Non-uniform Point Cloud Upsampling via Local Manifold Distribution

TL;DR

This work tackles non-uniform, sparse point cloud upsampling by modeling local neighborhoods as statistical manifolds and fitting local Gaussian components to capture point distributions. By constructing a unified manifold and enforcing distribution constraints via Fisher-Rao geodesic distances, the method guides upsampling to produce more uniform, detail-preserving dense clouds. Empirical results on synthetic, noisy, and real-scanned datasets show improved uniformity, robustness to noise, and better downstream reconstruction compared with state-of-the-art approaches. The approach offers a robust, geometry-aware framework that enhances the quality and consistency of upsampled point clouds for subsequent 3D tasks.

Abstract

Existing learning-based point cloud upsampling methods often overlook the intrinsic data distribution charac?teristics of point clouds, leading to suboptimal results when handling sparse and non-uniform point clouds. We propose a novel approach to point cloud upsampling by imposing constraints from the perspective of manifold distributions. Leveraging the strong fitting capability of Gaussian functions, our method employs a network to iteratively optimize Gaussian components and their weights, accurately representing local manifolds. By utilizing the probabilistic distribution properties of Gaussian functions, we construct a unified statistical manifold to impose distribution constraints on the point cloud. Experimental results on multiple datasets demonstrate that our method generates higher-quality and more uniformly distributed dense point clouds when processing sparse and non-uniform inputs, outperforming state-of-the-art point cloud upsampling techniques.

Figures (6)

• Figure 1: Our upsampling algorithm pipeline. For the input point cloud, we first construct a local coordinate system for each query point based on its surrounding neighborhood. We then perform local Gaussian fitting in the 2D parameter plane. Subsequently, geodesic constraints are applied on the statistical manifold formed by the local Gaussian functions. Finally, by resampling the constructed local Gaussian functions, we generate the upsampled point cloud.
• Figure 2: Visualization of the non-uniform PU1K dataset (1024) experiments based on different algorithms.
• Figure 3: Visualization of upsampling results for partial data with 256 and 4096 input points.
• Figure 4: Upsampling results for input point clouds with noise levels of 0.5%, 1%, and 2%.
• Figure 5: Upsampling results for LiDAR real-time scanned point cloud data.