## 2 Related Works
### Point Cloud Super-Resolution  
Point cloud super-resolution is similar to image super-resolution, employing super-resolution techniques to increase the density of points in a low-density point cloud. T-UNet [22] was designed as a point cloud super-resolution network utilizing an encoder-decoder framework that integrates temporal features. However, it simply incorporates temporal information directly without fully exploiting its potential. Therefore, there is room for improvement by introducing advanced feature processing methods [23; 24] into the encoder to enhance feature extraction capabilities. Consequently, there is still potential for improvement in fully utilizing temporal and spatial features. Pu-net [25] explores multi-level features for each point by implicitly expanding the point set through a multi-branch convolution unit in feature space. The augmented feature is subsequently partitioned into numerous features, which are later reconstructed to form a super-resolution point set. PUGee-Net [26] is a deep learning method based on geometric transformations that learns local parameters and normals for each point. Through sampling in the 2D parameter domain and utilizing the learned 3D transformations, the point cloud is upsampled, achieving precise and efficient results at super-resolution rates ranging from 4 to 16 times. Sspu-net [27] for self-supervised point cloud upsampling leverages the coherence between the initial sparse point cloud and the resultant dense point cloud in terms of shapes and rendered images. Meta-PU [28] is the first implementation supporting arbitrary-scale point cloud upsampling using a single model. This model integrates residual graph convolution blocks, a meta-subnetwork, and the farthest sampling block. Notably, Meta-PU surpasses the performance of existing methods, which are typically trained for specific scale factors. While these approaches do offer qualitative results for LiDAR point clouds, their emphasis is on augmenting the overall 3D point density of point clouds pertaining to individual objects rather than addressing larger scenes. LiDAR super-resolution aims to replicate a realistic point cloud resembling that of a high-beams LiDAR, given the point cloud from a low-beams LiDAR. As a result, its objective differs from the aforementioned approaches.  
Given the challenges and substantial computational requirements associated with upsampling LiDAR point clouds in 3D space, the majority of studies opt to represent the point cloud as a range image. Consequently, the LiDAR super-resolutions task is conducted within the confines of 2D image space. Ref. [29] employed a CNN with a U-Net architecture. Furthermore, it incorporates a Monte-Carlo dropout post-processing step to mitigate the presence of noisy points in the predictions. Local implicit image function (LIIF) [30] treats an image as a continuous function, positing that the RGB values of discrete pixel points are calculated by a function taking pixel position and depth as inputs. This function is approximated using a multi-layer perceptron. The model proposed in ref. [31] takes a range image from a point cloud as input and undergoes operations, including encoding, to predict parameters. The model also incorporates a self-attention mechanism. In comparison to directly using LIIF for image prediction, it exhibits fewer noise artifacts. HALS [32] also takes a range image as input after several rounds of dilated residual blocks (DRBs) for feature extraction and diverges into two paths. One path directly undergoes upsampling to generate the final result, while the other path continues with DRBs to generate deeper features before further upsampling. These two paths represent shadow and deep information, and they are finally combined through point-wise addition.