# Multi-Scale Twin Networks for Coastal Zone Change Detection in Remote Sensing Imagery
## 4 Experiment  
### Evaluation Indicators  
According to the widely used evaluation schemes in change detection research, the following evaluation metrics are used in this paper: Intersection over Union (IoU), precision, recall, F1 score, overall accuracy (OA), and the Kappa coefficient. IoU is commonly used to measure the overlap between the detected change region and the true change region, and it is the primary reference metric in this paper. Precision refers to the proportion of the detected change region that is correctly identified as changed. Recall indicates the proportion of the actual change regions successfully detected by the algorithm. The F1 score combines precision and recall, and a high F1 score indicates a good balance between precision and recall, considering both the accuracy and completeness of the detected change regions.  
Overall accuracy (OA) represents the proportion of correctly classified samples in a change detection task, i.e., the ratio of the total number of correctly classified samples to the total number of samples. The Kappa coefficient measures the consistency between the algorithm's detection results and the ground truth.  
All the above metrics are based on confusion matrices, which help analyze classifier performance by showing the relationship between the actual and predicted categories. The confusion matrix typically contains the following four key metrics:  
* True Positives (TP): the number of samples where the actual change class is correctly predicted as the change class;
* True Negatives (TN): the number of samples where the actual non-change class is correctly predicted as the non-change class;
* False Positives (FP): the number of samples where the actual non-change class is incorrectly predicted as the change class;
* False Negatives (FN): the number of samples where the actual change class is incorrectly predicted as the non-change class.  
The structure of the confusion matrix is illustrated in Table 1.  
The formulae for these evaluation indicators are shown below:  
\[\text{IoU}=\frac{\text{TP}}{\text{TP}+\text{FP}+\text{FN}} \tag{22}\]  
\[\text{Pr}=\frac{\text{TP}}{\text{TP}+\text{FP}} \tag{23}\]  
\[\text{Rc}=\frac{\text{TP}}{\text{TP}+\text{FN}} \tag{24}\]  
\[\text{F1}=\frac{2\times\text{Pr}\times\text{Rc}}{\text{Pr}+\text{Rc}} \tag{25}\]  
\[\text{OA}=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{TN}+\text{FP}+\text{FN}} \tag{26}\]  
\[\text{Kappa}=\frac{\text{P}_{\text{o}}-\text{P}_{\text{e}}}{1-\text{P}_{ \text{e}}} \tag{27}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Predicted Change Class** & **Predicted Change Class** \\  & **(Change)** & **(No Change)** \\ \hline Actual Change Class & TP & FN \\ Actual No Change Class & FP & TN \\ \hline \hline \end{tabular}
\end{table}
Table 1: Confusion matrix.  
where \(P_{o}\) denotes the case in which the model prediction and the actual are in agreement, i.e., the OA. \(P_{e}\) refers to the probability that the predicted outcome will be in agreement with the actual case, assuming random guessing, calculated as follows:  
\[P_{e}=\left(\frac{(TP+FP)\times(TP+FN)}{N^{2}}\right)+\left(\frac{(FN+TN)\times( FP+TN)}{N^{2}}\right) \tag{28}\]  
where \(N\) denotes the total number of samples, calculated as:  
\[\text{N}=\text{TP}+\text{FP}+\text{TN}+\text{FN} \tag{29}\]