## 4 Experiments and Results
### Inter-Class Separability and Intra-Class Consistency Validation Experiments  
#### 4.3.1 K-Means Clustering and ISODATA Clustering Test for Inter-Class Separability  
Region 2, region 3, region 4 and image B were selected as the regions to test the inter-class separability of the pseudo-TCT images. K-Means clustering was used for region 2, region 3 and region 4, and ISODATA clustering was used for region 4 and image B. The clustering effect is the best when the number of cluster centers K is generally slightly larger than the number of categories, so in this experiment, the K-Means were clustered into 10 categories and the number of iterations was set to 1. The categories in the clustering results were selected until the selected categories contained more than 99% of buildings and roads. The evaluation of clustering effects is usually performed with internal evaluation and external evaluation. Internal evaluation is usually used to evaluate the impacts of different algorithms or different ways of running algorithms on the clustering results based on the same raw data and is highly biased toward certain types of clustering models [45]. External evaluation requires knowing the category to which each pixel point belongs, which is very difficult in remote sensing image classification. Therefore, they cannot be used to evaluate the clustering results of this experiment. Since there are labels for buildings and roads, then the evaluation metrics commonly used in classification can be used to evaluate the clustering effects of buildings and roads. A better evaluation result can only indicate that the selected categories contain more buildings and roads and fewer background ground objects. The accuracy of the buildings and roads extracted by K-Means was evaluated using Accuracy, Precision, Recall, F1-score, IoU, Kappa, Recall of buildings and roads (1_Recall) and the number of categories. The image with the highest F1-score and the lowest number of selected categories is the one with the best separation of buildings and roads from the background ground objects. The evaluation metrics were defined as follows:  
\[\text{Accuracy}= \frac{\text{TP}+\text{TN}}{\text{TP}+\text{FN}+\text{FP}+\text{ TN}} \tag{11}\]  
\[\text{Precision}= \frac{\text{TP}}{\text{TP}+\text{FP}} \tag{12}\]  
\[\text{Recall}= \frac{\text{TP}}{\text{TP}+\text{FN}} \tag{13}\]  
\[\text{F1}= \frac{2\ \times\ \text{TP}}{2\ \times\ \text{TP}+\text{FP}+\text{ FN}} \tag{14}\]  
Figure 4: K-Means clustering results and vector labels for region 2, region 3, and region 4. (**a**) region 2 K-Means clustering result; (**b**) region 3 K-Means clustering result (**c**) region 4 K-Means clustering result (**d**) region 2 vector label (**e**) region 3 vector label; (**f**) region 4 vector label. \[\text{IoU}=\frac{\text{Precision}\ \times\ \text{Recall}}{\text{Precision}+\text{Recall}\ -\ \text{Precision}\ \times\ \text{Recall}} \tag{15}\]  
\[\text{Kappa}=\frac{\text{P}_{0}\ -\ \text{P}_{\text{e}}}{1\ -\ \text{P}_{\text{e}}} \tag{16}\]  
\[\text{1\_Recall}=\frac{\text{1\_TP}}{\text{1\_TP}+\text{1\_FN}} \tag{17}\]  
In the classification, true positives (TPs) and true negatives (TNs) denote the number of building and road pixels identified correctly and the number of background ground object pixels identified correctly, respectively, whereas false positives (FPs) and false negatives (FNs) denote the number of building and road pixels identified incorrectly and the number of background ground object pixels identified incorrectly, respectively. All evaluation metrics are calculated by macro-averaging, which calculates the corresponding evaluation metric for each category, and then averages the results together, so 1_Recall denotes the Recall of buildings and roads. The \(\text{P}_{0}\) in Kappa is the same as Accuracy and \(\text{P}_{\text{e}}\) is the sum of the product of the actual number of each class and the predicted number of each class divided by the square of the total number of samples. The range of Kappa is \([-1,\ 1]\).