# RE-PU: A Self-Supervised Arbitrary-Scale Point Cloud Upsampling Method Based on Reconstruction
## 2 Related Work
### Point Cloud AutoEncoder  
Numerous prior studies have leveraged the autoencoder framework to achieve self-supervised representation learning for point clouds. In this approach, an encoder and a decoder are trained concurrently, where the encoder transforms the input point cloud into a latent code, and the decoder aims to reconstruct the original point cloud from the latent code. Autoencoders have been widely used for point cloud reconstruction, denoising, and generation [39].  
[PERSON] et al. introduced TL-Net [40], which posits that point cloud representations should exhibit generative properties in 3D space and predictability when projected into 2D space. TL-Net utilizes a 3D autoencoder to reconstruct volumetric grids in 3D space and employs a 2D convolutional network to capture 2D features from the corresponding projected images. [PERSON] et al. innovatively devised FoldingNet [41], which incorporates a decoder based on folding principles. This decoder deforms a standard 2D grid to conform to the three-dimensional surface of the underlying object in a point cloud. [PERSON] et al. proposed AtlasNet [42], which represents three-dimensional shapes as a collection of parameterized surface elements. In contrast to methods that generate voxel grids or point clouds, this approach naturally infers the surface representation of the shape. L2 GAuto-encoder [43] incorporates hierarchical self-attention within the encoder to aggregate information and utilizes a recurrent neural network (RNN) as the decoder for both local and global point cloud reconstruction. [PERSON] et al. expanded the application of capsule networks to 3D point cloud processing, introducing a 3D capsule network that is capable of acquiring versatile representations from unorganized 3D data [44]. [PERSON] et al. formulated a deep autoencoder that leverages graph topology inference and filtering to extract concise representations from 3D point clouds [45]. [PERSON] et al. introduced a graph-based autoencoder capable of capturing intrinsic patterns within point-cloud structures, accommodating both global and local transformations [46]. [PERSON] et al. proposed a versatile method for 3D self-supervised representation learning to address the challenges of pre-training on 3D data [47]. The approach involves softly segmenting 3D points and leveraging a generative model for these partitions to maximize data likelihood, encouraging learned representations to capture rich geometric information. [PERSON] et al. presented a novel self-supervised learning approach called Masked Autoencoders for Point Cloud, leveraging techniques successful in natural language processing and computer vision, showcasing efficiency in pre-training and outperforming other self-supervised methods on downstream tasks [48]. [PERSON] et al. proposed Point-M2 AE [49], a novel hierarchical self-supervised learning framework utilizing Multi-scale Masked Autoencoders for effective 3D point cloud pre-training, demonstrating state-of-the-art performance in downstream tasks and surpassing fully trained methods in certain cases.  
Similar to FoldingNet [41] and AtlasNet [42], RE-PU can be considered as mapping a predefined prior distribution, such as a unit square, onto a three-dimensional surface representation of a point cloud. The role of RE-PU's decoder is to reconstruct the prior distribution into the input point cloud, while the encoder primarily serves to obtain the identification of the input point cloud. If a separate model is trained for each shape, the encoder can be removed, and the decoder can be trained alone.