# An Enhanced Aircraft Carrier Runway Detection Method Based on Image Dehazing
## 4 Experiment Results and Discussions
### Runway Localization Analysis
#### 4.2.2 localization Details  
Indeed, taking the left runway line as an example (e.g., Figure 14(a)), each runway line consists of two white lines and several yellow lines intersecting with the white lines. For clarity of representation, we simplify the two white lines as two green lines and depict the centerline using a red line. The predicted runway is painted by the blue line. Figure 14: Results of runway detection algorithms before and after dehazing. In Figure 15, we utilize the UFLD algorithm to detect the centerline of the left and right runway. Considering that the deck of aircraft carriers and similar vessels is a flat surface, the height values of the detected points should be close to each other. Based on this, we reduce the multidimensional linear regression problem to a two-dimensional information regression problem. Hence, the predicted centerline can be written to:  
\[f(x,y,z)=w_{0}+w_{1}x+w_{2}y,z=w_{3}=height. \tag{13}\]  
where \(w_{0},w_{1},w_{2}\) are the weight coefficients of the centerline equation. \(z=w_{3}=height\) is the height value of the detected point. Consequently, slope \(k=\frac{w_{1}}{w_{2}}\) and intercept \(b=\frac{w_{1}}{w_{2}}\) can be calculated. To quantify the impact of dehazing on runway detection accuracy, we used the UFLD algorithm as the baseline and compared it with two other conventional runway line detection algorithms. We conducted ten experiments in total, calculating the average slope \(k\), intercept \(b\), and height \(h\) of the localization lines. The angle difference \(\Delta\theta\) and intercept difference \(\Delta b\) between the localization runway lines and the ground truth runway lines are used as evaluation metrics. The experimental results are shown in Table 6.  
After our calculations in the simulation environment, the actual equations for the centerlines of the left and right runway should be:  
\[ \begin{split}& f_{left}(x,y)=0.16300x+y-35.788523,z=6.0800000,\\ & f_{right}(x,y,z)=0.15632x+y-20.889669,z=6.0800000.\end{split}  \tag{14}\]  
From Table 6, it can be seen that the four listed methods show little error in the height direction compared to the ground truth, but the slope and intercept values show significant differences for the UFLD [5], Lanedet [39], and SAD [40] algorithms. For example, the slope and intercept of the left runway line localization by the UFLD algorithm are 0.15 and 9.25 m less than the ground truth, respectively, with an angle difference of 8.5456\({}^{\circ}\) between the localization and ground truth left runway lines. The slope and intercept of the right runway \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **Direction** & \(k\) & \(b\) & \(h\) & \(\Delta\theta\) & \(|\Delta b|\) \\ \hline \multirow{2}{*}{UFLD [5]} & Left & \(-0.01243\) & 45.047335 & 6.0641224 & 8.5456\({}^{\circ}\) & 9.258812 \\  & Right & \(-0.085547\) & 26.223431 & 6.0570601 & 3.9949\({}^{\circ}\) & 5.333762 \\ \hline \multirow{2}{*}{Lanedet [39]} & Left & \(-0.292449\) & 22.275809 & 6.0754075 & 7.0437\({}^{\circ}\) & 13.51271 \\  & Right & \(-0.066909\) & 30.247141 & 6.0607728 & 5.0566\({}^{\circ}\) & 9.357472 \\ \hline \multirow{2}{*}{SAD [40]} & Left & \(-0.269742\) & 26.614948 & 6.0958085 & 5.8380\({}^{\circ}\) & 9.173575 \\  & Right & \(-0.107914\) & 25.097884 & 6.0965721 & 2.7254\({}^{\circ}\) & 4.208215 \\ \hline \multirow{2}{*}{ours (UFLD + dehazed)} & Left & \(-\textbf{0.139172}\) & **37.652321** & **6.0611483** & **1.3347\({}^{\circ}\)** & **1.863798** \\  & Right & \(-\textbf{0.15732}\) & **20.937649** & **6.0613821** & **0.0559\({}^{\circ}\)** & **0.047980** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of localization results for each algorithm’s performance. Figure 15: The predicted result by UFLD. line localization by the UFLD algorithm are approximately 0.07 and 5.33 m less than the ground truth, respectively, with an angle difference of 3.9949\({}^{\circ}\) between the localization and ground truth right runway lines.