# A Learning-Based Image Fusion for High-Resolution SAR and Panchromatic Imagery
## 3 Results and Discussion
### Validation of Random Forest Regression  
As mentioned above, the RF regression models were constructed independently for each class, thus, the predictive models were verified separately. The classification images of each site are shown in Figure 10, and the characteristics of each class are as follows: Classes 1 and 2 represent areas with high backscattered intensity and double bounce scattering characteristics, because of the artifacts in the SAR image, where the intensity of class 2 is lower than that of class 1. Classes 3 and 4 include the specular reflection characteristics of the SAR image and bare land or those of the high-brightness roofs in the panchromatic image, where class 4 is brighter than class 3 in the panchromatic image. Classes 5 and 6 are composed of vegetation, roads, or low buildings in the panchromatic image; the low backscattered intensity characteristics of class 5 and diffuse scattering characteristics of class 6 are shown in the SAR image.  
The evaluation was performed visually with a scatter plot and quantitatively using the coefficient of determination (\(R^{2}\)), as shown in Figure 11 and Table 3. The scatter plot represents the correlation between data, and there are high correlations among all classes regardless of the site. In particular, Site 1 showed a high correlation among classes 1, 2, and 4, whereas Sites 2 and 3 showed a high correlation between classes 1 and 4. The other classes showed a moderate bias but a sufficiently high correlation. Considering \(R^{2}\), a high value of which indicates the high precision and accuracy of the model, similar  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Site** & **Method** & **FQI** & **AG** & **SF** \\ \hline \multirow{4}{*}{Site 1} & Proposed method & 0.8489 & 18.5836 & 10.1753 \\  & ATWD & 0.7638 & 14.8698 & 7.5353 \\  & DWT & 0.7865 & 14.3675 & 7.0175 \\  & NSTC & 0.5775 & 20.0136 & 8.4952 \\  & NST-PCNN & 0.6499 & 20.4469 & 9.2749 \\ \hline \multirow{4}{*}{Site 2} & Proposed method & 0.8199 & 33.5763 & 17.0272 \\  & ATWD & 0.7921 & 21.1922 & 11.0085 \\  & DWT & 0.8146 & 21.1521 & 10.4409 \\  & NSTC & 0.6007 & 28.738 & 12.3708 \\  & NST-PCNN & 0.6527 & 30.0487 & 13.6092 \\ \hline \multirow{4}{*}{Site 3} & Proposed method & 0.7936 & 29.9653 & 15.7126 \\  & ATWD & 0.7659 & 19.2859 & 10.3327 \\ \cline{1-1}  & DWT & 0.7891 & 20.2947 & 10.2658 \\ \cline{1-1}  & NST & 0.5911 & 25.9567 & 11.4126 \\ \cline{1-1}  & NST-PCNN & 0.6468 & 27.9568 & 12.9668 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Evaluations for the image fusion methods (FQI: fusion quality index, AG: average gradient, SF: spatial frequency, ATWD: a-trous wavelet decomposition, DWT: discrete wavelet transforms, NST: non-subsampled contourlet transform, NST-PCNN: non-subsampled contourlet transform-pulse couple neural network).  
Figure 10: Classification images: (**a**) Site 1, (**b**) Site 2, (**c**) Site 3.  
tendencies are observed, as follows. For all sites, classes 1 and 4 had the highest \(R^{2}\), and both exhibited similar properties. However, for class 2, Sites 2 and 3 were somewhat lower than Site 1, which is thought to be because of the complex structure of many buildings. Furthermore, classes 3, 5, and 6 involved several characteristics, which can lead to relatively low \(R^{2}\) values. However, the overall results are reasonable; thus, the robustness of the constructed modes is confirmed.  
Figure 11: _Cont._