## 2 Related Work  
There are numerous objective quality metrics described in the literature. Many of these methods can properly mimic the behavior of the human visual system in typical image and video processing applications, e.g., several PSNR-based metrics: IV-PSNR (immersive video peak signal-to-noise ratio) [4], CS-PSNR (color-sensitivity-based combined PSNR) [5], PSNR-HA (modified PSNR, which considers the human visual system properties and the change in contrast and mean value), or PSNR-HMA (PSNR-HA, which additionally considers the visual masking of discrete cosine transform coefficients) [6]; metrics based on trained models such as VMAF (video multi-method assessment fusion) [7], VIF (visual information fidelity) [8], LPIPS (learned perceptual image patch similarity) [9], or SFF (sparse feature fidelity) [10]; metrics based on an idea of measuring the structural similarity of images: SSIM (structural similarity index) [11], MS-SSIM (multi-scale SSIM) [12]; the ones based on image feature similarity, e.g., FSIM (feature similarity index) [13], and metrics utilizing temporal information of video sequences [14; 15; 16]. All the abovementioned methods were designed for assessing the quality of typical, two-dimensional video; therefore, they are not optimal for video systems that allow the user to look around (360 video, 3 DoF--3 degrees of freedom--systems [1]) or navigate within an acquired scene (immersive video systems). Visual quality assessment of 360 videos is widely studied [17], and many efficient quality metrics were proposed. For instance, in [18], the authors have proposed the OV-PSNR metric, integrating both spatial and temporal aspects of distortions and focusing on temporal eye fixation analysis. In [19] and [20], the visual quality assessment is based on neural networks and is focused on the influence of projection of the 360 video into the view watched by a viewer [19] or the influence of viewing directions [20]. Some research focuses on adapting existing methods (e.g., VMAF) to 360 video [21]. However, 360 video systems do not provide a full immersion of the user into the scene, as they do not provide motion parallax, which is inconsistent with human visual perception and leads to visual discomfort [22]. Immersive video introduces the possibility of changing the position of the viewer, which is enabled by view rendering [3]. Most state-of-the-art metrics cannot accurately assess immersive video quality with its typical, rendering-induced distortions [4], such as a slight shift of reprojected pixels and different color characteristics of input views (cf. Section 3). Most of the existing methods designed for DIBR are computationally complex (e.g., require SIFT--scale-invariant feature transform--for detection of disoccluded areas [23] or perform an exhaustive search for similar regions in compared images [24]), designed for scenarios much simpler than immersive video, e.g., stereoscopic perspective [25; 26; 27; 28; 29] or omnidirectional video [30; 31; 32; 33]. The approaches to stereoscopic and omnidirectional video quality assessment vary significantly across the different studies. For instance, in [25], the authors introduce a novel blind stereoscopic video quality metric, which incorporates measurement of the disparity entropy for assessing the binocular vision quality. In [26], the authors focus on the efficiency of the proposed metric in terms of processing time, developing a real-time metric designed for stereoscopic video streaming scenarios. Otherapproaches can require the analysis of 3D saliency maps, both sparse [27] or dense [29], and the metrics designed for stereoscopic perspective video are often based on machine learning techniques [28,29]. The saliency map analysis, as well as neural networks, can also be used for omnidirectional video quality assessment [31]. Other state-of-the-art approaches are focused on the analysis of the behavior used in the omnidirectional scene [32,33].