# Application of Image Segmentation in Surface Water Extraction of Freshwater Lakes using Radar Data
## 3 Results and Discussion  
### Confusion Matrix  
The overall accuracy before test set rectification was 83.88% (Table 2) while the overall accuracy after test set rectification increased to 92.11% (Table 3). The diagonal elements (left to right, top to bottom) in the matrix represent the number of correctly classified pixels of each class, for example, the number of ground truth pixels with a label of water that was actually predicted as water during classification. In contrast, the cross-diagonal elements represent misclassified pixels. A large loss of accuracy (40 out of 93) occurs at the pixels that are water in ground truth data but are classified into nonwater (Figure 2a). This happens for two reasons. First, many of these points are located at boundary pixels between two classes. Second, most points are isolated from their neighbor clusters. The boundary area has the mixed pixels problem which means both water and nonwater contribute to the observed spectral response of the pixel. In addition, the penetrating ability of C-band is unable to detect water hidden below rocks or vegetation cover where the normalized difference vegetation index (NDVI) is greater than 0.7 [47]. By contrast, there are only nine pixels that are misclassified into water while they are labeled as nonwater in ground truth data (Figure 2c). This is likely because the VV band can be affected by wind so that the wavy water surface will be classified into nonwater because of the diffuse refection. On the other hand, we examined each of those misclassified points and discovered that human errors in test data also compromise the overall accuracy. Twenty-two out of 40 nonwater test points and three out of nine water test points were rectified by using Landsat 8 imagery as a reference. As a result, the overall accuracy increased nearly 9%. Note that the rectification of the test set \(T\) does not influence the training process nor the estimation of the optimal threshold \(\hat{\theta}\) provided by the Otsu Method. Since the Otsu Method is an unsupervised learning algorithm, it does not depend on the label \(y\) of data for its training process. This property presents the feature of data corruption tolerance of the Otsu Method. In other words, corruption in the input data's label does not influence the actual training or performance of the Otsu Method. In addition, the test set \(T\) is only used for the statistical estimation or evaluation for the performance of the classification based on the estimation of optimal threshold \(\hat{\theta}\) from the Otsu Method. Furthermore, for factors influencing the accuracy, it is worth noting that the radar dB value with its corresponding label is linear nonseparable data [48]. In other words, there does not exist a hyperplane to clearly separate the dB value corresponding to the label of Water and the dB value corresponding to Nonwater. Because there exists two different regions or pixels \(i\) and \(j\), where \(i\
eq j\), such that they have the same dB value \(x_{i}=x_{j}\), but they are actually having different label \(y_{i}\
eq y_{j}\), one region corresponds to water and another region corresponds to nonwater. Such linear nonseparability may decrease the accuracy of this learning algorithm, which is unavoidable because the Otsu Method is trying to use a linear threshold to separate the data. One possible example of such region \(i\) and \(j\) is shown in the Figure 2b. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Predicted Label**} \\ \cline{3-5}  & & **Water** & **Nonwater** & **Total** \\ \hline \multirow{3}{*}{Actual Label} & Water & 53 & 40 & 93 \\ \cline{2-5}  & Nonwater & 9 & 202 & 211 \\ \hline \multicolumn{5}{c}{Total} & 62 & 242 & 304 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Confusion Matrix Before Test Set Rectification.