# RE-PU: A Self-Supervised Arbitrary-Scale Point Cloud Upsampling Method Based on Reconstruction
## 2 Related Work
### Classical point cloud upsampling  
Classical point cloud upsampling networks generally consist of three components: a feature extraction module, a feature expansion module, and a point cloud reconstruction module [13]. The feature extraction module encodes the point cloud from three-dimensional Euclidean space into a high-dimensional feature space. The feature expansion module increases the number of features in the point cloud to the required amount. Due to the one-to-one correspondence between point cloud features and point cloud coordinates, the point cloud can be mapped back to the coordinate space from the feature space through the point cloud reconstruction module.  
Initially, [PERSON] et al. introduced the first deep learning-based point cloud upsampling method PU-Net [14] based on PointNet+ [15]. This network learns multi-scale features for each point and extends the point set in feature space through a multi-branch convolution. [PERSON] et al. employed dense connections to extract point cloud features and proposed a progressive network named MPU [16], which iteratively refines the input point cloud in multiple steps. It decomposes higher upsampling rates into stepwise doubling and avoids point clustering by concatenating a one-dimensional encoding to capture features of multiple details in the point cloud. [PERSON] et al. introduced PU-GCN [17] based on graph convolution, treating the point cloud as a graph with points as nodes. They utilized a novel inception-based module to extract multiscale information and proposed a NodeShuffle module for feature expansion. Viewing upsampling as a multi-objective task, [PERSON] et al. presented Dis-PU [18], a method consisting of two cascaded sub-networks. The former sub-network generates coarse but densely distributed points, while the latter sub-network refines the generated point cloud by adjusting the positions of the points. [PERSON] et al. investigated connections between different regions of the point cloud and among individual points, proposing PC2-PU [19]. This method incorporates adjacent point cloud patches as supplementary information into the neural network, requiring additional labels for adjacent point clouds. Combining graph filtering and channel-wise attention, [PERSON] et al. proposed a structure-sensitive upsampling algorithm [20]. [PERSON] et al. argued that existing upsampling techniques directly learn the mapping from sparse point sets to dense point sets, which is often uncertain and ill-posed. To alleviate the uncertainty and ambiguity in the upsampling mapping, they introduced a universal three-stage vector quantization framework comprising a Codebook Lookup Transformer and knowledge distillation for point cloud upsampling, named CPU [21].  
In addition to the typical three-stage approach mentioned above, some innovative methods have incorporated discrete differential geometry into point cloud upsampling, enabling the formulation of upsampling problems through mathematical expressions and providing additional mathematical assurances [22; 23; 24]. Moreover, point cloud upsampling can be viewed as a conditional generative task: given a sparse point cloud, generate a corresponding dense point cloud. Therefore, some approaches choose to integrate point cloud upsampling with Generative Adversarial Networks (GANs) [25; 26; 27].  
In general, supervised point cloud upsampling methods require that the training and testing data conform to similar distributions. For instance, models trained on synthetic datasets may face challenges in achieving optimal performance when applied to point clouds obtained from real-world scans. Moreover, adopting a fixed magnification factor for upsampling entails the necessity of training separate models tailored to different upsampling rates. This introduces notable inconvenience for practical applications. Furthermore, downstream tasks often require additional post-processing steps, such as furthest point sampling. These traits limit the applicability of conventional methods across diverse scenarios.