# A Fast and Reliable Luma Control Scheme for High-Quality HDR/WCG Video
## 4 Simulations and Results
This phenomenon tells us that better luminance perception may not always provide better overall signal perception, which justifies a new direction of luma control research based on a better perception metric or incorporating chroma modifications. Now, let us examine the tPSNR-Y performance of the proposed algorithm. The \"No Control\" case in the figure is the conventional signal conversion using the NCL Y'CbCr4:2:0 format without luma  
Figure 4: The enhancement results of different luma control algorithms in terms of tPSNR-Y in (**a**) and tPSNR-XYZ in (**b**). The number inside the brackets in the “E-Fast” row of (**a**) denotes the reduction factor, \(r\), in (12), which was employed for the best result for each test sequence. control. If we compare the \"Average\" result of each luma control with that of this \"No Control\" case, we can identify that the proposed scheme achieved the tPSNR-Y improvement of 14.79 dB on average, while the \"Fast\" and the \"E-Fast\" schemes achieved 10.73 and 13.49 dB, respectively. On a sequence basis, the proposed luma control scheme enhanced the \"Fast\" and the \"E-Fast\" algorithms by up to 7.44 and 3.53 dB on the \"Fireplace\" and on \"Market\" sequences, respectively. One important observation here about these improvements is that there is no case of negative improvement. The proposed scheme is, on average, always superior to the compared previous fast luma control algorithms in all test sequences. Compared with the \"Iterative\" case (i.e., the optimal case), the tPSNR-Y of the proposed scheme is less than only 0.04 dB on average, indicating that the proposed scheme achieves nearly the same performance. However, we must note that nearly the same performance comes without iterations, i.e., there is no uneven amount of computations per pixel, which can be of great help to the hardware implementation of the proposed algorithm. Finally, let us look into the numbers inside the brackets in the \"E-Fast\" row of Figure 4a. They are the reduction factors, \(r\), in (12), which were chosen as the best for each test sequence. As shown in the subfigure, the values are quite different for each test sequence (i.e., hard to use a fixed value) and the factor is known to have a great impact on the reconstruction quality (i.e., around 2 dB on average) [10]. On the other hand, in all the simulations summarized in Figure 4, we used the same values of \(a=6\) and \(b=4\) for the proposed algorithm in (22). In order to identify the influence of the parameters \(a\) and \(b\) on the reconstruction quality of the proposed algorithm, we tested a set of parameters and summarized the results in Table 2. The tested parameters are the equally spaced nine samples of the point \(\left(\hat{X}^{\prime}_{M},\hat{X}_{M}\right)\) between \(\left(\hat{X}^{\prime}_{min},\hat{X}_{min}\right)\) (i.e., \(a=10\) and \(b=0\)) and \(\left(\hat{X}^{\prime}_{max},\hat{X}_{max}\right)\) (i.e., \(a=0\) and \(b=10\)), except for the end points. Based on the assumption that the true optimal to be approximated is uniformly distributed over the range bounded by the two end points, we can expect the best quality comes from the point near the center (i.e., \(a\approx b\)) but slightly biased to the upper bound \(\left(\hat{X}^{\prime}_{max},\hat{X}_{max}\right)\) (i.e., \(a<b\)) considering the convexity of the EOTF. However, as can be seen from the boldface figures (the best results) in Table 2, the best reconstruction qualities including the best \"average\" quality come mostly from the points near center but slightly biased to the lower bound (i.e., \(a>b\)), indicating the lower bound is usually tighter than the upper bound. Moreover, the worst-case results (i.e., the underlined numbers in each row) are shown mostly from the points near the lower bounds, which seems reasonable from the convexity of EOTF. Above all these results, Table 2 shows that the parameters \(a\) and \(b\) do not cause a significant change of the performance of the proposed algorithm.