# An Efficient Hypergraph Approach to Robust Point Cloud Resampling

arXiv: https://arxiv.org/abs/2103.06999 · HTML: https://mlsanity.com/paper/2103.06999/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 31 references that are in the map.
- First posted on arXiv 11 Mar 2021.

## Builds on (most cited first, 8 of 8)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [3DSSD: Point-based 3D Single Stage Object Detector](https://mlsanity.com/paper/2002.10187/) (2020)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Semantic3D.net: A new Large-scale Point Cloud Classification Benchmark](https://mlsanity.com/paper/1704.03847/) (2017)
- [Fast Resampling of 3D Point Clouds via Graphs](https://mlsanity.com/paper/1702.06397/) (2017)
- [Introducing Hypergraph Signal Processing: Theoretical Foundation and Practical Applications](https://mlsanity.com/paper/1907.09203/) (2019)
- [Hypergraph Spectral Analysis and Processing in 3D Point Cloud](https://mlsanity.com/paper/2001.02384/) (2020)

## Built on by (most cited first, 3 of 3)

- [PointCAT: Contrastive Adversarial Training for Robust Point Cloud Recognition](https://mlsanity.com/paper/2209.07788/) (2022)
- [GraphReg: Dynamical Point Cloud Registration with Geometry-aware Graph Signal Processing](https://mlsanity.com/paper/2302.01109/) (2023)
- [HyperGCT: A Dynamic Hyper-GNN-Learned Geometric Constraint for 3D Registration](https://mlsanity.com/paper/2503.02195/) (2025)

## Abstract (arXiv)

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.