# 3D Point Cloud Completion Method Based on Building Contour Constraint Diffusion Probability Model
## 2 Related Works
### Deep Learning-Based Point Cloud Completion Methods
#### 2.2.3 Point-Based Method  
Point-based methods directly model each point in the point cloud. Multi-layer perceptrons (MLPs) are used by PointNet [29] to learn how the distribution and relationships of the points in the point cloud relate to one another, creating new points in the missing regions to fill them, so that the filled point cloud maintains a consistent geometric shapes. This approach ensures that the completed point cloud maintains consistent geometric shapes. PointNet++ [30] introduced hierarchical layers for multi-scale feature aggregation, enabling the learning of multi-scale features of point clouds. To mitigate structural losses introduced by MLPs, AtlasNet [31] reconstructs complete outputs by evaluating a set of parameterized surface elements, achieving full point cloud generation. PCN [16] can directly perform feature learning directly in the point cloud space to complete missing point clouds. However, PCN only utilizes global features and does not consider local geometric features, making it challenging to capture the topological structures of fine-grained building details. FinerPCN [32] combines PCN and pointwise convolution to extract local information, progressively generating detailed and complete point cloud data. LAKe-Net [33] completes point clouds using a keypoint-skeleton-shape prediction approach by locating aligned keypoints. AGGonv [34] enhances the flexibility of point cloud convolution by generating adaptive kernels based on dynamically learned features of points. This enables effective and precise capture of diverse relationships between pointsfrom different semantic parts, achieving adaptability within the convolution operation. Although point-based methods independently process points at the local level to maintain permutation invariance, they lose local features because they do not consider the geometric relationships between points and their positions. The latent space representation of point clouds provides crucial feature information for 3D shape reconstruction. Cycle4 Completion [35] allows models to learn how to completely complement a point cloud by learning the process of two simultaneous cyclic transformations of the potential space of a complete 3D shape and an incomplete 3D shape. ShapeInversion [36] introduces GAN into point cloud completion by searching for the latent code in a pre-trained GAN for the complete shape that best reconstructs the given input partial shape. It then uses gradient descent to backpropagate the loss function to update the latent code. PC-GAN [11] combines hierarchical and interpretable sampling with a combination of hierarchical Bayesian and implicit generative networks. This increases the model's stability and extracts more expressive features to generate more consistent point clouds, thus improving the quality of generated point clouds. PF-Net [37] uses a multi-layer network based on feature points to generate point clouds, taking in-complete point clouds as inputs, and utilizing multi-stage point cloud complementation and adversarial loss to produce more realistic point clouds of missing regions, thus better preserving the individual features of objects. CP3 [38] introduces an Incomplete-to-Incomplete (IOI) sampling mechanism as inverse prompt function, which randomly cuts the incomplete point cloud into a new incomplete point cloud. This new incomplete point cloud is then fed into a pre-trained generative network to recover the original incomplete point cloud. While GAN architectures can utilize discriminator-guided implicit learning to estimate sets of points provided by the generator, the unordered nature of point clouds can result in differently positioned corresponding areas in 3D space, leading to incorrect completions. Additionally, training GANs on complex raw point sets (exceeding 2048 points) can be challenging due to the difficulty in handling point distribution.