The extraction of building information with terrestrial laser scanning (TLS) has a number of important applications. As the density of projected points (DoPP) of facades is commonly greater than for other types of objects, building points can be extracted based on projection features. However, such methods usually suffer from density variation and parameter setting, as illustrated in previous studies. In this paper, we present a building extraction method for single-scan TLS data, mainly focusing on those problems. To adapt to the large density variation in TLS data, a filter using DoPP is applied on a polar grid, instead of a commonly used rectangular grid, to detect facade points. In DoPP filtering, the threshold to distinguish facades from other objects is generated adaptively for each cell by calculating the point number when placing the lowest building in it. Then, the DoPP filtering result is further refined by an object-oriented decision tree mainly based on grid features, such as compactness and horizontal hollow ratio. Finally, roof points are extracted by region growing on the non-facade points, using the highest point in each facade cell as a seed point. The experiments are conducted on two datasets with more than 1.7 billion points and with point density varying from millimeter to decimeter levels. The completeness and correctness of the first dataset containing more than 50 million points are 91.8% and 99.8%, with a running time of approximately 970 s. The second dataset is Semantic3D, of which the point number, completeness and correctness are about 1.65 billion, 90.2% and 94.5%, with a running time of about 14,464 s. The test shows that the proposed method achieves a better performance than previous grid-based methods and a similar level of accuracy to the point-based classification method and with much higher efficiency.

Point cloud classification is a key step for three-dimensional (3D) scene analysis in terrestrial laser scanning but is commonly affected by density variation. Many density-adaptive methods are used to weaken the impact of density variation and angular resolution, which denotes the angle between two horizontally or vertically adjacent laser beams and are commonly used as known parameters in those methods. However, it is difficult to avoid the case of unknown angular resolution, which limits the generality of such methods. Focusing on these problems, we propose a density-adaptive feature extraction method, considering the case when the angular resolution is unknown. Firstly, we present a method for angular resolution estimation called neighborhood analysis of randomly picked points (NARP). In NARP, n points are randomly picked from the original data and the k nearest points of each point are searched to form the neighborhood. The angles between the beams of each picked point and its corresponding neighboring points are used to construct a histogram, and the angular resolution is calculated by finding the adjacent beams of each picked point under this histogram. Then, a grid feature called relative projection density is proposed to weaken the effect of density variation based on the estimated angular resolution. Finally, a 12-dimensional feature vector is constructed by combining relative projection density and other commonly used geometric features, and the semantic label is generated utilizing a Random Forest classifier. Five datasets with a known angular resolution are used to validate the NARP method and an urban scene with a scanning distance of up to 1 km is used to compare the relative projection density with traditional projection density. The results demonstrate that our method achieves an estimation error of less than 0.001° in most cases and is stable with respect to different types of targets and parameter settings. Compared with traditional projection density, the proposed relative projection density can improve the performance of classification, particularly for small-size objects, such as cars, poles, and scanning artifacts.