# Line Segment Matching Fusing Local Gradient Order and Non-Local Structure Information
## 1 Introduction  
Feature matching is important for many applications [1, 2, 3, 4, 5]. A typical matching method usually includes three steps. To be more specific, extract salient and stable features from the image first, then construct descriptors with the appearance of geometric features of the encoding neighborhood, and finally evaluate the correspondence between features by measuring the similarity between descriptors to achieve feature matching. At present, researches on point feature are most common. Compared with point features, there are more line features in industrial environments and indoor scenes. Moreover, line features contain more scene and object structure information, which can better reflect environmental information. Based on the information from line features, the structural details can be described more comprehensively, and the line features of the image can be supplemented [6]. Therefore, it is essential to further explore the characteristics of line features. More and more researchers have made extensive research on the effective and reliable correspondence between lines in recent years. The latest matching algorithms fall into two categories. The first type of matching algorithm uses individual lines to match line pairs. They use the local appearance, geometric features, etc. For instance, color is a typical appearance feature. The color histogram is used for generating a set of a line segment correspondence [7]. Gradient and intensity also are common local appearances. The mean-standarddeviation line descriptor (MSLD) is constructed by counting the gradient vectors of each sub-region in the four directions of the pixel neighborhood. The method enables the length of descriptors fixed and improves the robustness of descriptors [8]. However, MSLD did not deal with the image of scale changes, resulting in its failure in scale changes image pairs. To overcome scale changes and segment fragmentation, the line band descriptor (LBD) uses the line segments extracted in the image pyramid [9]. LBD is similar to MSLD. The gradient mean and standard deviation of the four directions of the line band are calculated. Based on LBD, an optical flow method is introduced to reduce candidate matching line pairs [10]. On one hand, this method improves real-time performance. On the other hand, it reduces reliability under illumination change scenes. Recently, more and more attention has been paid to the illumination robustness of the line segment matching methods. There are two main methods: the methods based on intensity order [11; 12] and the purely geometric ones [13]. The former introduces the local feature descriptor based on intensity order by constructing several concentric ring structures. The intensity order-based method has been proved to be effective. The latter is regularized using geometric constraints. This method improves the real-time performance and illumination robustness at the cost of reducing the matching line pairs. Another type of method that matches lines in individual incorporate point matching into line matching. Among them line-point invariant (LPI) is widely used to encode the information between the line and the neighboring point [14; 15]. LPI is robust to the mismatched line, and it is extended to line matching across wide-baseline views [16]. However, those approaches fail when there is a lack of points in the scenes, such as low-textured scenes. Another type of line segment matching method is matching in the group, which determines the corresponding line pairs by using the topological relationship and radiometric information [17; 18; 19; 20; 21]. [PERSON] et al. [17] propose a new dual-line matching method, which introduce the ray-point-ray (RPR) structure to describe line segment groups. To improve the matching accuracy of low-texture images under uncontrolled illumination, [PERSON] et al. [18] study a two-view line matching algorithm by combining geometric characteristics of lines. [PERSON] et al. [19] use the intersection context of a common plane line pair to match the line.