# Lightweight Infrared and Visible Image Fusion Based on Nested Connections and Res2 Net
## 5 Experiments and Results Analysis
### Ablation Study
#### 5.3.3 The Loss Function during the Second Stage of Training  
We kept the numerical values obtained in the first stage unchanged and conducted an ablation study on the balancing parameters of the loss function during the second stage of training. Referring to the conclusions drawn in reference[23], we first set \(\beta\) to 700 and conducted ablation experiments for both \(\omega_{\text{vi}}\) and \(\omega_{\text{ir}}\). The experimental results are presented in Table 3.  
From Table 3, it can be observed that the combination of \(\omega_{\text{ir}}=5\) and \(\omega_{\text{vi}}=3\) performs the best across almost all key performance indicators. This combination not only maintains the richness of image information and contrast but also effectively preserves the structural similarity, feature information, and visual fidelity of the images. Therefore, this combination is considered the optimal parameter setting, providing the best image fusion results.  
To find the optimal value of \(\beta\), which controls the balance between \(L_{\text{detail}}\) and \(L_{\text{feature}}\), we conducted an ablation study by setting \(\omega_{\text{ir}}\) to 5 and \(\omega_{\text{vi}}\) to 3. Due to the larger difference in magnitudes between \(L_{\text{detail}}\) and \(L_{\text{feature}}\), we experimented with \(\beta\) values of 100, 300, 500, 700, and 1000. The experimental results are presented in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\mu\) & \(\lambda\) & **EN** & **SD** & **SSIM** & **MI** & **FMI\({}_{det}\)** & **FMI\({}_{w}\)** & **VIF** \\ \hline \multirow{3}{*}{1} & 0.1 & 6.6176 & 41.9542 & 0.7021 & 13.4094 & 0.3125 & 0.4003 & 0.6629 \\  & 1 & 6.6268 & 42.1055 & 0.7113 & 13.4598 & 0.3317 & 0.4206 & 0.6831 \\  & 10 & 6.6341 & 42.2104 & 0.7168 & 13.4783 & 0.3354 & 0.4239 & 0.6876 \\ \hline \multirow{3}{*}{10} & 0.1 & 6.6194 & 41.9845 & 0.7081 & 13.4297 & 0.3177 & 0.4056 & 0.6687 \\  & 1 & 6.6331 & 42.1588 & 0.7170 & 13.4722 & 0.3380 & 0.4261 & 0.6888 \\  & 10 & 6.6404 & 42.2558 & 0.7195 & 13.4984 & 0.3411 & 0.4291 & 0.6922 \\ \hline \multirow{3}{*}{100} & 0.1 & 6.6430 & 42.2992 & 0.7129 & 13.4419 & 0.3233 & 0.4119 & 0.6742 \\  & 1 & **6.6659** & **42.6404** & 0.7186 & **13.8028** & **0.3511** & **0.4387** & **0.7065** \\  & 10 & 6.6593 & 42.4887 & 0.7217 & 13.5089 & 0.3461 & 0.4340 & 0.6969 \\ \hline \multirow{3}{*}{1000} & 0.1 & 6.6465 & 42.3545 & 0.7082 & 13.4724 & 0.3294 & 0.4166 & 0.6805 \\  & 1 & 6.6567 & 42.5179 & 0.7192 & 13.5304 & 0.3394 & 0.4263 & 0.6899 \\ \cline{1-1}  & 10 & 6.6654 & 42.6293 & **0.7254** & 13.5709 & 0.3448 & 0.4327 & 0.7019 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The average values of objective metrics obtained by setting different balancing parameters for the loss functions during the first stage of training.  
From Table 4, it can be observed that when \(\beta\) is set to 500, all metrics except for \(\text{FMI}_{w}\) are at their optimal values, with the value of \(\text{FMI}_{w}\) being only slightly below the optimum. Considering all key performance indicators comprehensively, \(\beta\) = 500 offers the best overall performance. Therefore, we set \(\beta\) to 500 in our experiments.