# Geometric Detail-Preserved Point Cloud Upsampling via a Feature Enhanced Self-Supervised Network
## 1 Introduction  
The fields of robotics, autonomous driving, and the digital industry increasingly depend on point clouds captured by 3D sensors to represent 3D data. However, the current 3D sensors often produce sparse and noisy point clouds, especially when dealing with smaller objects, which presents significant challenges in processing. Point cloud super-resolution has become a crucial research area, focusing on converting sparse and noisy inputs into dense and clear outputs [1, 2, 3].  
Deep learning methods, which have been successful in image super-resolution [4, 5], have also inspired advancements in point cloud super-resolution. Mainstream deep learning techniques for point cloud upsampling typically involve three key steps: local feature extraction, high-dimensional feature expansion, and supervised feature learning. However, these methods have limitations, such as feature homogenization, especially for sparse point clouds, and the blurring of non-flat region information (such as corner points and edge points). Additionally, supervised learning upsampling methods often show limited generalization capabilities when faced with a diverse range of 3D point cloud models [6, 7, 8, 9].  
The reasons why current methods do not work well for point cloud upsampling are twofold. First, existing networks, which learn from point coordinates, often produce features without sufficient discrimination. This results in higher similarity or homogeneity, which leads to closely spaced points during coordinate reconstruction. Second, the current supervised or self-supervised learning methods primarily focus on the relationship between the dense output and the sparse input (or dataset labels), neglecting to fully exploit the structural (both global and local) properties of the output point clouds [10, 11, 12].  
To this end, we introduce a novel end-to-end self-supervised deep learning network, SSPU-FENet, designed for geometric detail-preserved point cloud upsampling. First, we propose a feature enhancement module (FEM) that effectively distinguishes sharp feature points (i.e., corner points and edge points in the non-flat regions) from other flat regions using a unique descriptor rooted in local geometry information. Second, the geometry reconstruction with a 3D noise perturbation module (NPM) uses high-dimensional feature distances to prevent the generated points from being too close due to feature similarity. Finally, we introduce a comprehensive joint loss function tailored for self-supervised learning, which not only considers the global shape relationship between the dense and sparse point clouds but also exploits the similarity of local geometric structures within the dense point cloud, thereby enabling the generation of dense point clouds.  
**Contributions.** Our contributions are summarized as follows.  
* We design feature enhancement and geometric coordinate reconstruction modules that effectively preserve geometric details of output dense point clouds, such as non-flat regions, which outperforms existing methods in upsampling and related downstream tasks.
* Our end-to-end self-supervised network model considers the relationships between dense and sparse point clouds, including both global shapes and similar local geometric structures. This allows us to obtain more geometric information-rich dense point clouds, as validated by our experiments.