## 4 Conclusions  
This paper details a method combining SMLF energy and the IDPCNN model for side-scan sonar image fusion in the NSCT domain. Compared with the common fusion criteria, such as mean, STD, SML, and PCNN, the optimal selection of low frequency fusion criteria is analyzed using the aircraft debris data. The experimental results demonstrate that SMLF energy can effectively eliminate the pseudo-contour effect of block flow from the target edge. In addition, in order to analyze the high frequency fusion criteria more comprehensively, experiments are carried out with aircraft debris and rich geomorphic data, and maximum energy, local directional contrast, and PCNN are utilized. It is revealed that the IDPCNN model can extract more detailed feature information from the source image and reduce the ability of misjudgment. Finally, the superiority of combined fusion criterion in the NSCT domain is demonstrated by using the measured sonar data of the port. Multiple areas display that the overall and detailed information processed by the proposed method were effectively integrated, which reflect the complete target contour and rich features of seabed topography fluctuation. In addition, the fused image clearly shows the stitching conversion line left by the image registration. In the future, in order to ensure the image brightness on both sides is the same, the image fusion of eliminating the stitching conversion line is the next topic to be further studied.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Indexes** & **Technique 1** & **Technique 2** & **Technique 3** & **Technique 4** & **Proposed Technique 5** \\ \hline AG & 1.3041 & 1.3036 & 1.3045 & 1.2342 & 1.3042 \\ E & 3.9577 & 3.9626 & 4.0599 & 3.9346 & 4.0776 \\ FD & 1.4626 & 1.4614 & 1.4667 & 1.3894 & 1.4708 \\ RCE & 0.0641 & 0.0641 & 0.0730 & 0.1097 & 0.1290 \\ MI & 1.5594 & 1.5631 & 1.6243 & 1.5281 & 1.6661 \\ Q\({}^{AB\text{F}}\) & 0.4272 & 0.4259 & 0.4285 & 0.3922 & 0.4302 \\ SSIM & 0.8409 & 0.8390 & 0.8397 & 0.8313 & 0.8624 \\ IFQI & 0.1967 & 0.2001 & 0.2007 & 0.1606 & 0.2027 \\ WFQI & 0.6059 & 0.6100 & 0.6269 & 0.4535 & 0.5781 \\ EFQI & 0.2765 & 0.2760 & 0.2790 & 0.2649 & 0.2862 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Objective evaluation indexes of fused underwater port image.  
**Author Contributions:** [PERSON] and [PERSON] conceived the model methodology. [PERSON] helped to build the paper framework. [PERSON] collected the data. [PERSON] and [PERSON] wrote the initial draft. [PERSON] and [PERSON] revised the manuscript. All authors have read and agreed to the published version of the manuscript.  
**Funding:** The project was supported by the National Natural Science Foundation of China under Grant No. 41674015, 41901296.  
**Acknowledgments:** Data 1 is originated from the sonar imagery library of JaWS MARINE. Data 2 is derived from products in Chesapeake Technology's image library. Data 3 is collected from Edgetech JSF 4125 side-scan sonar data for the 2011 Port Area of Rhode Island, USA. The author thanked [PERSON] of Chesapeake Technology for his help and provision of his company's processing software for image pre-processing, which made an important contribution to the preliminary experiment.  
**Conflicts of Interest:** The authors declare no conflict of interest.