## 3 Materials and Methods
### Hierarchical Segmentation Model for Crowdsourced Trajectories
#### 3.2.1 Category-Level Segmentation  
Previous studies proposed to use the velocity change, direction change and straight curve ratio of trajectory points to recognize the trajectory points at road intersections. However, vehicles that pass through residential areas, gas stations and parking lots may have the similar moving characteristics with those passing through road intersections. Hence, based on the trajectory data after adaptive density homogenization, we try to use three indicators, namely speed change \(\Delta v\), direction change \(\Delta\theta\) and turning distance ratio \(\Delta R\) to distinguish the road-intersection trajectory points from non-intersection trajectory points. For one trajectory consisting of \(m\) points, i.e., \(T=\{p_{1}\dots p_{m}\}\), the speed change \(\Delta v_{i}\) and direction change \(\Delta\theta_{i}\) of one point \(p_{i}\) are calculated according to Formula (5), respectively.  
\[\Delta v_{i} =\begin{cases}v_{i}-v_{i-1},&i>1\\ v_{i+1}-v_{i},&i=1\end{cases} \tag{5}\] \[\Delta\theta_{i} =\begin{cases}\theta_{i}-\theta_{i-1},&i>1\\ \theta_{i+1}-\theta_{i},&i=1\end{cases}\]  
Particularly, the turning distance ratio \(\Delta R\) is an indicator to measure the turning degree of one trajectory point, and its calculation process is shown in Figure 4. Firstly, the trajectory \(T=\{p_{1}\dots p_{m}\}\) was segmented as a bend hierarchical tree according to the method of [55], and the turning distance \(h_{i}\) of each trajectory point \(p_{i}\) and the baseline length \(bend_{i}\) of the bend segment were recorded, respectively. As shown in Figure 4, for trajectory point \(p_{2}\), the baseline length of its belonging bend segment was the Euclidean distance between \(p_{1}\) and \(p_{10}\), i.e., \(bend_{2}=\left\lfloor p_{1}p_{10}\right\rfloor\), and the turning distance \(h_{2}\) of trajectory point \(p_{2}\) is equal to the perpendicular distance from \(p_{2}\) to the baseline \(p_{1}p_{10}\). Then, the turning distance ratio of trajectory point \(p_{2}\) was calculated as \(\Delta R_{2}=h_{2}/bend_{2}\), so did other trajectory points. When the three indicators of speed change \(\Delta v\), direction change \(\Delta\theta\) and turning distance ratio \(\Delta R\) are all greater than the given thresholds \(T_{v}\), \(T_{a}\) and \(T_{dt}\), the track point will be identified as a candidate of road-intersection trajectory point.  
As illustrated in Figure 5, take the blue trace for example. The identified road-intersection trajectory points based on speed change, direction change and turning distance ratio are marked as red dots in Figures 5a, 5b and 5c, respectively. It can be seen that only using the indicator of speed change or direction change may lead to misidentifying some non-intersection trajectory points that suddenly change the speed or direction (see the cyan ellipse in Figure 5) and some local-turning trajectory points that pass through residential areas, gas stations and parking lots (see the cyan rectangle in Figure 5) as the candidates of road-intersection trajectory points. Comparatively, the turning distance ratio can efficiently  
Figure 4: Calculating the turning distance ratio based on bend hierarchical tree.  
distinguish irregular-turning trajectory points at specific places (e.g., gas stations) and regular-turning trajectory points at actual intersections.