# Graph Matching Optimization Network for Point Cloud Registration

arXiv: https://arxiv.org/abs/2302.05844 · HTML: https://mlsanity.com/paper/2302.05844/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 59 references that are in the map.
- First posted on arXiv 12 Feb 2023.

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [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)
- [Geometric Transformer for Fast and Robust Point Cloud Registration](https://mlsanity.com/paper/2202.06688/) (2022)
- [PPFNet: Global Context Aware Local Features for Robust 3D Point Matching](https://mlsanity.com/paper/1802.02669/) (2018)
- [D3Feat: Joint Learning of Dense Detection and Description of 3D Local Features](https://mlsanity.com/paper/2003.03164/) (2020)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [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)
- [PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local Descriptors](https://mlsanity.com/paper/1808.10322/) (2018)
- [Gromov-Wasserstein Learning for Graph Matching and Node Embedding](https://mlsanity.com/paper/1901.06003/) (2019)
- [Unbalanced minibatch Optimal Transport; applications to Domain Adaptation](https://mlsanity.com/paper/2103.03606/) (2021)
- [3D Point Capsule Networks](https://mlsanity.com/paper/1812.10775/) (2018)
- [3DFeat-Net: Weakly Supervised Local 3D Features for Point Cloud Registration](https://mlsanity.com/paper/1807.09413/) (2018)
- [Unsupervised Alignment of Embeddings with Wasserstein Procrustes](https://mlsanity.com/paper/1805.11222/) (2018)
- [Robust Point Cloud Registration Framework Based on Deep Graph Matching](https://mlsanity.com/paper/2103.04256/) (2021)
- [REGTR: End-to-end Point Cloud Correspondences with Transformers](https://mlsanity.com/paper/2203.14517/) (2022)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [Learning with minibatch Wasserstein : asymptotic and gradient properties](https://mlsanity.com/paper/1910.04091/) (2019)
- [Lepard: Learning partial point cloud matching in rigid and deformable scenes](https://mlsanity.com/paper/2111.12591/) (2021)
- [Neural Graph Matching Network: Learning Lawler's Quadratic Assignment Problem with Extension to Hypergraph and Multiple-graph Matching](https://mlsanity.com/paper/1911.11308/) (2019)
- [Deep Shells: Unsupervised Shape Correspondence with Optimal Transport](https://mlsanity.com/paper/2010.15261/) (2020)
- [Multi-view Self-supervised Deep Learning for 6D Pose Estimation in the Amazon Picking Challenge](https://mlsanity.com/paper/1609.09475/) (2016)
- [You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptors](https://mlsanity.com/paper/2109.00182/) (2021)
- [LO-Net: Deep Real-time Lidar Odometry](https://mlsanity.com/paper/1904.08242/) (2019)
- [Deep Hough Voting for Robust Global Registration](https://mlsanity.com/paper/2109.04310/) (2021)

## Built on by (most cited first, 2 of 2)

- [3D Geometric Shape Assembly via Efficient Point Cloud Matching](https://mlsanity.com/paper/2407.10542/) (2024)
- [Diff-Reg v1: Diffusion Matching Model for Registration Problem](https://mlsanity.com/paper/2403.19919/) (2024)

## Abstract (arXiv)

Point Cloud Registration is a fundamental and challenging problem in 3D computer vision. Recent works often utilize the geometric structure information in point feature embedding or outlier rejection for registration while neglecting to consider explicitly isometry-preserving constraint (e.g., point pair linked edge's length preserving after transformation) in training. We claim that the explicit isometry-preserving constraint is also important for improving feature representation abilities in the feature training stage. To this end, we propose a underlineGraph underlineMatching underlineOptimization based underlineNetwork (GMONet for short), which utilizes the graph-matching optimizer to explicitly exert the isometry preserving constraints in the point feature training to improve the point feature representation. Specifically, we exploit a partial graph-matching optimizer to optimize the super point (i.e., down-sampled key points) features and a full graph-matching optimizer to optimize fine-level point features in the overlap region. Meanwhile, we leverage the inexact proximal point method and the mini-batch sampling technique to accelerate these two graph-matching optimizers. Given high discriminative point features in the evaluation stage, we utilize the RANSAC approach to estimate the transformation between the scanned pairs. The proposed method has been evaluated on the 3DMatch/3DLoMatch benchmarks and the KITTI benchmark. The experimental results show that our method performs competitively compared to state-of-the-art baselines.