# 3D Reconstruction Based on Iterative Optimization of Moving Least-Squares Function
## 2 Related Work  
At present, there are many 3D reconstruction methods for point clouds based on deep learning [7; 8], which use auto-encoder to obtain the feature information of shapes, and although the output forms are different (occupancy values [9], SDF [10], neural unsigned distance fields (UDF) [11]), the surface can be extracted by marching cubes and back projection algorithms [12]. Three-dimensional reconstruction based on octree structure. At present, the most typical 3D reconstruction method based on octree is octree-based convolutional neural networks (O-CNN) [13]. This method first combines the target shape, then divides it into eight equal parts and performs convolutional neural network extraction of voxel features within each octant; based on O-CNN, adaptive O-CNN [14] proposed a planar fitting method for three-dimensional surfaces, in addition to using the pre-set depth of the octree and whether the number of point clouds within the octree reaches a threshold as the partition conditions for the octree, and using the ability to fit the current shape within the octree as an additional partition condition; based on O-CNN, DeepMLS proposed to perform convolutional neural network feature extraction in each smallest octant, and output MLS point cloud through MLP. The moving least-square function is used to approximate the signed distance function, which is used as an implicit function to extract three-dimensional surfaces; dual graph neural networks (GNN) [15] utilized graph convolution to combine voxel features of different scales and transmit octahedral feature information of different depths; Neural-IMLS [16] proposed different weight functions based on DeepMLS and learns SDF directly from the original point cloud in a self-supervised manner. Towardsimplicit text-guided 3D-shape generation (TISG) [17] generated 3D shapes from text based on an octree; dynamic code cloud-deep implicit functions (DCC-DIF) [18] discretized the space into regular 3D meshes (or octree) and store local codes in grid points (or octant nodes) to calculate local features by interpolating their adjacent local codes and their positions. Three-dimensional surface generation based on local and global integration. Points2 surf [19] used autoencoders to obtain more accurate distance values from local sources and more accurate sign values from global sources. The combination of the two has both local and global information, which can quickly and conveniently obtain sign distance values and improve reconstruction efficiency; latent partition implicit (LPI) [20] combined local regions into global shapes in implicit space, and the use of affinity vectors allowed the reconstruction results to include both local region features and cleverly integrate global information, resulting in currently outstanding reconstruction results; implicit functions in reconstruction and completion (IFRC) [21] proposed an implicit feature network that does not use a single vector to encode three-dimensional shapes. Instead, it extracts a learnable deep feature tensor for three-dimensional multi-scale deep features and aligns it with the original Euclidean space of the embedded shape, allowing the model to make decisions based on global and local shape structures; Octifield [22] proposed adaptive decomposition in 3D scenes, which only distributes local implicit functions around the surface of interest, connects the shape features of different layers, and possesses both local and global information, achieving excellent reconstruction accuracy. Learning consistency-aware unsigned distance functions (Learning CU) [23] used a cyclic optimization approach to reconstruct sparse point clouds into dense point clouds surrounding the shape, while maintaining the normal consistency of the point cloud; learning local pattern-specific deep implicit function (LP-DIF) [24] proposed a new local pattern-specific implicit function that simplifies the learning of fine geometric details by reducing the diversity of local regions seen by each decoder.