# Hierarchical Fine Extraction Method of Street Tree Information from Mobile LiDAR Point Cloud Data
## 2 Materials and Methods
### Regional Growth Algorithm for Gaussian Distribution (GDRG) to Extract Trunks  
The trunk portion of the street tree in candidate point \(T1\) has strong vertical geometric properties, which can be used to extract part of the trunk point cloud and locate the  
Figure 2: Projection differences of different ground objects (the yellow border represents the outer rectangle of the clusters). position of the trunk. The verticality eigenvalues are calculated via principal component analysis (PCA) [52; 53] of the global point cloud and solution for the eigenvalues, which are calculated as follows (3). \[Linearity=\frac{\lambda_{1}-\lambda_{2}}{\lambda_{1}}, \tag{3}\]  
\(Linearity\) indicates the verticality eigenvalue of each point in the range 0 to 1; \(\lambda_{1}\) and \(\lambda_{2}\) (\(\lambda_{1}>\lambda_{2}\)) are the first and second eigenvalues, respectively. The candidate point set includes a large number of trees and some point clouds containing pole parts such as streetlights and billboards. Calculating the vertical linear features can extract the pole parts of different infrastructures and filter part of the point cloud set that does not have vertical features (such as cars and canopy of trees). The verticality of the point cloud is calculated based on the neighborhood points of each point, then some points are incorrectly represented as vertical, e.g., the points in the tree canopy have irregularity and the vertical feature values of some points are calculated to meet the threshold, or some points in the tree trunk are lacking of extraction from the same trunk because they are obscured and subject to neighborhood noise points that do not reach the threshold. The candidate point set \(T1\) was extracted after verticality to obtain a point set with missing points in the pole part of the infrastructure point cloud and to extract an incomplete trunk point set. This section proposes a method for finding missing rod points in the extracted point set from the original point cloud data, a region growth algorithm based on Gaussian distribution (GDRG). The extracted points are used as seed points to find the points that match the rules in the original point cloud through the Gaussian distribution law, and the grown points are clustered and merged into a single trunk point set. The GDRG algorithm is an interval estimation method that focuses on the points within the confidence interval of the Gaussian distribution in the sample point set as the candidate seeds for growth. Confidence interval estimation for a Gaussian distribution involves creating an interval containing the parameters to be estimated for the normal distribution of the sample at a given probability value. This confidence interval \([a,b]\) is an interval of values derived from the sample that may contain the overall parameters and is usually obtained by adding or subtracting the estimation error from the sample statistic. The lower and upper limits of the confidence interval \(a\) and \(b\) are calculated in (4). \[ \begin{cases}a=\overline{x}-Z_{\frac{a}{2}}\frac{\sigma_{Z}}{\sqrt{n}},\\ b=\overline{x}+Z_{\frac{a}{2}}\frac{\sigma_{Z}}{\sqrt{n}}\end{cases} , \tag{4}\]  
where \(\overline{x}\) denotes the mean of the estimated parameters; \(Z_{a/2}\) denotes the value in the table of normally distributed \(Z\) values at a confidence level of \(a\); \(n\) denotes the number of samples; \(\sigma_{Z}\) denotes the standard deviation of the sample, reflecting the degree of dispersion of the whole sample from the sample mean; and \(\frac{\sigma_{Z}}{\sqrt{n}}\) is the standard error of the sample. The seed points are selected from the trunk points and searched in the neighborhood. The set of points searched is used as a sample, and the difference between the sample points and the seed points in the \(x\) and \(y\) directions, \(\Delta x\) and \(\Delta y\), respectively, are used as parameters for interval estimation.