# HyperGCT: A Dynamic Hyper-GNN-Learned Geometric Constraint for 3D Registration

arXiv: https://arxiv.org/abs/2503.02195 · HTML: https://mlsanity.com/paper/2503.02195/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 56 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Builds on (most cited first, 21 of 21)

- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [MAGSAC++, a fast, reliable and accurate robust estimator](https://mlsanity.com/paper/1912.05909/) (2019)
- [CoFiNet: Reliable Coarse-to-fine Correspondences for Robust Point Cloud Registration](https://mlsanity.com/paper/2110.14076/) (2021)
- [PointDSC: Robust Point Cloud Registration using Deep Spatial Consistency](https://mlsanity.com/paper/2103.05465/) (2021)
- [Graph-Cut RANSAC](https://mlsanity.com/paper/1706.00984/) (2017)
- [UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks](https://mlsanity.com/paper/2105.00956/) (2021)
- [3DRegNet: A Deep Neural Network for 3D Point Registration](https://mlsanity.com/paper/1904.01701/) (2019)
- [GeoTransformer: Fast and Robust Point Cloud Registration with Geometric Transformer](https://mlsanity.com/paper/2308.03768/) (2023)
- [Deep Hough Voting for Robust Global Registration](https://mlsanity.com/paper/2109.04310/) (2021)
- [Robust Outlier Rejection for 3D Registration with Variational Bayes](https://mlsanity.com/paper/2304.01514/) (2023)
- [Parallel Maximum Clique Algorithms with Applications to Network Analysis and Storage](https://mlsanity.com/paper/1302.6256/) (2013)
- [Hypergraph Spectral Analysis and Processing in 3D Point Cloud](https://mlsanity.com/paper/2001.02384/) (2020)
- [TriVoC: Efficient Voting-based Consensus Maximization for Robust Point Cloud Registration with Extreme Outlier Ratios](https://mlsanity.com/paper/2111.00657/) (2021)
- [G3Reg: Pyramid Graph-based Global Registration using Gaussian Ellipsoid Model](https://mlsanity.com/paper/2308.11573/) (2023)
- [An Efficient Hypergraph Approach to Robust Point Cloud Resampling](https://mlsanity.com/paper/2103.06999/) (2021)
- [3D Registration in 30 Years: A Survey](https://mlsanity.com/paper/2412.13735/) (2024)
- [On Efficient and Robust Metrics for RANSAC Hypotheses and 3D Rigid Registration](https://mlsanity.com/paper/2011.04862/) (2020)

## Built on by (most cited first, 4 of 4)

- [DualReg: Dual-Space Filtering and Reinforcement for Rigid Registration](https://mlsanity.com/paper/2508.17034/) (2025)
- [Angle-I2P: Angle-Consistent-Aware Hierarchical Attention for Cross-Modality Outlier Rejection](https://mlsanity.com/paper/2605.04541/) (2026)
- [Levy-Driven Correspondence Estimation for Registration](https://mlsanity.com/paper/2609.32612/) (2026)
- [Byzantine-Resilient Federated Large Language Model via Hypergraph Message Passing](https://mlsanity.com/paper/2610.12711/) (2026)

## Abstract (arXiv)

Geometric constraints between feature matches are critical in 3D point cloud registration problems. Existing approaches typically model unordered matches as a consistency graph and sample consistent matches to generate hypotheses. However, explicit graph construction introduces noise, posing great challenges for handcrafted geometric constraints to render consistency. To overcome this, we propose HyperGCT, a flexible dynamic Hyper-GNN-learned geometric ConstrainT that leverages high-order consistency among 3D correspondences. To our knowledge, HyperGCT is the first method that mines robust geometric constraints from dynamic hypergraphs for 3D registration. By dynamically optimizing the hypergraph through vertex and edge feature aggregation, HyperGCT effectively captures the correlations among correspondences, leading to accurate hypothesis generation. Extensive experiments on 3DMatch, 3DLoMatch, KITTI-LC, and ETH show that HyperGCT achieves state-of-the-art performance. Furthermore, HyperGCT is robust to graph noise, demonstrating a significant advantage in terms of generalization.