# Line Structure Extraction from LiDAR Point Cloud Based on the Persistence of Tensor Feature
## 2 Related Works  
Line structure is the concise representation of 3D scenes, and the process relates to description of line features, segmentation and recognition of objects, and scene understanding of point cloud datasets [5; 6; 7; 8], etc. One of the heated research fields is edge map detection from depth or RBG image, to get the layout information of indoor scenes [2; 8]. The edge feature is computed by view relations between the 3D scene to the 2D image, using neural network or some image-based edge detection algorithms. Hence, it's also applied to the 3D point cloud [11; 21; 22]. [PERSON] et al. [21] proposed a 3D line segment detection method from the multi-view stereo: project 3D points into planar sets on different camera matrices and computing line relations based on 2D images, then remove false matching relations, cast line features back to the 3D space of point clouds, and get 3D line segments. Another similar line segment detection strategy is the work conducted by [PERSON] et al. [22]. The point cloud dataset is segmented into super planes based on region growing and merging. Then, points belonging to each plane are projected onto it, and 3D points in each plane become 2D images, followed by line extraction using 2D image contour extraction and least-square-fitting based line detection. In these line feature extraction methods, 3D line features can be duplicated or lost during dimensional transformation. However, line structure extraction directly from 3D point cloud can be conducted by an intuitive way. The first kind of intuitive method is the 3D shape detection from 3D point cloud, according to fitting error between the point cloud and the predefined geometric model. Hough transformation [13] is usually applied to shape detection situations, especially line segments, along with the random sample consensus (RANSAC) [12], which can extract geometric shapes from noisy point cloud data; besides, there are also some shape detection methods based on neural network that also works for the similar propose. Nevertheless, these methods depend on the predefined geometric model, which limited the capability of application. The other kind of intuitive method is the line structure extraction based on the 3D point cloud segmentation [1; 4; 23; 24], where the point cloud dataset is directly divided into different object groups, and the rim of geometric objects is extracted to construct edge structures. [PERSON] et al. [24] proposed an automatic 2D floorplan CAD generation method based on plane detection,and points segmented into floors are preserved to build 2D CAD line segments. For 3D line structure detection, [PERSON] et al. [4] proposed a line extraction method by segmenting point cloud into facets and extracting boundary of each facet to get the 3D line. Although the structure information can be further refined using some semantic information, lines are extracted under the assumption of predefined geometric model or rules, i.e., the straight-line restriction. There are also some neural-network-based point cloud segmentation methods [5; 7; 11] that can extract boundaries more precisely than the predefined geometric models or rules, but these methods need large amounts of training data. In addition, some post-processing operations are also applied to maintain connection relations of geometric structures. Another heated research field is line structure extraction from point clouds based on the line feature representation [25; 26]. Using the consecutive geometric feature contained in point cloud, line structures can be detected and traced along the consecutive direction of geometric feature [6; 9; 10; 27; 28], such as angle differences between the normal vector and its neighboring points, curvature computed from assumed point cloud surface, etc. These methods usually need normal vectors recorded in the point cloud dataset.