# Hypergraph Spectral Analysis and Processing in 3D Point Cloud

arXiv: https://arxiv.org/abs/2001.02384 · HTML: https://mlsanity.com/paper/2001.02384/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2020.

## Built on by (most cited first, 14 of 14)

- [Parameter-Efficient Fine-Tuning in Spectral Domain for Point Cloud Learning](https://mlsanity.com/paper/2410.08114/) (2024)
- [Hyper-3DG: Text-to-3D Gaussian Generation via Hypergraph](https://mlsanity.com/paper/2403.09236/) (2024)
- [Exploring the Devil in Graph Spectral Domain for 3D Point Cloud Attacks](https://mlsanity.com/paper/2202.07261/) (2022)
- [Point Cloud Attacks in Graph Spectral Domain: When 3D Geometry Meets Graph Signal Processing](https://mlsanity.com/paper/2207.13326/) (2022)
- [LPF-Defense: 3D Adversarial Defense based on Frequency Analysis](https://mlsanity.com/paper/2202.11287/) (2022)
- [EvolveHypergraph: Group-Aware Dynamic Relational Reasoning for Trajectory Prediction](https://mlsanity.com/paper/2208.05470/) (2022)
- [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)
- [An Efficient Hypergraph Approach to Robust Point Cloud Resampling](https://mlsanity.com/paper/2103.06999/) (2021)
- [HPGNN: Using Hierarchical Graph Neural Networks for Outdoor Point Cloud Processing](https://mlsanity.com/paper/2206.02153/) (2022)
- [3D Test-time Adaptation via Graph Spectral Driven Point Shift](https://mlsanity.com/paper/2507.18225/) (2025)
- [STS-Mixer: Spatio-Temporal-Spectral Mixer for 4D Point Cloud Video Understanding](https://mlsanity.com/paper/2604.11637/) (2026)
- [ROAD: Reciprocal-Objective Alignment of Discriminative Semantics for 3D Shape Generation](https://mlsanity.com/paper/2607.28581/) (2026)

## Abstract (arXiv)

Along with increasingly popular virtual reality applications, the three-dimensional (3D) point cloud has become a fundamental data structure to characterize 3D objects and surroundings. To process 3D point clouds efficiently, a suitable model for the underlying structure and outlier noises is always critical. In this work, we propose a hypergraph-based new point cloud model that is amenable to efficient analysis and processing. We introduce tensor-based methods to estimate hypergraph spectrum components and frequency coefficients of point clouds in both ideal and noisy settings. We establish an analytical connection between hypergraph frequencies and structural features. We further evaluate the efficacy of hypergraph spectrum estimation in two common point cloud applications of sampling and denoising for which also we elaborate specific hypergraph filter design and spectral properties. The empirical performance demonstrates the strength of hypergraph signal processing as a tool in 3D point clouds and the underlying properties.