Algorithm 1. Optimized Boundary Extraction Method

Input: Source point cloud S  Output: Boundary point cloud T without outliers 1V$\leftarrow$Voxel Down-sampling S 2for each point ${\mathit{p}}_i$ in V, do 3 ${\overline{\mathit{p}}}_i=\frac{1}{k}{\displaystyle \sum {\mathit{p}}_i^a}$ 4 $\mathit{C}=\frac{1}{k}{\displaystyle \sum \left({\mathit{p}}_i^a-{\overline{\mathit{p}}}_i\right)}{\left({\mathit{p}}_i^a-{\overline{\mathit{p}}}_i\right)}^T$ 5 $\mathit{C}{\mathit{v}}_j={\lambda }_j{\mathit{v}}_j$, $j\in \left\{1,2,3\right\}$ 6 Boundary identification 7 Add boundary points into R 8end 9Z$\leftarrow$radius search for each point in R 10for each point ${\mathit{q}}_i$ in Z do 11 Search for the k-nearest points: ${\mathit{q}}_i^a$, $i\in \left(1,k\right)$ 12 $d_i=\frac{{\displaystyle \sum {\Vert {\mathit{q}}_i-{\mathit{q}}_i^a\Vert }_2}}{k}$ 13end 14$\mu \leftarrow \frac{{\displaystyle \sum d_i}}{n}$ 15$\sigma \leftarrow \sqrt{\frac{{\displaystyle \sum d_i^2-\frac{{\left({\displaystyle \sum d_i}\right)}^2}{n}}}{n-1}}$ 16for each point ${\mathit{q}}_i$ in Z, do 17 if $d_i\ge \mu +\alpha \sigma$ then 18  continue 19 end 20 Boundary identification 21 Add boundary points into T 22end