# Geometric Similarity Measurement Method for Micro Scene Generalization
## 3 Experiments and Analysis
### Similarity Measurement for Micro Scene Generalization  
The purpose of this part of the study was to verify the usability of the experimental methods in the detection of changes in the shape, direction, and position of micro scenes. We extracted five micro scenes (Figure 15a-e) from the remote sensing image: Figure 15a,b depicts the complex river section formed by islands and rivers, Figure 15c is the river system composed of rivers and lakes, Figure 15d depicts the urban waterfront, and Figure 15e shows the block composed of roads and buildings. Four basic operations of displacement, simplification, merging, and deletion in cartographic generalization were carried out sequentially. Similarities between each micro scene were computed, and the experimental results are shown in Figure 16.  
Figure 14: The original remote sensing image. Figure 16: _Cont_. Figure 15: Original data and generalization data: (**a–e**) the original data; (**a1–e1**) the data after the displacement operation; (**a2–e2**) the data after the simplify operation; (**a3–e3**) the data after the merge operation; and (**a4–e4**) the data after the delete operation. Figure 16a shows that the shape similarities of the five micro scenes obtained by the proposed method are all one, and the directional and positional similarities change considerably. Taking the set (a, a1) as an example, the positional similarities of the first and third types of triangulation are both one, indicating that the relative position of island to island and river bank to river bank has not changed; the similarity of the second type of triangulation is 0.740, indicating that the relative position between the islands and the river banks changed. The similarities calculated by the Fourier shape descriptor are all one, which is inconsistent with the actual situation. This is because Fourier calculates the similarities of line features and polygon features separately, ignoring the direction and position relationship between the elements of the micro scenes. Figure 16b provides the calculation result of the similarity between the original data and the simplified data. The shapes of the five micro scenes calculated by the proposed method changed markedly, but the changes in position and direction are small, which is consistent with the actual situation. The Fourier calculation results only showed that the similarities of the line group and polygon group reduced, and the specific operations could not be deduced from the calculation results. According to the calculation results of the proposed method, we found that the position similarity of the five micro scenes was relatively low, and the direction and shape similarities were high (Figure 16c). The Fourier calculation results showed that the similarity of line features did not change, but the similarity of polygon features changed considerably. The above results showed that the two methods are complementary under the merge operation. Figure 16: The similarity of the original data and generalization data calculated by the proposed method and the Fourier shape descriptor: (**a**) displacement operation; (**b**) simplify operation; (**c**) merge operation; (**d**) delete operation. From the calculation results of the proposed method, we found that the position similarity changes greatly, and the changes in shape and direction similarities were small (Figure 16d), which is in line with the characteristics of the deletion operation. Fourier detected that the object of the deletion operation was mainly polygon features, but in the (d, d1) set, we deleted both line features and polygon features, and the calculation results did not show the type of cartography operation. In conclusion, Fourier divides micro scenes into independent line features and polygon features to calculate similarity, which breaks the overall connection between the objects in the micro scenes and cannot express the direction and position changes in the process of generalization.