GP-PCS: One-shot Feature-Preserving Point Cloud Simplification with Gaussian Processes on Riemannian Manifolds

TL;DR

A novel, one-shot point cloud simplification method which preserves both the salient structural features and the overall shape of a point cloud without any prior surface reconstruction step is proposed.

Abstract

The processing, storage and transmission of large-scale point clouds is an ongoing challenge in the computer vision community which hinders progress in the application of 3D models to real-world settings, such as autonomous driving, virtual reality and remote sensing. We propose a novel, one-shot point cloud simplification method which preserves both the salient structural features and the overall shape of a point cloud without any prior surface reconstruction step. Our method employs Gaussian processes suitable for functions defined on Riemannian manifolds, allowing us to model the surface variation function across any given point cloud. A simplified version of the original cloud is obtained by sequentially selecting points using a greedy sparsification scheme. The selection criterion used for this scheme ensures that the simplified cloud best represents the surface variation of the original point cloud. We evaluate our method on several benchmark and self-acquired point clouds, compare it to a range of existing methods, demonstrate its application in downstream tasks of registration and surface reconstruction, and show that our method is competitive both in terms of empirical performance and computational efficiency. The code is available at \href{https://github.com/stutipathak5/gps-for-point-clouds}{https://github.com/stutipathak5/gps-for-point-clouds}.

Figures (11)

• Figure 1: Point cloud simplification methods typically fail to strike a balance between preserving sharp features and maintaining the overall structure of the original cloud. Our approach circumvents this trade-off by achieving both targets, as is evident from the simplified versions of the Stanford Bunny levoy2005stanford obtained using the proposed technique and three pre-existing methods; Hierarchical Clustering (HC) pauly2002efficient, Weighted Locally Optimal Projection (WLOP) huang2009consolidation, and Potamias et al.potamias2022revisiting simplification.
• Figure 1: The original Stanford meshes and the angel mesh.
• Figure 2: Simplified representations of the Dragon point cloud for simplification ratio $\alpha=0.03$ (top row) and associated reconstructed meshes (bottom row) for all evaluated simplification techniques.
• Figure 2: Surface reconstruction results of the simplified version of the Lucy point cloud for simplification ratio $\alpha=0.002$ for all evaluated simplification techniques except PC-Simp.
• Figure 3: Simplification results of a noisy Armadillo with Gaussian noise added to every point position (of standard deviation $\sigma = 2.5\times 10^{-3} \times d$, where $d$ is the bounding box diagonal length) for simplification ratio $\alpha=0.05$ for all evaluated simplification techniques.