# A Fast and Reliable Luma Control Scheme for High-Quality HDR/WCG Video
## 1 Introduction  
High dynamic range and wide color gamut (HDR/WCG) video has recently received much attention due to its significant impact on the improvement of video quality by using a much higher contrast range, wider color primaries, and higher bit depth than conventional standard dynamic range (SDR) video. In order to facilitate the usage of such HDR/WCG video, standardization efforts have been made, including the production format of HDR-TV [1], the HDR electro-optical transfer function (EOTF) [2], the common media format for consumer electronics [3], and so on. In dealing with such HDR/WCG video, chroma subsampling, which is a key component for a video preprocessing system, introduces a severe quality problem on subjective luminance perception. Several Moving Picture Experts Group (MPEG) contributions identified this problem [4; 5], which is likely caused by the combination of the Y'CbCr 4:2:0 nonconstant luminance (NCL) format with the highly nonlinear transfer function of [2]. Appearing as a type of false contouring or noise-like speckles in the smooth area, the artifacts of this problem sometimes become very annoying to viewers even without compression. To ameliorate such artifacts from chroma subsampling, various luma control schemes have been suggested in the literature [6; 7; 8; 9; 10]. Luma control implies an intentional change of luma signal, which is not subsampled, for the purpose of reducing the perception error introduced by chroma subsampling. In one category of such luma control schemes, the perception error is defined in a nonlinear light domain using the signals obtained after the application of an optoelectrical transfer function (OETF) and quantization [6; 7]. The schemes in this category can be easily applied to conventional imagingsystems, but the incorporated perception error could not be correctly matched to the human visual system (HVS) because most HVS measures (i.e., CIEDE2000 [11]) are defined in the linear light domain. For this reason, the other category of luma control methods optimizes the error function defined in the linear light domain. One solution proposed in [8] was to simulate the NCL Y'CbCr 4:2:0 signal conversion followed by chroma upsampling for iterating over different luma values to choose the best one, resulting in the closest linear luminance to that of the original 4:4:4 signal. By searching for the best possible luma value, the solution achieved a significant linear luminance gain (i.e., more than 17 dB of tPSNR-Y in [8]) over the plain NCL Y'CbCr 4:2:0 signal. However, the iterative nature of searching, even done quickly with the tight bounds (also proposed in [8]), requires an uneven amount of complex computations per processing unit. To avoid such iterations for luma control, [PERSON] proposed a closed form solution in [9] based on a truncated Taylor series approximation for the nonlinear HDR EOTF function. This solution requires a fixed number of operations per pixel and thus is well suited for a real-time and/or hardware implementation of the NCL Y'CbCr 4:2:0 HDR system, but its performance is limited for some videos that have highly saturated colors. To fill the performance gap between the above two schemes, the authors proposed an enhanced fast luma control algorithm in [10]. Based on the fact that the linear approximation for a convex function using truncated Taylor series is always less than the function value, the enhanced luma control scheme modifies the linear approximation, resulting in a meaningful gain over the previous fast scheme. However, there still remains a nonnegligible performance gap and the algorithm requires a parameter which is not determined automatically.