## 5 Experiments
### Ablation Study  
In addition to comparing with other methods, we also conducted experiments to evaluate the effectiveness of the main modules of our proposed method. Firstly, we performed ablation experiments to assess the effectiveness of the railway track reconstruction method. We manually annotated the images in our dataset and then compared the tracks reconstructed by the track reconstruction method with the tracks projected back onto the images. We conducted pixel-wise comparisons between the projected tracks and the manually annotated ground truth. We used two metrics, MPA (mean pixel accuracy) and MIoU (mean intersection over union), for quantitative analysis, as shown in Equations (17) and (18) [47; 48]. \[MIoU=\frac{1}{n+1}\sum_{i=0}^{n}\frac{Tp_{i}}{Tp_{i}+Fp_{i}+Fn_{i}} \tag{17}\]  
\[MPA=\frac{1}{n+1}\sum_{i=0}^{n}\frac{Tp_{i}}{Tp_{i}+Fn_{i}} \tag{18}\]  
We manually annotated the images in our dataset and then compared the tracks reconstructed by the track reconstruction method with the tracks projected back onto the images. We conducted pixel-wise comparisons between the projected tracks and the manually annotated ground truth. We used two metrics, _MPA_ (mean pixel accuracy) and _MIoU_ (mean intersection over union), for quantitative analysis. In the experiments shown  
Figure 17: Data Case 2. The intruding object is located at a distance and there are some errors in the semantic segmentation results. in Table 5, \"\(n\)\" represents the category, representing only two categories: \"track\" and \"non-track\". The meanings of \"\(Tp\)\", \"\(Fp\)\", and \"\(Fn\)\" are the same as in Equations (13)-(16). In accordance with Equations (17) and (18), the experimental results are shown in Table 5. \"Semantic Segmentation\" refers to the semantic segmentation results without any further processing. \"Polynomial Fitting\" represents fitting the entire track into a single polynomial curve. \"Piecewise Polynomial Fitting\" involves dividing the entire track into 10 segments and fitting each segment with a polynomial curve. \"Extreme Case Constraints\" indicates the utilization of prior information about the tracks to constrain the curves. \"Extension\" denotes the appropriate extension of the track when the distance between detected key points is insufficient. From Table 5, it can be seen that our post-processing methods effectively corrected the results of the semantic segmentation network. Furthermore, we obtained the equations representing the railway tracks as well as their projections in space, delineating the track zones. Table 6 illustrates the impact of different intrusion criteria for trackside objects on the experimental results. \"Height Criteria\" represents the minimum threshold for intrusion detection when scanning with a sliding window. From the experimental results in Table 6, it is found that setting the height threshold too low can increase false alarms, thereby affecting precision-related metrics, while setting it too high can lead to missed detections, negatively impacting recall-related metrics. Meanwhile, \"Density Criteria\" represents the threshold for the minimum point cloud density required to detect intrusion within a fixed window. We compared three settings: a fixed threshold of 100 points, 300 points, and the density threshold mentioned in the paper, which decays with distance. Based on the experimental results in Table 6, we believe that selecting a fixed height threshold of 0.4 m and a density threshold function that decays with distance is a reasonable choice. We conducted a quantitative analysis of the algorithm's resource utilization, the results of which are presented in Figure 18. It depicts the qualitative analysis results with a bird's-eye view perspective. It is evident that the tracks reconstructed by our algorithm align well with the real tracks and that intrusions within the track are accurately and promptly detected.