# Line Segment Matching Fusing Local Gradient Order and Non-Local Structure Information
## 4 Experiment
### Comparative Experiments  
In this section, the image pairs in Figure 10 are compared with MSLD [8], LPI [15], and LJL [20], whose codes are obtained on the Internet [36]. MSLD and LPI are both classical line segment matching methods. The framework based on MSLD is still being improved [9,11]. LPI is improved based on LP [14] proposed by the original paper author [15], and it was extended in 2016 [16]. Therefore, these two methods still have the value of research and are widely used in the comparative experiments of the latest papers. In addition, we compare  
Figure 9: Parameter selection experiment. (**a–e**), respectively, show the influence of the setting of \(h\), \(B\), \(R\), \(M\), and \(V\) on our experiment. the LJL [20]. It is another type of method that matches line segments in the group. The comparative experiments compare three different types of line segment matching methods. All the line segments used are extracted through EDLines [23]. To evaluate line segment matching performance, three commonly used metrics are adopted: precision, recall, and F1-Measure. Figure 10: _Cont._ \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Value** \\ \hline \(h\) & the length of LSR & 45 \\ \(B\) & the number of sub-regions & 4 \\ \(R\) & the sampling radius & 5 \\ \(M\) & the number of groups & 3 \\ \(V\) & the number of anchor points & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters summary. According to Figure 9(c), the matching performance of the approach is close to LJL in most scenes. In the scene of large-scale change, the approach is lower than LJL. By analyzing Figure 9(a),b, the precision of the proposed method is as same as LJL. However, the recall of the approach is lower than LJL under these scenes, which limits the comprehensive matching performance of our approach. Both LJL and the proposed approach use the same method that matches lines in the image pyramids. However, LJL matches line segments in groups and the proposed method matches line segments in individuals. It is difficult to keep the appearance of the line segments unchanged during large-scale change so that LJL obtains more matched line segments. Figure 10 also shows our comparison with the other two methods. The proposed method outperforms MSLD and LPI in precision, recall, and F1-measure in eight pairs of images. Figure 9(c),d are image pairs with rotation. The matching precision of the proposed method is close to 1, while the recall is much higher than that of MSLD and LPI. This is mainly because our computation is based on a rotation-invariant local coordinate system. Secondly, our encoding order is based on the maximum gradient direction, which is also rotationally invariant. Finally, the adaptive sub-regions obtained using the intensity histogram are only intensity-dependent and are independent of image rotation. In the illumination changes image pairs (Figure 9(e),f), we still obtained an accuracy close to 1 and a high recall, with better performance than either of the other two methods. The main reason is that the gradient order does not change greatly when the illumination changes. MSLD based on direction estimation. Although illumination changes, its mean value will also change in different directions, as a result, more line segments cannot be correctly matched. LPI relies on line-point invariants. However, the endpoints of line segments extracted from image pairs will change when the illumination changes. This makes the invariants between line and point are unreliable. This unreliability is also evident in the image pairs of viewpoint changes and occlusion. LJL, MSLD, and LPI are among the best and most classic open source codes. They are widely used in comparative experiments in the recent studies. However, in order to prove that our method is competitive with the latest paper, we select two latest line segment matching methods for comparison. References [11; 22], they were published in 2020 and 2021.