## 3 Experimental Results
### Quantitative Evaluation
#### 3.2.2 Objective Quantitative Evaluation  
Different multi-focus image fusion algorithms may exhibit significant differences across various evaluation metrics. To objectively and quantitatively analyze the fusion effect of the fusion algorithms, five evaluation metrics: standard deviation (STD) [32], information entropy (IE) [33], average gradient (AG) [34], structural similarity index (SSIM) [35], and nonlinear correlation information entropy (\(Q_{\text{nci}}\)) [36] are selected for the quantitative analysis of the fusion results. For the calculation of the full-reference metrics SSIM and \(Q_{\text{nci}}\), the fused image generated from the nine source images was evaluated by computing the structural similarity and nonlinear correlation information entropy between the fused image and each individual source image, followed by averaging all the results. The fusion results shown in Figures 17-22 are evaluated using these five criteria, with the results presented in Table 2, Table 3, Table 4, Table 5, Table 6, and Table 7, respectively. All evaluation criteria follow the principle that the larger the value, the better the fusion effect. The best performance is highlighted in blue, while the second-best performance is marked in orange. To evaluate the data reduction and feature loss during the down-sampling process, we additionally introduced an objective evaluation of the fused images obtained without down-sampling. The fused images without down-sampling are represented by \"Proposed \"*\". \begin{table}
\begin{tabular}{c c c c c c} \hline  & **AG** & **STD** & **IE** & **SSIM** & \(\mathbf{Q_{\text{n}}}\)**cie** \\ \hline CVT [27] & 31.9613 & 18.9883 & 5.61926 & 0.793585 & 0.804661 \\ DSIFT [25] & 32.2706 & 24.6258 & 5.6433 & 0.804718 & 0.806639 \\ DTCWT [28] & 31.3471 & 18.5883 & 5.54529 & 0.797095 & 0.804772 \\ DWT [30] & 30.4422 & 24.8534 & 5.64766 & 0.816291 & 0.806505 \\ GF [31] & 31.0241 & 24.0161 & 5.64718 & 0.819189 & 0.806654 \\ LP [26] & 33.4949 & 20.8382 & 5.60456 & 0.799082 & 0.805762 \\ NSCT [29] & 31.4199 & 18.7381 & 5.50142 & 0.807033 & 0.815033 \\ CNN [17] & 30.5334 & 18.3291 & 5.43541 & 0.843392 & 0.816261 \\ Proposed & 31.1584 & 24.3391 & 5.6408 & 0.82323 & 0.806973 \\ Proposed * & 31.1687 & 24.4215 & 5.6132 & 0.84312 & 0.809014 \\ \hline \end{tabular}
\end{table} 
Table 4: The evaluation results of the fused images shown in Figure 19 for housefly wing w.m. sample. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **AG** & **STD** & **IE** & **SSIM** & \(\mathbf{Q_{\text{n}}}\)**cie** \\ \hline CVT [27] & 19.3246 & 27.3442 & 6.07645 & 0.847888 & 0.810852 \\ DSIFT [25] & 20.7745 & 29.5445 & 6.22825 & 0.877708 & 0.815088 \\ DTCWT [28] & 18.3885 & 27.221 & 6.03925 & 0.85066 & 0.811746 \\ DWT [30] & 20.0187 & 30.5857 & 6.24273 & 0.88202 & 0.815357 \\ GF [31] & 20.187 & 29.7431 & 6.1772 & 0.87989 & 0.814651 \\ LP [26] & 20.7483 & 28.8912 & 6.14031 & 0.868556 & 0.811973 \\ NSCT [29] & 18.3428 & 27.2727 & 6.05721 & 0.856632 & 0.81205 \\ CNN [17] & 17.3523 & 27.1024 & 6.08908 & 0.876586 & 0.81058 \\ Proposed & 20.3064 & 29.8402 & 6.25856 & 0.828212 & 0.815447 \\ Proposed * & 20.3165 & 29.9202 & 6.25086 & 0.872812 & 0.82517 \\ \hline \end{tabular}
\end{table} 
Table 2: The evaluation results of the fused images shown in Figure 17 for ten-year pine stem c.s.