# Robust Outlier Rejection for 3D Registration with Variational Bayes

arXiv: https://arxiv.org/abs/2304.01514 · HTML: https://mlsanity.com/paper/2304.01514/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 55 references that are in the map.
- First posted on arXiv 4 Apr 2023.

## Builds on (most cited first, 30 of 31)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [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)
- [Geometric Transformer for Fast and Robust Point Cloud Registration](https://mlsanity.com/paper/2202.06688/) (2022)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)
- [D3Feat: Joint Learning of Dense Detection and Description of 3D Local Features](https://mlsanity.com/paper/2003.03164/) (2020)
- [Learning to Find Good Correspondences](https://mlsanity.com/paper/1711.05971/) (2017)
- [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)
- [Graph-Cut RANSAC](https://mlsanity.com/paper/1706.00984/) (2017)
- [Neural-Guided RANSAC: Learning Where to Sample Model Hypotheses](https://mlsanity.com/paper/1905.04132/) (2019)
- [Robust Point Cloud Registration Framework Based on Deep Graph Matching](https://mlsanity.com/paper/2103.04256/) (2021)
- [3DRegNet: A Deep Neural Network for 3D Point Registration](https://mlsanity.com/paper/1904.01701/) (2019)
- [REGTR: End-to-end Point Cloud Correspondences with Transformers](https://mlsanity.com/paper/2203.14517/) (2022)
- [Lepard: Learning partial point cloud matching in rigid and deformable scenes](https://mlsanity.com/paper/2111.12591/) (2021)
- [You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptors](https://mlsanity.com/paper/2109.00182/) (2021)
- [SC^2-PCR: A Second Order Spatial Compatibility for Efficient and Robust Point Cloud Registration](https://mlsanity.com/paper/2203.14453/) (2022)
- [Deep Hough Voting for Robust Global Registration](https://mlsanity.com/paper/2109.04310/) (2021)
- [IMLS-SLAM: scan-to-model matching based on 3D data](https://mlsanity.com/paper/1802.08633/) (2018)
- [SegICP: Integrated Deep Semantic Segmentation and Pose Estimation](https://mlsanity.com/paper/1703.01661/) (2017)
- [SDRSAC: Semidefinite-Based Randomized Approach for Robust Point Cloud Registration without Correspondences](https://mlsanity.com/paper/1904.03483/) (2019)
- [Sampling Network Guided Cross-Entropy Method for Unsupervised Point Cloud Registration](https://mlsanity.com/paper/2109.06619/) (2021)
- [Reliable Inlier Evaluation for Unsupervised Point Cloud Registration](https://mlsanity.com/paper/2202.11292/) (2022)
- [MatchNorm: Learning-based Point Cloud Registration for 6D Object Pose Estimation in the Real World](https://mlsanity.com/paper/2203.15309/) (2022)
- [A Performance Evaluation of Correspondence Grouping Methods for 3D Rigid Data Matching](https://mlsanity.com/paper/1907.02890/) (2019)
- [Planning with Learned Dynamic Model for Unsupervised Point Cloud Registration](https://mlsanity.com/paper/2108.02613/) (2021)

## Built on by (most cited first, 30 of 31)

- [Scalable 3D Registration via Truncated Entry-wise Absolute Residuals](https://mlsanity.com/paper/2404.00915/) (2024)
- [TurboReg: TurboClique for Robust and Efficient Point Cloud Registration](https://mlsanity.com/paper/2507.01439/) (2025)
- [SPAZER: Spatial-Semantic Progressive Reasoning Agent for Zero-shot 3D Visual Grounding](https://mlsanity.com/paper/2506.21924/) (2025)
- [Efficient and Robust Point Cloud Registration via Heuristics-guided Parameter Search](https://mlsanity.com/paper/2404.06155/) (2024)
- [PointDifformer: Robust Point Cloud Registration With Neural Diffusion and Transformer](https://mlsanity.com/paper/2404.14034/) (2024)
- [VGGT-360: Geometry-Consistent Zero-Shot Panoramic Depth Estimation](https://mlsanity.com/paper/2603.18943/) (2026)
- [Point Tree Transformer for Point Cloud Registration](https://mlsanity.com/paper/2406.17530/) (2024)
- [Progressive Correspondence Regenerator for Robust 3D Registration](https://mlsanity.com/paper/2502.02163/) (2025)
- [RARE: Refine Any Registration of Pairwise Point Clouds via Zero-Shot Learning](https://mlsanity.com/paper/2507.19950/) (2025)
- [PointRegGPT: Boosting 3D Point Cloud Registration using Generative Point-Cloud Pairs for Training](https://mlsanity.com/paper/2407.14054/) (2024)
- [HyperGCT: A Dynamic Hyper-GNN-Learned Geometric Constraint for 3D Registration](https://mlsanity.com/paper/2503.02195/) (2025)
- [Transformation Decoupling Strategy based on Screw Theory for Deterministic Point Cloud Registration with Gravity Prior](https://mlsanity.com/paper/2311.01432/) (2023)
- [Diff-Reg v1: Diffusion Matching Model for Registration Problem](https://mlsanity.com/paper/2403.19919/) (2024)
- [FUSER: Feed-Forward MUltiview 3D Registration Transformer and SE(3)N Diffusion Refinement](https://mlsanity.com/paper/2512.09373/) (2025)
- [RGBD-Glue: General Feature Combination for Robust RGB-D Point Cloud Registration](https://mlsanity.com/paper/2405.07594/) (2024)
- [Deep-PE: A Learning-Based Pose Evaluator for Point Cloud Registration](https://mlsanity.com/paper/2405.16085/) (2024)
- [Incremental Multiview Point Cloud Registration with Two-stage Candidate Retrieval](https://mlsanity.com/paper/2407.07525/) (2024)
- [Registering Neural 4D Gaussians for Endoscopic Surgery](https://mlsanity.com/paper/2407.20213/) (2024)
- [3D Registration in 30 Years: A Survey](https://mlsanity.com/paper/2412.13735/) (2024)
- [HybridReg: Robust 3D Point Cloud Registration with Hybrid Motions](https://mlsanity.com/paper/2503.07019/) (2025)
- [MonoSE(3)-Diffusion: A Monocular SE(3) Diffusion Framework for Robust Camera-to-Robot Pose Estimation](https://mlsanity.com/paper/2510.10434/) (2025)
- [CSCPR: Cross-Source-Context Indoor RGB-D Place Recognition](https://mlsanity.com/paper/2407.17457/) (2024)
- [Matching Distance and Geometric Distribution Aided Learning Multiview Point Cloud Registration](https://mlsanity.com/paper/2505.03692/) (2025)
- [DualReg: Dual-Space Filtering and Reinforcement for Rigid Registration](https://mlsanity.com/paper/2508.17034/) (2025)
- [DINOReg: Strong Point Cloud Registration with Vision Foundation Model](https://mlsanity.com/paper/2509.24370/) (2025)
- [ViGG: Robust RGB-D Point Cloud Registration using Visual-Geometric Mutual Guidance](https://mlsanity.com/paper/2511.22908/) (2025)
- [Non-Minimal Sampling and Consensus for Prohibitively Large Datasets](https://mlsanity.com/paper/2604.22518/) (2026)
- [A Cross-view Fusion Framework for Robust 6-DoF Grasp Pose Estimation](https://mlsanity.com/paper/2606.06878/) (2026)
- [RBE-Flow: Recurrent Bayesian Estimation on Feature Manifolds for Cross-Modal Registration](https://mlsanity.com/paper/2606.30492/) (2026)
- [PARTE: Plane-Assisted Robust Transformation Estimation for Point Cloud Registration](https://mlsanity.com/paper/2609.25375/) (2026)

## Abstract (arXiv)

Learning-based outlier (mismatched correspondence) rejection for robust 3D registration generally formulates the outlier removal as an inlier/outlier classification problem. The core for this to be successful is to learn the discriminative inlier/outlier feature representations. In this paper, we develop a novel variational non-local network-based outlier rejection framework for robust alignment. By reformulating the non-local feature learning with variational Bayesian inference, the Bayesian-driven long-range dependencies can be modeled to aggregate discriminative geometric context information for inlier/outlier distinction. Specifically, to achieve such Bayesian-driven contextual dependencies, each query/key/value component in our non-local network predicts a prior feature distribution and a posterior one. Embedded with the inlier/outlier label, the posterior feature distribution is label-dependent and discriminative. Thus, pushing the prior to be close to the discriminative posterior in the training step enables the features sampled from this prior at test time to model high-quality long-range dependencies. Notably, to achieve effective posterior feature guidance, a specific probabilistic graphical model is designed over our non-local model, which lets us derive a variational low bound as our optimization objective for model training. Finally, we propose a voting-based inlier searching strategy to cluster the high-quality hypothetical inliers for transformation estimation. Extensive experiments on 3DMatch, 3DLoMatch, and KITTI datasets verify the effectiveness of our method.