control schemes, we used the tPSNR, defined in the Annex F of [15], on the luminance signal (i.e., tPSNR-Y) and on the overall XYZ color signal (i.e., tPSNR-XYZ). The tPSNR measure is a new metric for HDR material involving the color conversion to CIE XYZ space and the average of two transfer functions, ST.2084 and Philips, for the calculation of PSNR. Figure 4 summarizes the simulation results, where each number represents the tPSNR value averaged over all the frames of each test sequence. First, from each subfigure, we can easily identify that the performance difference is larger in tPSNR-Y (i.e., in Figure 4a) than in tPSNR-XYZ (i.e., in Figure 4b). This result is attributed to the objective function of luma control (i.e., Equation (1)), which concerns only the luminance perception error. Luma control optimizes such luminance error by modifying luma values and thereby directly enhances the luminance perception (i.e., tPSNR-Y) while indirectly enhancing the reconstructed color components (i.e., the \(\hat{R}\), \(\hat{G}\), \(\hat{B}\), in Equation (1)). Because of the weights, \((w_{R},w_{G},w_{B})\) in the objective function, the improvement of tPSNR-X (closely related to the red color) is usually larger than that of tPSNR-Z (closely related to the blue color), and these indirect improvements are much less than that of tPSNR-Y. This limited improvement on tPSNR-X and tPSNR-Y restricts the difference of tPSNR-XYZ performance among tested luma control algorithms. One interesting point in the tPSNR-XYZ result given in Figure 4b is that the averaged result of the proposed scheme is better than that of the \"Iterative\" scheme (which is regarded as the optimal solution for luminance perception), although the gain is only 0.01 dB.