# 3D Reconstruction Based on Iterative Optimization of Moving Least-Squares Function
## 2 Related Work
A kernel density estimator is used to introduce region reweighting modules to each specific pattern decoder, which dynamically reweights regions during the learning process; neural galerkin solver [25] discretized the interior of the target implicit field into a linear combination of spatially varying basis functions inferred by an adaptive sparse convolutional neural network. Three-dimensional reconstruction based on loop optimization. To generate higher precision surfaces, current methods revolve around the iterative strategy of \"loops\" for network optimization or feature optimization. For example, alternately denoising and reconstructing (ADR) unoriented point sets [26] used iterative poisson surface reconstruction (iPSR) [27] to support undirected surface reconstruction, iteratively executing iPSR as an outer loop of iPSR. Considering that the depth of the octree significantly affects the reconstruction results, an adaptive depth-selection strategy is proposed to ensure appropriate depth selection; deep-shape representation (DSR) [28] first extracted edge points from input points using an edge detection network and then preserved the sharp features of the real model while restoring the implicit surface. The two-stage training process ensures that the sharp features of the input points are learned while fitting surface details; USR [29] proposed generating target objects through part assembly, which iteratively retrieves parts from the shape parts library through a self-supervised method, improves their positions, and combines parts into the surface of the target object; octree-guided unoriented surface reconstruction (OGUSR) [30] constructed a discrete octree with inner and outer labels, and optimized the continuous and high fidelity shape using an implicit neural representation guided by the octree labels. This method generates a three-dimensional surface using an unoriented point cloud as input, achieving results comparable to those generated by directed point clouds; unsupervised single sparse point (USSP) [31] used parameterized surfaces as coarse surface samplers to provide many coarse surface estimates during training iterations. Based on these estimates, the SDF was statistically inferred as a smooth function using a thin plate spline (TPS) network. This significantly improved the generalization ability and accuracy in invisible point clouds; real-time coherent 3D reconstruction from monocular video (NeuralRecon) [32] used gated recurrent units to capture local smoothing priors and global shape priors of three-dimensional surfaces during sequential surface reconstruction, thereby achieving accurate, coherent, and real-time surface reconstruction of images. Towards better gradient consistency (TBGC) for neural signed [33] adaptively constrained the gradient at the query and its projection on the zero level set, cyclically aligning all level sets to the zero level set, minimizing the level set alignment loss to obtain more accurate signed distance function, and, thus, generating a three-dimensional surface. A new iPSR [34] showed that, in each iteration, the surface obtained from the previous iteration directly calculates the normal vector as input sample points, generating a new surface with better quality. Based on adaptive octree based on cosine similarity, we achieve iterative optimization of information through GRU. In the paper, we describe the method in detail in Section 3 and analyze the experimental results in Section 4.