## 5 Conclusions  
No-reference image quality assessment is a basic problem in the field of computer vision and also a research hotspot. The research community has put a lot of effort into building high-performance models. Despite the strides made in this field, there is still much room for improvement. To this end, we proposed a novel blind image quality index for synthetic and authentic distortions with hierarchical feature fusion. The underlying idea of the proposed metric was to simulate the hierarchical information processing mechanism and the local and global combination mechanism of the human visual system. A flexible vision transformer framework was used to extract the preliminary features, and then an efficient fusion module was proposed to integrate the features of different scales. Unlike  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Training** & **CSIQ** & **TID2013** \\
**Testing** & **TID2013** & **CSIQ** \\ \hline DIIVINE [61] & 0.417 & 0.583 \\ BRISQUE [22] & 0.461 & 0.586 \\ BLIINES-II [29] & 0.453 & 0.593 \\ HOSA [28] & 0.341 & 0.609 \\ WaDIaM-NR [24] & 0.315 & 0.683 \\ PQR [35] & 0.524 & 0.637 \\ DBCNN [39] & 0.520 & 0.807 \\ HFNet & **0.531** & **0.823** \\ \hline \hline \end{tabular}
\end{table}
Table 6: The SRCC of the cross-database tests on the synthetic distortion.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Training** & **LIVEC** & \multicolumn{2}{c}{**BID**} & \multicolumn{2}{c}{**KonIQ-10k**} \\
**Testing** & **BID** & **KonIQ** & **LIVEC** & **KonIQ** & **LIVEC** & **BID** \\ \hline PQR [35] & 0.714 & 0.757 & 0.680 & 0.636 & 0.770 & 0.755 \\ DBCNN [39] & 0.762 & 0.754 & 0.725 & 0.724 & 0.755 & 0.816 \\ HyperNet [25] & 0.756 & 0.772 & 0.770 & 0.688 & **0.785** & 0.819 \\ HFNet & **0.807** & **0.780** & **0.781** & **0.734** & 0.765 & **0.820** \\ \hline \hline \end{tabular}
\end{table}
Table 7: The SRCC of the cross-database tests on the authentic distortion.  
the previous quality metrics, not only were the features at the highest level used for quality regression, but the features at every level were used for quality regression. In order to more realistically simulate human observation, local features and global features were extracted and input into the quality regression network. Sufficient experimental results showed that the proposed metric was superior to the compared algorithms in terms of both the prediction performance and the generalization ability.  
Although the proposed method achieved good performance, it cannot indicate where and what kind of distortion exists in the distorted image, which is of great concern in the industrial community. Therefore, we will study how to construct a model that can mark the distortion region and type in the future. In addition, the hierarchical feature fusion methods that are usually used on top of deep architectures, such as DCA and CCA, will be explored for more robust performance. Finally, time complexity is important for an algorithm, and it is very much expected in applications. To this end, studying lightweight CNN architectures (e.g., PCANet [65] and MDFNet [66]) will help improve the efficiency of the algorithm.  
Investigation, B.H.; Methodology, L.H. and T.Z.; Resources, W.Y.; Supervision, B.H.; Writing--original draft, L.H.; Writing--review and editing, J.P. All authors have read and agreed to the published version of the manuscript.  
This work was supported partially by the Science and Technology Research Program of Chongqing Municipal Education Commission under Grants KJQN202201904, KJQN202100628, KJQN202200638, and KJQN201901908 and partially by the National Natural Science Foundation of China under Grant 62101084.  
Not applicable.  
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.  
Data Availability Statement: Not applicable.  
The authors declare no conflict of interest.