# Deep Graph-based Spatial Consistency for Robust Non-rigid Point Cloud Registration

arXiv: https://arxiv.org/abs/2303.09950 · HTML: https://mlsanity.com/paper/2303.09950/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 71 references that are in the map.
- First posted on arXiv 17 Mar 2023.

## Builds on (most cited first, 30 of 44)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [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)
- [FlowNet3D: Learning Scene Flow in 3D Point Clouds](https://mlsanity.com/paper/1806.01411/) (2018)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (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)
- [The Perfect Match: 3D Point Cloud Matching with Smoothed Densities](https://mlsanity.com/paper/1811.06879/) (2018)
- [MAGSAC++, a fast, reliable and accurate robust estimator](https://mlsanity.com/paper/1912.05909/) (2019)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [CoFiNet: Reliable Coarse-to-fine Correspondences for Robust Point Cloud Registration](https://mlsanity.com/paper/2110.14076/) (2021)
- [SpinNet: Learning a General Surface Descriptor for 3D Point Cloud Registration](https://mlsanity.com/paper/2011.12149/) (2020)
- [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)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [Graph-Cut RANSAC](https://mlsanity.com/paper/1706.00984/) (2017)
- [FLOT: Scene Flow on Point Clouds Guided by Optimal Transport](https://mlsanity.com/paper/2007.11142/) (2020)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020)
- [4DComplete: Non-Rigid Motion Estimation Beyond the Observable Surface](https://mlsanity.com/paper/2105.01905/) (2021)
- [RAFT-3D: Scene Flow using Rigid-Motion Embeddings](https://mlsanity.com/paper/2012.00726/) (2020)
- [3DRegNet: A Deep Neural Network for 3D Point Registration](https://mlsanity.com/paper/1904.01701/) (2019)

## Built on by (most cited first, 15 of 15)

- [Scalable 3D Registration via Truncated Entry-wise Absolute Residuals](https://mlsanity.com/paper/2404.00915/) (2024)
- [Correspondence-Free Non-Rigid Point Set Registration Using Unsupervised Clustering Analysis](https://mlsanity.com/paper/2406.18817/) (2024)
- [EM-MIAs: Enhancing Membership Inference Attacks in Large Language Models through Ensemble Modeling](https://mlsanity.com/paper/2412.17249/) (2024)
- [Occlusion-aware Non-Rigid Point Cloud Registration via Unsupervised Neural Deformation Correntropy](https://mlsanity.com/paper/2502.10704/) (2025)
- [Diff-Reg v1: Diffusion Matching Model for Registration Problem](https://mlsanity.com/paper/2403.19919/) (2024)
- [Toward Reliable AR-Guided Surgical Navigation: Interactive Deformation Modeling with Data-Driven Biomechanics and Prompts](https://mlsanity.com/paper/2506.08048/) (2025)
- [Equivariant Local Reference Frames for Unsupervised Non-rigid Point Cloud Shape Correspondence](https://mlsanity.com/paper/2404.00959/) (2024)
- [DefTransNet: A Transformer-based Method for Non-Rigid Point Cloud Registration in the Simulation of Soft Tissue Deformation](https://mlsanity.com/paper/2502.06336/) (2025)
- [DC-Reg: Globally Optimal Point Cloud Registration via Tight Bounding with Difference of Convex Programming](https://mlsanity.com/paper/2603.25442/) (2026)
- [SPARE: Symmetrized Point-to-Plane Distance for Robust Non-Rigid 3D Registration](https://mlsanity.com/paper/2405.20188/) (2024)
- [ERNet: Efficient Non-Rigid Registration Network for Point Sequences](https://mlsanity.com/paper/2510.15800/) (2025)
- [Angle-I2P: Angle-Consistent-Aware Hierarchical Attention for Cross-Modality Outlier Rejection](https://mlsanity.com/paper/2605.04541/) (2026)
- [BridgeMatch: Conditional Transport Bridges in Matching Matrix Space for 3D Deformable Registration](https://mlsanity.com/paper/2609.11472/) (2026)
- [GRIP: Gaussian Rendering as a Cross-Modal Bridge for Image-to-Point Cloud Registration](https://mlsanity.com/paper/2609.25966/) (2026)
- [Levy-Driven Correspondence Estimation for Registration](https://mlsanity.com/paper/2609.32612/) (2026)

## Abstract (arXiv)

We study the problem of outlier correspondence pruning for non-rigid point cloud registration. In rigid registration, spatial consistency has been a commonly used criterion to discriminate outliers from inliers. It measures the compatibility of two correspondences by the discrepancy between the respective distances in two point clouds. However, spatial consistency no longer holds in non-rigid cases and outlier rejection for non-rigid registration has not been well studied. In this work, we propose Graph-based Spatial Consistency Network (GraphSCNet) to filter outliers for non-rigid registration. Our method is based on the fact that non-rigid deformations are usually locally rigid, or local shape preserving. We first design a local spatial consistency measure over the deformation graph of the point cloud, which evaluates the spatial compatibility only between the correspondences in the vicinity of a graph node. An attention-based non-rigid correspondence embedding module is then devised to learn a robust representation of non-rigid correspondences from local spatial consistency. Despite its simplicity, GraphSCNet effectively improves the quality of the putative correspondences and attains state-of-the-art performance on three challenging benchmarks. Our code and models are available at https://github.com/qinzheng93/GraphSCNet.