Point Cloud Upsampling through Patch-based Frequency Superposition

3D Gaussian Splatting (3DGS) is a technique for creating and rendering 3D scenes, however its performance depends heavily on the quality of initial seed points. To improve 3DGS initialization, this study presents and evaluates several point cloud upsampling approaches: linear interpolation, triangular interpolation, spline-based surface reconstruction, moving least squares surface fitting, and Voronoi-based point generation. Additionally, this research introduces a depth-guided point lifting method that leverages depth maps to maintain geometric consistency with Structure-from-Motion (SfM) reconstructions. Through extensive experiments on the Mip-NeRF360 and Replica datasets, the proposed methods demonstrate improvements in reconstruction quality across diverse scene types. Results indicate that different upsampling strategies excel in different scenarios: surface reconstruction methods perform better with organic, detailed scenes, while simpler interpolation approaches are more suited for scenes dominated by piecewise-smooth geometries. In comparison, the depth-guided approach shows promise for adding geometry-aware points across the entire scene, importantly in texture-less regions. These findings, which provide preliminary practical guidelines for selecting appropriate upsampling methods based on scene characteristics and computational constraints, advances the understanding of how point cloud initialization affects 3DGS quality.

Point-based Neural Networks (PNNs) have become a key approach for point cloud processing. However, a core operation in these models, Farthest Point Sampling (FPS), often introduces significant inference latency, especially for large-scale processing. Despite existing CUDA- and hardware-level optimizations, FPS remains a major bottleneck due to exhaustive computations across multiple network layers in PNNs, which hinders scalability. Through systematic analysis, we identify three substantial redundancies in FPS, including unnecessary full-cloud computations, redundant late-stage iterations, and predictable inter-layer outputs that make later FPS computations avoidable. To address these, we propose \textbf{\textit{FlashFPS}}, a hardware-agnostic, plug-and-play framework for FPS acceleration, composed of \textit{FPS-Prune} and \textit{FPS-Cache}. \textit{FPS-Prune} introduces candidate pruning and iteration pruning to reduce redundant computations in FPS while preserving sampling quality, and \textit{FPS-Cache} eliminates layer-wise redundancy via cache-and-reuse. Integrated into existing CUDA libraries and state-of-the-art PNN accelerators, \textit{FlashFPS} achieves 5.16$\times$ speedup over the standard CUDA baseline on GPU and 2.69$\times$ on PNN accelerators, with negligible accuracy loss, enabling efficient and scalable PNN inference. Codes are released at https://github.com/Yuzhe-Fu/FlashFPS.

Point cloud completion commonly follows a coarse-to-fine paradigm, where a low-density coarse shape is first predicted and then upsampled to the target resolution. Although recent methods have improved global structure recovery, the fine stage often remains limited by simple upsampling and insufficient interaction with coarse structural features, making local detail reconstruction challenging. We propose SUMI, a diffusion-enhanced refinement module for coarse-to-fine point cloud completion. Unlike prior diffusion-based completion methods that use diffusion as a standalone point generator, SUMI injects noisy geometric features into cross-attention with coarse structural features, enabling reverse denoising to refine local geometry while preserving global consistency. SUMI can also be integrated into existing coarse-to-fine models as a flexible refinement module. Experiments on PCN, ShapeNet-55/34, and MVP demonstrate consistent improvements over strong baselines. SUMI achieves the best overall CD and F1-score on PCN, reduces CD by up to 16.1% on ShapeNet-55, and obtains the best CD across all output densities on MVP.