# 3D Reconstruction Based on Iterative Optimization of Moving Least-Squares Function
[PERSON]  
1 The School of Computer Engineering, Jimei University, Xiamen 361021, China; [EMAIL_ADDRESS] (S.L. ); [EMAIL_ADDRESS] (G.J. ); [EMAIL_ADDRESS] (Z.H. ); [EMAIL_ADDRESS] (X.Z.) [PERSON]  
1 The School of Computer Engineering, Jimei University, Xiamen 361021, China; [EMAIL_ADDRESS] (S.L. ); [EMAIL_ADDRESS] (G.J. ); [EMAIL_ADDRESS] (Z.H. ); [EMAIL_ADDRESS] (X.Z.) [PERSON]  
1 The School of Computer Engineering, Jimei University, Xiamen 361021, China; [EMAIL_ADDRESS] (S.L. ); [EMAIL_ADDRESS] (G.J. ); [EMAIL_ADDRESS] (Z.H. ); [EMAIL_ADDRESS] (X.Z.) [PERSON]  
1 The School of Computer Engineering, Jimei University, Xiamen 361021, China; [EMAIL_ADDRESS] (S.L. ); [EMAIL_ADDRESS] (G.J. ); [EMAIL_ADDRESS] (Z.H. ); [EMAIL_ADDRESS] (X.Z.) [PERSON]  
1 The School of Computer Engineering, Jimei University, Xiamen 361021, China; [EMAIL_ADDRESS] (S.L. ); [EMAIL_ADDRESS] (G.J. ); [EMAIL_ADDRESS] (Z.H. ); [EMAIL_ADDRESS] (X.Z.) [PERSON]  
1 The School of Computer Engineering, Jimei University, Xiamen 361021, China; [EMAIL_ADDRESS] (S.L. ); [EMAIL_ADDRESS] (G.J. ); [EMAIL_ADDRESS] (Z.H. ); [EMAIL_ADDRESS] (X.Z.) [PERSON]  
1 The School of Computer Engineering, Jimei University, Xiamen 361021, China; [EMAIL_ADDRESS] (S.L. ); [EMAIL_ADDRESS] (G.J. ); [EMAIL_ADDRESS] (Z.H. ); [EMAIL_ADDRESS] (X.Z.) [PERSON]  
1 The School of Computer Engineering, Jimei University, Xiamen 361021, China; [EMAIL_ADDRESS] (S.L. ); [EMAIL_ADDRESS] (G.J. ); [EMAIL_ADDRESS] (Z.H. ); [EMAIL_ADDRESS] (X.Z.) least octree to extract features. The MLS point set is obtained by the shallow multi-layer perceptron (MLP), and the SDF is obtained under the action of the moving least-square function. This method transforms the uneven point cloud into a uniform MLS point cloud distributed near the shape surface, which effectively alleviates the problem of unevenness and noise of the original point cloud. However, the octree partitioning method employed in this approach leads to storage memory inefficiency, and local voxel features may induce discontinuities in the generated surface. In the paper, we present further enhancements to the DeepMLS method. Firstly, we leverage an adaptive octree based on cosine similarity to partition the target shape point cloud from global to local, obtaining local shapes at different scales. Secondly, by introducing the gated recurrent unit (GRU) [6] module, voxel features of different scales are inherited in octrees of different depths. This crucial step facilitates the iterative optimization of local shape features and integrates local and global feature information. Under the guidance of this iteratively optimized GRU module, optimized shape features are generated. Subsequently, accurate and interpretable MLS point clouds are generated through the processing of an MLP. Finally, the signed distance function is approximated by the moving least-square function, and the 3D surface is extracted by the marching-cubes method. In summary, our method implements GRU modules in octrees of different depths so that the final shape features contain local information and global information. Through the feature iteration and optimization of different scales, the MLS point set generated after entering the MLP is more suitable for the shape surface and easier to express the details of the shape. Our method offers several key advantages:  
* Adaptive octree partitioning: This scheme speeds up iteration and saves memory space by dynamically adjusting the partitioning based on local shape characteristics;
* GRU-based feature optimization: The GRU module iteratively optimizes local features, capturing the correlation and contextual information between shape features and achieving dynamic learning of feature changes;
* Excellent visualization results: Our method achieves state-of-the-art results on ShapeNet, ABC, and Famous datasets, demonstrating its effectiveness in generating high-quality 3D surfaces.