# Quadratic Curve Fitting-Based Image Edge Line Segment Detection: A Novel Methodology
## 3 Edge Line Segment Extraction Based on Quadratic Curve Fitting
Conversely, the QF-LSD algorithm proposed in this paper removes the edge segments from the contour after extraction, which improves the algorithm's efficiency in identifying new edge segments within the remaining pixels. These measures effectively reduce the time cost of the QF-LSD algorithm. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Algorithm** & & & & **Number of Line Segments** & & & & **(a–h) Average Precision** & **(a–h) Average Recall** \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} LSD \\ method \\ \end{tabular} } & Serial Number & a & b & c & d & e & f & g & h & \\ \cline{2-10}  & True Positive & 67 & 133 & 130 & 194 & 190 & 161 & 569 & 154 & \\ \cline{2-10}  & False Positive & 74 & 139 & 154 & 230 & 201 & 183 & 620 & 223 & \\ \cline{2-10}  & False Negative & 109 & 207 & 223 & 329 & 295 & 268 & 887 & 257 & \\ \hline \multirow{4}{*}{
\begin{tabular}{c} QF-LSD \\ method \\ \end{tabular} } & Serial Number & a & b & c & d & e & f & g & h & \\ \cline{2-10}  & True Positive & 49 & 103 & 80 & 115 & 103 & 70 & 123 & 105 & \\ \cline{2-10}  & False Positive & 13 & 10 & 13 & 11 & 6 & 14 & 12 & 17 & \\ \cline{2-10}  & False Negative & 127 & 237 & 273 & 408 & 382 & 359 & 1333 & 306 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Evaluation metrics for line segment detection in undistorted images (unit: number of line segments). In conclusion, compared to traditional straight line segment detection algorithms, the QF-LSD algorithm proposed in this paper is highly suitable for edge segment extraction from images with substantial distortion. It does not depend on the camera's distortion parameters during edge detection, and it does not require a pre-processing of the distorted images. In addition, from the overall running time tested on the dataset, it is evident that the algorithm proposed in this paper achieves an average efficiency that is \(27\) times faster than traditional algorithms. Therefore, compared to traditional algorithms, it exhibits greater competitiveness and advantages in terms of real-time performance. ## 5 Conclusions

In this research, we introduced a method for image edge line segment detection that is founded on quadratic curve fitting. This approach capitalizes on the principle that a straight line in a three-dimensional space projects as a quadratic curve in a two-dimensional distorted image. The experiments demonstrate that, in addition to excellent detection accuracy, the method proposed in this paper is independent of camera distortion parameters and does not require a pre-correction of distorted images, thus exhibiting good practicality. Moreover, the algorithm's computational efficiency is \(27\) times faster than those of the traditional approaches. We firmly believe that this algorithm will contribute to improving the real-time performance of vision-based autonomous driving technologies. Conceptualization, R.Q., G.X., P.W. and Y.C. ; methodology, R.Q. and P.W. ; resources, G.X., Y.C. and W.D. ; software, R.Q. and P.W. ; formal analysis, R.Q., G.X. and P.W. ; writing--original draft, R.Q. ; writing--review and editing, G.X., P.W. and R.Q. All authors have read and agreed to the published version of the manuscript. This research was supported by the National Natural Science Foundation of China under grant numbers 62073161 and 61905112, as well as by the National Natural Science Foundation of China under grant number 62001198. Not applicable. The authors declare no conflict of interest.