## 4 Analysis of Experimental Results
### Evaluation Results  
To verify the statistical significance of the observed improvements, we calculated confidence intervals for the performance metrics (e.g., average initialization frames, false trajectory occupancy rates). We ran 60 iterations for each dataset and averaged the results to minimize random variations. The improvements in the MDF-clustering algorithm's performance were consistent across iterations, with 95% confidence intervals demonstrating that the differences are statistically significant. Average number of frames required for target stabilization initialization  
The number of stable initialization frames for each algorithm across different false alarm rates was counted, and the average stable initialization frames for each scenario were calculated. The results are shown in the following figures. Tables 4-6 and Figures 2-4 depict the average number of frames required for stable initialization by each algorithm at varying false alarm rates across three scenarios. The performance comparison reveals a consistent trend in the image curves. The MDF-clustering algorithm outperforms other algorithms in all scenarios and false alarm rates, reducing the number of stabilized initialized frames by 2.14, 0.87, 4.15, and 9.07 frames compared to the nearest-neighbor, Hough transform, intuition, and sliding-window methods, respectively. Notably, as the false alarm rate increases, this algorithm shows a more moderate growth rate in the average number of frames for stable initialization at 0.013, whereas other algorithms experience growth rates of 0.035, 0.039, 0.028, and 0.030, indicating a higher level of robustness and adaptability of the MDF-clustering algorithm. By counting the occupancy rate of false trajectories in each scenario and calculating the average occupancy rate of false trajectories for different algorithms in each scenario, the following figures are derived. Tables 7-9 and Figures 5-7 display the average false trajectory occupancy of each algorithm across three scenarios with varying false alarm rates. Through comparative analysis, the MDF-clustering algorithm exhibits the lowest false trajectory occupancy rates of 0.04%, 0.05%, and 0.04% in all scenarios, showcasing its superior performance  
Figure 3: The average number of stabilized starting frames for each algorithm with different false alarm rates in the trajectory crossing scenarios. Figure 2: The average number of stable starting frames for each algorithm with different false alarm rates in target leakage scenarios. in mitigating false initializations. On the other hand, while the nearest-neighbor, Hough transform, and sliding-window methods show moderate effectiveness in specific scenarios, their ability to suppress false trajectories diminishes as the false alarm rate increases. Hence, the MDF-clustering algorithm outperforms other methods in terms of tracking accuracy, especially in complex dynamic environments. Figure 5: Average false trajectory occupancy by algorithms with different false alarm rates in target leakage scenarios. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**False Alarm Rate** & **MDF Clustering** & **NN** & **Hough Transform** & **Intuitivenotion** & **Sliding Window** \\ \hline
3\% & 0.00\% & 84.52\% & 54.73\% & 78.63\% & 95.35\% \\
4\% & 0.00\% & 84.64\% & 55.36\% & 79.85\% & 95.48\% \\
5\% &  
Statistics on the average initialization rate of correct trajectories in each scenario and calculation of the average initialization rate of correct trajectories for different algorithms in each scenario lead to the following figure. Tables 10-12 and Figures 8-10 display the average initialization rate of each algorithm for correct trajectories across three different scenarios with varying false alarm rates. Upon examining the data presented in the figures, it is evident that the MDF-clustering algorithm maintains an average initialization rate of correct trajectories at 99.63%, 99.59%, and 99.53% in the respective scenarios.