# Point Cloud Upsampling Algorithm: A Systematic Review
## 4 Deep Learning-Based Point Cloud Upsampling
### Supervised Upsampling
#### 4.1.2 Upsampling Component
\(C\), \(C^{\prime}\) and \(C^{*}\) are the features of the point, \(r\) is the upsampling rate, \(w\) is the weight. Subfigures are described in detail in Section 4.1.2.  
feature to self-correct the expanded feature. For the up-feature operator, PU-GAN first duplicates the input features and adopts the 2D grid mechanism in FoldingNet [37] to generate a unique 2D vector for each feature-map, and appends this vector to each point feature. A self-attention unit and a set of MLPs are then used to generate output upsampled features. The down-feature operator consists of a reshape operation and a set of MLPs. Up-UNet [38] also applies upsampling operations. Up-UNet first upsamples the point features through the up-feature operator, which can adjust the point features according to the adjacent point features through the channel attention operator while extracting the local point features. Then, in order to keep the consistency of the guided point cloud, the first N point features are split from the upsampling features. The first down-feature operator only conducts the sampling operation without changing the number of points to extract adjacent features, which extracts neighboring information and builds the relation of closing points. The second down-feature operator performs real downsampling to extract key point and important point features. Then, through continuous upsampling operations, together with extension paths, the network can propagate context information and reconstruct extended features. This approach is better able to mine the deep relationship between the generated point cloud and the original point cloud, thus providing higher quality upsampling results. **Disentangled refinement. ** [PERSON] et al. [39] proposed a network model for disentanglement refinement, Dis-PU, which divides upsampling into two steps, a feature expansion unit and a spatial refinement unit. The feature expansion unit first expands the features through regular expansion operations and generates rough point sets through a set of MLPs. The spatial refiner is used to further fine-tune the spatial position of each point in the coarse point set and generate a high-quality dense point set Q with uniform distribution. Coarse but dense point clouds and associated features are fed into local and global refinement units. The two outputs generated by the two refinement units are added to obtain the refined feature map. Finally, residual learning is used to regress the offset Q at each point. This upsampling strategy allows each sub-network to better focus on its specific sub-goal, while complementing each other in the upsampling task. **Meta upscale. ** The previous methods need to predefine the upsampling factor, such as training different upsampling modules for different factors, which is inefficient and limits the application of the model. [PERSON] et al. [40] proposed a model that can be sampled at any scale, Meta-PU. Its backbone is based on a graph convolution network, which consists of several residual graph convolution blocks. It dynamically adjusts the weight of the residual graph convolution block by learning the meta-subnetwork. Then meta-convolution uses these weights to extract features, adaptively customize the scale factor, and jointly train multi-scale factors under the same model. PU-EVA [31] decouples the upsampling rate from the network structure, and adopts an approximate solution based on edge vectors to generate new points by encoding neighboring connectivity, enabling arbitrary upsampling rates in one-shot training. **Others. ** The above several methods achieve the purpose of upsampling by extending the features of the feature space, and other upsampling methods exist. [PERSON] et al. [41] proposed an interpolation-based point cloud upsampling model. Firstly, the dense point cloud is obtained using an interpolation algorithm based on dynamic point expansion, and then the coordinates of the insertion points are adjusted through two network models.