# 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 distribution of the trunk point set is robust, with possible trunk and seed points having parameter errors within the confidence interval of the Gaussian distribution, while the outliers have larger errors and are not within the confidence interval, and the points within the confidence interval are added to the growing point set. The GDRG algorithm is shown in Figure 3. The pseudocode of the algorithm set is in Table 1.  
Find the black neighborhood points (points to be judged) based on the yellow points (points that have grown). Randomly select a yellow point as the initial seed point to find the 20 nearest neighbor points, calculate the distance difference between the neighborhood points and the seed point in the x and y directions, and then calculate the Gaussian distribution of the difference, set to establish a confidence level of 0.05 confidence interval. The points that meet this confidence interval are added to the red point set, and the next nearest point in the remaining neighborhood point set is repeatedly grown as a new seed point. The algorithm is terminated when there are no new points to be added or when all remaining points to be added do not qualify for the confidence interval. The set of points \(P\) that ends the growth is the set of clustering points of the first trunk; the new initial seed points that are not marked by the growth are reselected in the candidate \begin{table}
\begin{tabular}{l l} \hline
1. & The creation of a KD tree with vertically characterized points denoted as \(P\). \\
2. & The creation of a KD tree with the original data points represented as \(Q\), \(P\in Q\). \\
3. & Creating an empty set of lists \(C\) and a queue \(K\) of points to be examined. \\
4. & For each vertical point \(p_{i}\in P\in Q\): \\  & \(\bullet\) & Compute its \(d\) (\(d\) = 20) nearest neighbors in \(Q\); \\  & \(\bullet\) & Compute the set of points that, if they meet the condition, \((1-(Q-P))/Q>0.2\); \\  & \(\bullet\) & Denoted as \(k_{i}\) added to the queue \(K\). \\
5. & Then, for each point \(k_{i}\in K\in Q\), the following process is performed: \\  & \(\bullet\) & Calculate its \(d\) (\(d\) = 20) nearest neighbors \(K_{i}\) in \(Q\). \\  & \(\bullet\) & Calculate the distance differences \(\triangle x\) and \(\triangle y\) of \(K_{i}\) and \(k_{i}\) in the \(x\) and \(y\) directions, respectively. \\  & \(\bullet\) & Make Gaussian distributions \(F(x)\) and \(F(y)\) with the difference of \(K_{i}\) in \(x\) and \(y\) directions, respectively. \\  & \(\bullet\) & For each point \(K_{i}\): \\  & \(\bullet\) & If the distance with \(k_{i}\) in \(F(x)\mid F(y)\) of the confidence interval, 0.05. \\  & \(\bullet\) & Add \(K_{i}\) point to \(K\) and transfer the current \(k_{i}\) point from \(K\) to \(C\). \\
6. & No eligible \(K_{i}\) points in \(Q\) join is added to \(K\cup k_{i}\) in \(K\) all transfer to \(C\). \\
7. & The points in \(C\) are labeled as trunk points. \\ program determination. \\ \hline \end{tabular}
\end{table} 
Table 1: Algorithm table for GDRG. Figure 3: Region growth algorithm based on Gaussian distribution (yellow points represent partial trunk points extracted by vertical features, black points represent points in the original data, red points represent tree points grown by Gaussian distribution algorithm, and green points are tree crown points). point set, and the algorithm is repeated to obtain the set of clustering points of the next \(N\) trunks, which is the set of clustering points of the \(N\) trunks in the candidate point set \(T2\). The extracted point set is processed by a GDRG algorithm to obtain a candidate point set \(T2\). The candidate point set \(T2\) complements the clustering of various rod point sets, but there are still pseudo-rod point sets clustered due to the irregular growth of the canopy point cloud.