# Hierarchical Gradient Similarity Based Video Quality Assessment Metric
## 3 Experimental Results  
The effectiveness of the proposed VQA metrics is evaluated by the consistency between the objective scores and the subjective scores, including Mean Opinion Score (MOS) and Difference Mean Opinion Score (DMOS). The consistency is measured by the Pearson correlation coefficient (PCC) and the Spearman rank order correlation coefficient (SROCC). The LIVE [21] and the EPFL-PoliMI [22; 23] video quality assessment databases were used to evaluate the performance of the proposed VQA metric. There are 10 reference videos and 150 distorted videos in the LIVE database. All the video sequences are with the size of \(768\times 432\). There are four types of distortion: MPEG-2 compression, H.264 compression, and simulated transmission through error-prone IP networks and wireless networks. There are 12 reference videos and 144 distorted videos in the EPFL-PoliMI database. The video sequences have the resolutions of CIF and 4 CIF. The videos are encoded using H.264/AVC. The bit streams are corrupted by dropping packets with loss values of 0.1%, 0.4%, 1%, 3%, 5%, and 10% [22]. Results with the state-of-the-art VQA metrics, including PSNR, SW-SSIM [8], MC-SSIM [9], STSI [13], VQM [24], MOVIE [25], ST-MAD [26], STAQ [27], and VRF [28] are compared. Since the reference methods are platform-independent, we copied the values from the reference articles. The results of PSNR and Picture Quality Analyzer are quoted from [13]. The mapping function adopted for regression of the computational quality score is a four-parameter mapping function, which is also used in STSI [13]:  
\[f(x)=\frac{\beta_{1}-\beta_{2}}{1+exp(-\frac{x-\beta_{3}}{\beta_{4}})}+\beta_ {2}, \tag{8}\]  
where \(\{\beta_{1},\beta_{2},\beta_{3},\beta_{4}\}\) are the fitting parameters. Table 1 shows the PCC and SROCC of metrics performed on the LIVE database. It is observed that the proposed hierarchical VQA (HVQA) metric significantly outperforms all of the other metrics according to both indicators. The gradient similarity-based VQA metrics (HVQA and STSI) perform better than SSIM-based metrics such as SW-SSIM and MC-SSIM. This indicates that the change of the edge gradient is highly related to the degradation of the perceptual visual quality. This is reasonable for the areas V1 and V2 which are sensitive to the edge patterns. However, the proposed HVQA metric performs significantly better than STSI and ST-MAD. The reason is that degradations over the large regions (e.g., the packet-loss on the flat regions) cannot be represented efficiently by only the pixel-level gradient similarities. The similarities of area V4 and visual attention can improve the  
efficiency of the metrics. Furthermore, the proposed metric is compared with the optical flow-based VQA metric, MOVIE. HVQA significantly outperforms the MOVIE index (SROCC increment: 0.046), which performs the best in all of the comparison metrics. To evaluate the effectiveness of the gradient similarities at each visual area, different combinations are reported in Table 1. The combinations can be classified into three categories. The category I methods use only one of the three measures, including DP, VP, VA. The category II methods use two of the three measures, including DP&VP, VP&VA, DP&VA. The category III method uses all three measures--that is, HVQA. It is observed that the average SROCC and PCC of the category I methods are 0.757. Thus, the similarities of single measure are efficient to represent the degradation of perceptual visual quality. The category II methods significantly outperform the category I methods. This indicates that the combination of two measures will improve the performance. The measures in different visual areas are not with the complete duplicate functions in visual evaluations. Furthermore, the category III method HVQA outperforms any other combinations. That is, the proposed metric is the most efficient for perceptual video quality evaluation.