# Line Structure Extraction from LiDAR Point Cloud Based on the Persistence of Tensor Feature
## 1 Introduction  
Light detection and ranging (LiDAR) is a method to measure the distance between the object and the receiver based on the reflection of light and obtain massive points for the surface of an area instantly [1, 2, 3]. With high efficiency and versatile performance, it has been extensively applied in surveying and mapping, automatic driving, scene understanding [4, 5], etc. In recent years, LiDAR sensors have been equipped in consumer electronic devices, such as Kinect, iPhone, etc., which has made it more and more convenient to acquire point cloud data for common users, and many applications have been constructed [6, 7], such as line structure extraction, shape recognition, object detection and classification, and some high-level applications (scene understanding, simultaneous localization and mapping, etc.).  
With these easy-to-use LiDAR devices, plenty of point cloud datasets are provided, and abundant information can be extracted, such as geometric feature, semantic labeling, and scenario relations [8]. However, it also brings many problems in dealing with these redundant point cloud datasets, since not all points are needed, and it's difficult to extract the structure information, compress the data, and represent these redundant datasets by simple geometric structures [9, 10]. To solve these problems and obtain structure information, different studies have been conducted using, e.g., deep learning-based feature extraction methods and geometric model fitting methods [7, 8, 11, 12]. These methods either need predefined geometric models [12, 13] or large amounts of training datasets [7]. In addition, some post-processing operations are also needed to maintain connection relations of geometric structures, and results can be affected by the quality of the point cloud datasets [14, 15].  
(1) How to extract line information from the quality-unstable point cloud dataset collected by consumer electronic devices, and (2) how to construct line structures without predefined geometric models and manually selected training datasets, remain challenges.  
To address the issue, a line structure extraction method based on the tensor voting [16; 17] and the persistent homology theory [18; 19; 20] is proposed. The line structure extraction framework is designed for point cloud datasets collected by the iPhone-based LiDAR sensor. The line feature in each point is encoded by the tensor voting, then the line segment is represented as the connection of each point with the highest local line feature value, and the line structure is constructed from line segments along with their structure connections. Contributions are as follows: (1) We compute the line feature from the point cloud based on the tensor voting theory, decompose the tensor feature, and make a combination of different dimensional geometric features, to get the line candidate dataset. (2) We represent line feature by the tensor of the Morse-Smale complex, calculate the line structure from LiDAR point cloud based on the persistent homology theory, and extract the line structure using the connect relations of critical points. (3) We propose the unified framework, design the algorithm to extract line structure from point cloud collected by the iPhone-based LiDAR sensor, and make a comparison between line structure extraction results.  
The remainder of this paper is structured as follows. The next section gives an overview of works related to this paper. Section 3 provides a detailed description of the line structure extraction method based on the persistence of tensor feature, including tensor voting, tensor feature decomposition, critical point representation in the discrete Morse theory, and the line structure extraction. Experiments are conducted. The results are discussed in Section 4, followed by conclusions in Section 5.