## 4 Experiments
### Ablation Study
#### 4.4.1 The Effects of the Features Fused in the CMFFM  
The Cross-Modality Feature Fusion Module (CMFFM) is crucial for pansharpening. As a result, our ablation study evaluates various implementations of CMFFM within the Dual Cross-Modality Fusion Network (DCMFN). The detailed architectures are illustrated in Figure 9, showcasing four different methods for fusing a pair of features:  
* PAN-Fused and MS (P-F & M) As illustrated in Figure 9a, the first method involves concatenating the PAN feature with the fused feature. This approach allows details from the features of the PAN to be added to the fused features. Meanwhile, the MS features are directly input into the CAB module without concatenation with the fused features. The computation can be expressed as follows: \[F_{1}=[CA(F_{PAN},F_{Fused});CA(F_{MS})]\] (4)
* PAN and MS-Fused (P & M-F) As is shown in Figure 9b, the second implementation involves concatenating the MS feature with the fused feature. In this implementation, the fused feature is integrated alongside the MS feature to improve the richness of the detailed information. Conversely, the PAN features are directly input into the CAB module without concatenation with the fused features. The computation can be expressed as follows: \[F_{2}=[CA(F_{PAN});CA(F_{MS},F_{Fused})]\] (5)
* PAN-MS and PAN-MS (P-M & P-M) As illustrated in Figure 9c, the modality features are extracted not only from MS but also from PAN through concatenation, facilitating the subsequent integration of these cross-modality features into the reconstruction image. The calculation is \[F_{3}=[CA(F_{PAN},F_{MS});CA(F_{MS},F_{PAN})]\] (6)
* PAN-Fused and MS-Fused (P-F & M-F) (ours) As depicted in Figure 9d, the modality features of MS and PAN are derived by integrating the PAN feature and MS feature with the fused feature. This approach facilitates the subsequent fusion of these two cross-modality features into the reconstruction image. The calculation is \[F_{4}=[CA(F_{PAN},F_{Fused});CA(F_{MS},F_{Fused})]\] (7)The results of the four architectures are presented in Table 4. In Tables 4 and 5, we just show the average values at first to keep it simple. We perform statistical analyses like \(t\)-tests and F-tests to check the significance of differences between groups. The \(p\)-values are below 0.05, so the results are statistically significant. Both the PAN-Fused and MS, and MS-Fused and PAN approaches enhance the performance relative to the basic concatenation baseline, whose structure is shown in Figure 9c. However, the performance of the PAN and MS-Fused strategy is comparatively lower. In addition to \(D_{\text{S}}\), the best results are achieved by integrating these two strategies of cross-attention, which we designate as DCMFN.  
In the cross-attention model, the results demonstrate that information exchange among different modalities plays a significant role in producing enhanced fusion representations, which implies that the CMFFM significantly enhances the overall effectiveness.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Modules** & **P-F \& M** & **P \& M-F** & **P-M \& P-F \& M-F (Ours)** \\ \hline SAM \(\downarrow\) & 1.4716 & 1.5907 & 1.6050 & **1.4240** \\ ERGAS \(\downarrow\) & 1.3011 & 1.5063 & 1.5103 & **1.2587** \\ Q2N \(\uparrow\) & 0.8900 & 0.8782 & 0.8751 & **0.8924** \\ CC \(\uparrow\) & 0.9789 & 0.9737 & 0.9736 & **0.9901** \\ D\({}_{\lambda}^{\text{K}}\downarrow\) & 0.0789 & 0.0806 & 0.0931 & **0.0786** \\ D\({}_{\text{S}}\downarrow\) & 0.0535 & **0.0449** & 0.0636 & 0.0529 \\ HQNR \(\uparrow\) & 0.8713 & 0.8712 & 0.8492 & **0.8727** \\ \hline \end{tabular}
\end{table}
Table 4: Quantitative results from the ablation studies are presented as follows. This table shows the results of various metrics from the ablation studies, with performance comparisons across different configurations. The best results are highlighted in bold.  
Figure 9: Four different ways to implement the CMFFM. (**a**) PAN-Fused and MS, (**b**) PAN and MS-Fused, (**c**) PAN-MS and PAN-MS, and (**d**) PAN-Fused and MS-Fused (ours).