## 5 Experiment
### Results of the Tracking of Contact Points
#### 5.1.2 Tracking Result Compared with State-of-the-Art Tracking Method  
We compared our tracking and positioning method with several state-of-the-art methods, including the positioning results of a single tracker and the results of combining the tracker with our closed-loop positioning framework. Through the following figure and the table, we can see that the positioning accuracy of the proposed method is significantly better than other methods, with 90% to 95% accuracy. In terms of the actual positioning, because of the existence of sub-pixel corner approximation, more than 90% of the successful positioning results can achieve a sub-pixel level feature point location. Accordingly, for the algorithm, even if there was a significant failure in the performance of TLD [24] or MOSSE [25] alone, combined with the closed-loop tracking framework provided by us this would represent a significant improvement in positioning accuracy. This shows that the closed-loop parameter adaptive algorithm proposed in this paper has universality in the selection of tracking methods for contact point tracking, which improves the accuracy greatly and achieves the optimum positioning method. Compared with ground-truthed high-precision positioning and the balance of positioning accuracy of diversified data  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **Speed (FPS)** & **Success Rate** & **Missing Rate** & **Error Rate** & **Accuracy (pixel)** & **Success\_50 Rate** \\ \hline global method & 67.62 & 31.96\% & 3.26\% & 64.77\% & 3.083 & 87.30\% \\ global+l1 & 88.48 & 89.63\% & 0.40\% & 9.97\% & 0.212 & 94.58\% \\ local+global+l1 & 247.50 & 69.55\% & 0.81\% & 29.64\% & 1.616 & 94.08\% \\ our method & 175.80 & 87.91\% & 3.31\% & 11.75\% & 0.399 & 95.89\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: The speed (frames per second) and accuracy of each tracking method.  
Figure 7: Illustration of tracking results in long-term datasets.  
testing, the effectiveness of our method for contact point positioning of trains running outdoors over a long time frame is verified.  
In Figure 8c,d, the stability of our method in dealing with changes in the external environment is more obvious. It can be seen that with an increased length of the dataset sequence, especially when illumination changes occur, many methods have different degrees of decline, and for some methods continuous tracking failure for the later frame sequence occurs. Even if we integrate those methods with the closed-loop model proposed by this paper, those tracking results also reduce the follow-up accuracy to a certain extent. However, it is obvious that our method can directly realize continuous tracking in most scenes, and a small number of tracking failures will reinitialize the tracker in a short time and adjust the template parameters accordingly to adapt to the current image. Thus, stable tracking and positioning for the whole data set is ensured. At the same time, it can be seen from the image that multiple trackers can maintain stable tracking when there is no obvious change in the external environment and light conditions. Therefore, the test effect with our dataset can show that with the original data set, the algorithm can achieve effective positioning over a much longer time when there is a large number of repeated scenes under long-term train operation, and the various light conditions in the test dataset used here, as well as the complexity of most images of train operation, show that our method has obvious advantages compared with other algorithms under the conditions of all-weather train operation. The proposed method proposed can meet the requirements of pantograph catenary contact state analysis in practical use.