## 3 Experiment  
To validate the method in this paper, the road intersections in an area were automatically extracted. The trajectory dataset was from Baidu Map navigation data for the Haizhou district of Lianyungang City in China. The data time covered the whole day of 1 January 2019; this dataset contained a total of about 5 \(\times\) 10\({}^{5}\) sampling points and about 5 \(\times\) 10\({}^{3}\) raw trajectories, and contained fields for vehicle identification, sampling time, longitude and latitude. The spatial distribution of all sampling points is shown in Figure 8.  
From the original trajectory dataset, 53,960 continuous trajectories were extracted, of which 25,373 were valid continuous trajectories. The maximum reconstruction error method was used to extract 28,399 straight-line segments from the valid continuous trajectory. These extracted straight-line segments are shown in Figure 9.  
The merged straight-line segments amount was 2502, only about 10% of the total amount of extracted straight-line segments; it not only reduced the amount of data to be calculated for the intersections, but also enhanced the structure of the road network represented by the individual line segments. These merged line segments are shown in Figure 10.  
Figure 8: Scatter of original GPS data. Figure 9: Extracted straight-line segments. When calculating the intersection points using the merged trajectories, we removed the short trajectories and the actual number of line segments involved in the intersection point calculation was 1243. The intersection of any two straight lines requires 1243 \(\times\) (1243\(-\)1)/2 (about 7.7 \(\times\) 10\({}^{5}\)) intersections. Through the bounding box filter and orthogonality filter, the intersection point calculation is reduced by 96.3%, requiring only 2.8 \(\times\) 10\({}^{4}\) calculations (of which the bounding box filter reduced the calculation by about 90% and the orthogonality filter reduced the calculation by about 6%). As the complexity of the filtering calculation is much less than that of the intersection calculation of straight-line segments and as multiple lines can be filtered simultaneously by vector operations, the total calculation time was reduced by 94.3%, which significantly improved the efficiency of the calculation. The final number of intersection points was 4273 and the spatial distribution of all intersection points are shown in Figure 11 as red dots. Finally, after clustering the calculated intersection points by spatial location, adaptive thresholding was used for intersection extraction and 65 intersections were extracted, with the results shown in Figure 12. The black crosses are extracted road intersections. Compared with intersection extraction methods based on features such as trajectory steering angles and stopping points, the method in this paper is less affected by trajectory sampling amount; it can identify intersections with lower sampling amounts and, at the same time, be well suited to the situation where the density of trajectories is unevenly distributed in a wide range of road networks. Figure 11: Scatter of intersection points. Figure 10: Merged straight-line segments. The real locations and number of intersections in the study area are shown in Figure 13, where the dots are the intersections successfully identified in this paper, but there were still some road intersections that were not identified (triangles) for the following reason: the road intersections were T-junctions and straight-line trajectories did not have direct intersection points. The square locations in the figure are the roundabouts and overpasses, respectively, which were misidentified as intersections, corresponding to the circular dashed boxed area in Figure 12.  
To further validate the method in this paper, the density peak clustering method based on vehicle turning point features proposed by GAO [11] was compared with the global threshold (DPCA). As can be seen from Table 1, the recognition accuracy of the method in this paper is better than the benchmark method.