# Quality Assessment of HDR/WCG Images Using HDR Uniform Color Spaces
## 1 Introduction  
Screen technologies have made incredible progress in recent years. They are able to display brighter and darker pixels with more vivid colors than ever and, thus, create more impressive and realistic images. Indeed, the new generation of screens can display a luminance that can go below 0.01 cd/m\({}^{2}\) and up to 10,000 cd/m\({}^{2}\), thus, allowing them to handle images and video with a High Dynamic Range (HDR) of luminance. For comparison, screens with a standard dynamic range (SDR) are traditionally able to display luminance between 1 and 100 cd/m\({}^{2}\). To handle HDR images, new transfer functions have to be used to transform the true linear light to perceptually linear light (Opto-Electronic Transfer Function (OETF)). The function used to transform back the perceptually linear light to true linear light is called the Electro-Optic Transfer Function (EOTF). The OETF and the EOTF functions are not exactly the inverse of each other. This non-linearity compensates the differences in tonal perception between the environment of the camera and that of the display. The SDR legacy transfer functions called gamma functions are normalized in BT.709 [1] and BT.1886 [2]. For HDR video compression, two transfer functions were standardized: PQ [3] (Perceptual Quantizer) and HLG (Hybrid-Log-Gamma) [4]. Screen enhancements do not only focus on increasing the luminance range but also on the size of the color space it can cover. Indeed, the color space that a screen can display is limited by the chromatic coordinates of its three primary colors (Red, Green and Blue) corresponding to the three kinds of display photo-transmitters. The gamut, i.e., a subset of visible colors that can be represented by a colorspace, used to encode SDR images (normalized in BT.709 [1]) is not wide enough to cover the gamut that could be displayed by a Wide Color Gamut (WCG) screen. The BT.2020 [5] recommendation define how to handle this wider gamut. For the moment, there is no screen that can cover this gamut in its totality, but some are really close. The standard BT.2100 [6] sums up all the aforementioned HDR/WCG standards. For these new images and videos, new quality assessment metrics are required. Indeed, quality metrics are key tools to assess performances of diverse image processing applications such as image and video compression. Unfortunately, SDR image quality metrics are not appropriate for HDR/WCG contents. To overcome this problem, we can follow two strategies. The first one is to adapt existing SDR metrics to a higher dynamic range. For instance, instead of using a classical gamma transfer function, [PERSON] et al. [7] defined a transfer function, called the Perceptually Uniform (PU) function, which corresponds to the gamma non-linearity (defined in BT.1886 [2]) for luminance value between 0.1 and 80 cd/m\({}^{2}\) while retaining perceptual linearity above. This method can be used for any metrics using the luminance corrected with the gamma function, such as PSNR, SSIM [8], VIF [9], Multiscale-SSIM [10] (MS-SSIM). In this paper, the metrics using the Perceptually Uniform (PU) function have the prefix PU- (PU-PSNR, PU-SSIM). The second strategy is to design dedicated metrics for HDR contents. We can mention HDR-VDP2 [11; 12] for still images and HDR-VQM [13] for videos. Several studies have already benchmarked the performances of HDR metrics. In [14], the authors assessed the performances of 35 quality metrics over 240 HDR images compressed with JPEG XT [15]. They conclude that HDR-VDP2 (version 2.2.1 [12]) and HDR-VQM were the best performing metrics, closely followed by PU-MS-SSIM. In [16], the authors came to the conclusion that HDR-VDP2 (version 2.1.1) can be successfully used for predicting the quality of video pair comparison contrary to HDR-VQM. In [17], authors showed that HDR-VDP2, HDR-VQM, PU-VIF and PU-SSIM provide similar performances. In [18], results indicate that PU-VIF and HDR-VDP2 have similar performances, although PU-VIF has a slightly better reliability than HDR-VDP2 for lower quality scores.