# Geometric Similarity Measurement Method for Micro Scene Generalization
## 3 Experiments and Analysis
### Quality Assessment of Micro Scene Generalization  
The main purpose of this part of the study was to verify the effectiveness of applying geometric similarity to assessing the quality of micro scene generalization. We chose Figure 17a-e as the original data, and small-scale maps were generated on this basis. The similarities between each micro scene were computed, and the experimental results are shown in Tables 2 and 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Micro Scene** & \begin{tabular}{c} **Shape** \\ **Similarity** \\ \end{tabular} & \begin{tabular}{c} **Direction** \\ **Similarity** \\ \end{tabular} & \
\begin{tabular}{c} **Position** \\ **Similarity** \\ \end{tabular} &
\begin{tabular}{c} **Micro Scene** \\ **Similarity** \\ \end{tabular} \\ \hline (a, a1) & 0.923 & 0.836 & 0.769 & 0.840 \\ (a, a2) & 0.818 & 0.742 & 0.692 & 0.749 \\ (b, b1) & 0.937 & 0.858 & 0.893 & 0.895 \\ (b, b2) & 0.812 & 0.786 & 0.676 & 0.756 \\ (c, c1) & 0.802 & 0.819 & 0.853 & 0.824 \\ (c, c2) & 0.721 & 0.730 & 0.747 & 0.733 \\ (d, d1) & 0.769 & 0.842 & 0.785 & 0.798 \\ (d, d2) & 0.697 & 0.715 & 0.703 & 0.705 \\ (e, e1) & 0.930 & 0.871 & 0.852 & 0.884 \\ (e, e2) & 0.865 & 0.822 & 0.739 & 0.807 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculation results produced by the method proposed in this paper. Figure 17: Generalization results of micro scenes: (**a–e**) original data; (**a1–e1**) the results of the first generalization; (**a2–e2**) the results of the second generalization. From the calculation results in Tables 2 and 3, we found that as the degree of generalization increased, the similarity between the two methods gradually decreased. However, the Fourier shape descriptor breaks the overall connection between the objects in the micro scenes and cannot express the direction and position changes in the process of generalization. Only the similarity of a single feature can be described through the Fourier shape descriptor; it cannot be directly applied to the quality evaluation of micro scene generalization. However, the proposed method compensates for this deficiency. In the map generalization process, we used the selection and merging methods. Some islands, buildings, and lakes were discarded, and smaller units were merged, which caused (1) the similarity of the second and third types of triangular nets to be reduced, and (2) the direction difference between composite features to increase and the similarity between micro scenes to decrease. In addition, the simplification method reduces the details, and the shape similarity is decreased. The details of the similarity changes between micro scenes are as follows:  
In the river + islands micro scene, such as in Figure 17a-a2,b-b2, the simplification operation of the river caused the main shape to change, and the changes in direction similarity and position similarity mainly occurred due to the deletion of islands. In Figure 17a-a2, the shape similarities dropped from 0.923 to 0.818; the position similarities of the first type changed from 0.847 to 0.759, and the second changed from 0.791 to 0.656. These calculation results are consistent with the actual situation. In the river + lakes micro scene, as shown in Figure 17c-c2, due to the generalization operation between river and lakes, the directional similarity decreased, and the changes in position similarity occurred due to the merge operation. In Figure 17c-c2, the directional similarity dropped from 0.819 to 0.730, and the positional similarities of the first type dropped from 0.864 to 0.679. The calculation results detected the changes in the position and direction before and after generalization. In the rivers + buildings micro scene, such as in Figure 17d-d2, the change in direction similarity was small, and the change was mainly due to the merge operation. For Figure 17d-d2, the change rate of directional similarity was 5.05%, and the positional similarities dropped from 0.785 to 0.703.