# Composite Kernel Method for PolSAR Image Classification Based on Polarimetric-Spatial Information
## 4 Experiment
### Results  
#### 4.3.1. Flevoland Data Set  
As expected, we can see Figure 6a that, regarding polarimetric features alone, the building area and woodland area in black ellipses show large variation, i.e., pixels of the same land cover type may have very different scattering mechanisms, while pixels of different land cover types may have very similar scattering mechanisms. Moreover, in Figure 6b, morphological features alone may also lead to incorrect classification results, e.g., those two farmland areas in white ellipses that are classified as woodland area. Further, feature fusion via vector stacking also has some flaws; e.g., in Figure 6c, the farmland in yellow ellipses shows obvious variation. However, when combining those two features via composite kernels, the performance of the PolSAR image improves; e.g., in Figure 6d, in black ellipses, building and woodland can be clearly classified, in white ellipses, farmland can be classified, and in yellow ellipses, farmland can also be classified--much better than the vector stacking method. And Figure 6e is the reference map of Flevoland Data Set.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Class** & **City Area** & **Water** & **Vegetation** \\ \hline Number of Samples in the Reference Map & 391,407 & 315,320 & 135,508 \\ Number of Training Samples & 3914 & 3153 & 1355 \\ Number of Testing Samples & 387,439 & 312,167 & 134,153 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Number of samples of the San Francisco Bay data set used for quantitative evaluation.  
Figure 5: Accuracy versus weight \(\eta\) for Flevoland data set (**a**) and San Francisco Bay data set (**b**).  
From Table 5, we can see that using polarimetric features alone lead to low accuracy, especially in building areas and woodland areas. Morphological features account for the spatial structural information, which helps to produce more accurate classification results. However, this approach has a slightly low accuracy in farmland area because this approach only considers spatial information. The overall accuracy is distinctly boosted when fusing the two types of information together. The kappa coefficient also notably increases to 0.94. Admittedly, the overall accuracy of vector stacking is similar to that of the composite kernel approach, but it is worth noting that, when the vector stacking method is used, different features should be normalized before stacking. Further, the vector stacking approach does not take the inter-relation of different features into consideration.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & **Building** & **Woodland** & **Farmland** & **Water** & **Overall** & **Kappa** \\  & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **Accuracy (\%)** & **Coefficient** \\ \hline Only POL & 78.8 & 80.1 & 92.8 & 93.4 & 87.7 & 0.842 \\ Only MP & 94.6 & 92.7 & 92.3 & **98.9** & 93.8 & 0.909 \\ Vector Stacking & 95.2 & 93.7 & 96.2 & 97.4 & 95.7 & 0.920 \\ Composite Kernel & **95.6** & **94.3** & **96.2** & 98.8 & **96.1** & **0.942** \\ \hline \hline \end{tabular} Kappa Coefficient measures the percentage of data values in the main diagonal of the table and then adjusts these values for the amount of agreement that could be expected due to chance alone [40].  
\end{table}
Table 5: Classification accuracy measures on the Flevoland data set. The best performance in each column is shown in bold.  
Figure 6: Classification maps of Flevoland data with different methods. (**a**) Only polarimetric features. (**b**) Only morphological features. (**c**) Feature fusion via vector stacking. (**d**) Feature fusion via composite kernels. (**e**) Reference map.