An Efficient Hypergraph Approach to Robust Point Cloud Resampling

TL;DR

This paper introduces a hypergraph signal processing approach for efficient and robust point cloud resampling, capturing complex relationships and surface features without extensive hypergraph construction.

Contribution

It proposes a novel hypergraph spectral filtering method that directly estimates hypergraph spectra from point clouds, enhancing feature preservation and robustness.

Findings

Effective hypergraph characterization of point clouds

Robustness under noisy observations

Improved surface outline preservation

Abstract

Efficient processing and feature extraction of largescale point clouds are important in related computer vision and cyber-physical systems. This work investigates point cloud resampling based on hypergraph signal processing (HGSP) to better explore the underlying relationship among different cloud points and to extract contour-enhanced features. Specifically, we design hypergraph spectral filters to capture multi-lateral interactions among the signal nodes of point clouds and to better preserve their surface outlines. Without the need and the computation to first construct the underlying hypergraph, our low complexity approach directly estimates hypergraph spectrum of point clouds by leveraging hypergraph stationary processes from the observed 3D coordinates. Evaluating the proposed resampling methods with several metrics, our test results validate the high efficacy of hypergraph characterization of point clouds and demonstrate the robustness of hypergraph-based resampling under noisy observations.