# A Coal Mine Excavation Tunnels Modeling Method Based on Point Clouds
## 2 Related Works  
Implicit surface reconstruction algorithms consider the input point cloud as samples of the zero level set of an implicit function in three-dimensional space. Firstly, a smooth implicit function is fitted based on the positions of the point cloud, and then a contour surface is constructed. The zero level set of the implicit function is discretized into a triangular mesh. The Poisson reconstruction algorithm [15; 26; 27] is applied, which defines the model's interior values as greater than zero, exterior values as less than zero, and the iso-surface as zero, obtaining an implicit equation describing the model's surface, i.e., the Poisson equation. This equation is used to extract iso-surfaces, which are then assembled to represent the surface of the target entity. The radial basis function method [16; 28; 29; 30], which first calculates the normal vectors of each point in space, then constrains the values along their normal vectors by sampling, obtains radial basis functions that express the curvature details of the target model surface, and interpolates them to reconstruct the entire three-dimensional model. Surface reconstruction methods based on computational geometry connect discrete points in three-dimensional space to form different polygons representing the surface structure of the original target model. They have the advantages of a simple reconstruction process and uniform model format, making them more suitable for reconstructing the surface of complex models. The region growing method [18; 31; 32] firstly constructs initial tetrahedra and then continuously expands outward according to rules, selecting appropriate points to form new tetrahedra until all discrete points in space are included in the three-dimensional mesh. The planar projection method [17] firstly partitions the target point cloud model in space, projects the local surface of the point cloud model onto a two-dimensional plane according to certain rules, then performs triangulation on this plane based on the Delaunay criterion. The greedy projection triangulation algorithm [33] establishes the step of determining the tangent plane by looking for neighboring points instead of the planar projection method to convert the three-dimensional point cloud into a two-dimensional plane. The ball-pivoting algorithm [34; 35] is based on local sphere fitting. It rotates along the boundary of a sphere on the point cloud surface, connects points according to certain geometric rules, and finally generates a triangular mesh. The VCG algorithm [36] selects seed points in the point cloud and constructs local meshes using points and normal vector information around them. These local meshes are then gradually merged according to consistency constraints to generate a complete triangular mesh surface. In recent years, with the development of deep learning technology, algorithms based on deep learning have been proposed. The basic idea of deep learning-based surface reconstruction algorithms is to learn a classifier similar to an implicit function based on point cloud data, classify the vertices of an octree, and then extract the surface using the Marching Cubes method. ONet [37] learns a continuous 3D occupancy function using deep neural networks to enable high-resolution 3D surface reconstruction from various inputs with efficient memory usage. SSRNet [38] introduces a scalable 3D surface reconstruction method that leverages local geometry-aware features and tangent convolution to classify octree vertices, enabling efficient parallel processing of large-scale point clouds. DeepDT [39] introduces a method that utilizes Delaunay triangulation and graph convolutional networks to classify tetrahedrons as inside or outside a surface. By integrating local geometry features with structural information from the triangulation, DeepDT enables accurate surface reconstruction through a multi-label supervision strategy. NKF [40] combines a neural network to learn kernel parameters with kernel ridge regression to reconstruct 3D surfaces.