# 3D Reconstruction Based on Iterative Optimization of Moving Least-Squares Function
## 4 Experiments
### Ablation Studies
#### 4.5.3 Robustness Test on Noise  
We train on a clean point cloud while adding a value of 0.01 (\(\sigma=0.01\)) Gaussian noise to the input point cloud during testing, which is to simulate the noise of the data in the actual scene, and then verify the surface-generation ability of the network model for the noisy point cloud. By inputting the noise point clouds into the network and comparing the surface-generation capabilities of the proposed method with the advanced OSP method, the adaptability of the proposed method to the noisy point clouds can be more clearly evaluated, as shown in Figure 10. To ensure the comparability of the experiments on OSP and the method in the paper, a control experiment on OSP was conducted in the paper, and the experimental settings of the two methods were optimally adjusted according to the experimental needs. For example, for the OSP method, set the number of input point clouds to 2 k and perform 30 k iterations. For the proposed method, 3 k input point clouds were used, and GPU*4 (such as Figure 9) was used for experiments.  
Figure 9: Varying the number of GRU results to generate a 3D surface-comparison result. (The red frames and arrows display the local comparison results of the shape).  
According to the analysis of the experimental results, it can be observed that the OSP method performs the worst in the surface generation of column and hand shapes, and there are holes and unevenness anomalies in the generated results. This indicates that the OSP method has certain limitations when dealing with shapes with complex structures and detailed features in the presence of noise, and it is difficult to effectively capture and reconstruct the features of these complex shapes, resulting in a poor quality of the generated results. In contrast, the method proposed in the paper is slightly superior to OSP in the surface generation of the two shapes, especially in the modeling of the hand region, and avoids the formation of adhesions or holes. This method is of great significance in practical application because it can better deal with complex shapes and can still generate 3D surfaces close to the real situation for various shapes in a noisy environment. In the real world, the shapes of many objects have complex structural and detailed features, such as hand shapes, so the performance advantages of this method will have a positive impact on the 3D shape-surface-generation task of realistic scanning.  
To verify the effectiveness of the proposed method in a noisy environment, a comparative experiment on the 3D surface-generation method NKSR [42], based on deep learning, is presented in Figure 11. NKSR is a new method for reconstructing 3D implicit surfaces from large-scale, sparse, and noisy point clouds using a linear combination of learned kernel basis functions to evaluate the value of the function at the corners of the voxels and then extracting the 3D surface using double-marching cubes. In the face of a noisy environment, compared with NKSR, which uses hierarchical sparse data structures to achieve feature mapping, the cyclic iterative optimization method based on GRU in the paper is more  
Figure 10: Visualization and comparison of different methods after adding Gaussian noise. (Famous dataset, and the red frames display the local comparison results of the shape).  
advantageous. In Figure 11, it can be observed that the surface generation results of the two are not much different in the plane region (e.g., the \"package\" in the second row), but in the face of shapes with fine structures (such as the \"chair\" in the fourth row), this paper can better model the shape surface, which effectively alleviates the influence of noise on the 3D surface generation.