# Point Cloud Upsampling Algorithm: A Systematic Review
## 4 Deep Learning-Based Point Cloud Upsampling
### Supervised Upsampling
#### 4.1.2 Upsampling Component  
The main function of the upsampling component is to expand the feature space, which is equivalent to expanding the number of points, because points and features are interchangeable. Figure 3 shows several common upsampling component frameworks. **Multi-branch upsampling. ** As the first deep learning-based point cloud upsampling model, PU-Net [5] uses a multi-branch feature expansion module to expand features through multiple parallel sub-pixel convolutional layers. SPE-Net [30] adopts a similar upsampling strategy. This approach can lead to agglomeration of points around the original point location, which needs to be mitigated by introducing a repulsion loss. GC-PCU [32] introduces perturbation learning to try to solve this problem. It applies an MLP learning 2D perturbation to each set of features after feature expansion. Different convolutions are used for each set of features, so that the weighting parameters are not shared across the MLPs. In this manner, the resulting perturbation depends on the shape of the input point cloud, and thereby guarantees the geometric consistency. These perturbations are then appended to the duplicated features for further residual learning. In residual learning, three convolution operations are performed to map input features to residual values. Then the input features are added to these residuals using skip connections to further refine the features, resulting in expanded features. **Multi-step upsampling. ** Multi-step supervision is a common practice in image super-resolution. The MPU [16] introduces this mechanism into point cloud upsampling. The MPU uses an upsampling unit that consists of a feature extraction unit and a feature expansion unit (in Section 4.1.1). For the feature expansion component, the MPU first duplicates the features, then assigns each duplicated feature a 1D code, with a value of \(-1\) or \(1\), to transform them to different locations. Finally, MPU compresses the duplicated features using a set of MLPs as residuals, and adds residuals to input coordinates to generate output points. The MPU introduces inter-level skip-connections between upsampling units for features extracted with different scopes of the receptive fields. AR-GCN [20] adopts the same upsampling strategy. An upsampling unit is formed using the residual graph convolution block and the unpooling block to progressively upsample the point cloud. The unpooling block predicts the residuals of the input and output point clouds through a graph convolutional layer. This exploits the similarity between the input and output point clouds, resulting in faster convergence and better performance. This multi-step upsampling method has better geometric detail and lower noise, but is computationally expensive, and requires more data to supervise the mid-term output of the network. **NodeShuffle. ** PixelShuffle has achieved success in the field of image super-resolution, and inspired PU-GCN [14] and led to the proposal of NodeShuffle. NodeShuffle uses graph convolution layers to expand features, and rearranges the expanded features through shuffle operations. NodeShuffle employs graph convolutions instead of CNNs to expand features, enable the upsampler to encode spatial information from point neighborhoods, and learn new points from the latent space, rather than simply duplicating the original points. PU-GACNet [36] improves NodeShuffle and proposes edge-aware NodeShuffle (ENS). The ENS module can not only smoothly expand local point features but also properly emphasizes local edge features with graph convolution operations. **Up-and-down sampling. ** [PERSON] et al. [13] introduced the mechanism of up-and-down sampling in PU-GAN. It upsamples the point feature to obtain the expanded feature, which is then downsampled to compute the difference between the features before and after upsampling. The difference is upsampled and added to the first-step expanded  
Figure 3: Several common upsampling component frameworks.