# SC^2-PCR: A Second Order Spatial Compatibility for Efficient and Robust Point Cloud Registration

arXiv: https://arxiv.org/abs/2203.14453 · HTML: https://mlsanity.com/paper/2203.14453/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 68 references that are in the map.
- First posted on arXiv 28 Mar 2022.

## Builds on (most cited first, 28 of 28)

- [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)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [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)
- [Learning to Find Good Correspondences](https://mlsanity.com/paper/1711.05971/) (2017)
- [CoFiNet: Reliable Coarse-to-fine Correspondences for Robust Point Cloud Registration](https://mlsanity.com/paper/2110.14076/) (2021)
- [Learning Two-View Correspondences and Geometry Using Order-Aware Network](https://mlsanity.com/paper/1908.04964/) (2019)
- [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)
- [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)
- [MAGSAC: marginalizing sample consensus](https://mlsanity.com/paper/1803.07469/) (2018)
- [3DFeat-Net: Weakly Supervised Local 3D Features for Point Cloud Registration](https://mlsanity.com/paper/1807.09413/) (2018)
- [3DRegNet: A Deep Neural Network for 3D Point Registration](https://mlsanity.com/paper/1904.01701/) (2019)
- [Learning to Match Features with Seeded Graph Matching Network](https://mlsanity.com/paper/2108.08771/) (2021)
- [Deep Hough Voting for Robust Global Registration](https://mlsanity.com/paper/2109.04310/) (2021)
- [OMNet: Learning Overlapping Mask for Partial-to-Partial Point Cloud Registration](https://mlsanity.com/paper/2103.00937/) (2021)
- [Progressive Correspondence Pruning by Consensus Learning](https://mlsanity.com/paper/2101.00591/) (2021)
- [NM-Net: Mining Reliable Neighbors for Robust Feature Correspondences](https://mlsanity.com/paper/1904.00320/) (2019)
- [Learnable Motion Coherence for Correspondence Pruning](https://mlsanity.com/paper/2011.14563/) (2020)
- [DetarNet: Decoupling Translation and Rotation by Siamese Network for Point Cloud Registration](https://mlsanity.com/paper/2112.14059/) (2021)
- [Cascade Network with Guided Loss and Hybrid Attention for Finding Good Correspondences](https://mlsanity.com/paper/2102.00411/) (2021)

## Built on by (most cited first, 30 of 62)

- [3D Registration with Maximal Cliques](https://mlsanity.com/paper/2305.10854/) (2023)
- [RegFormer: An Efficient Projection-Aware Transformer Network for Large-Scale Point Cloud Registration](https://mlsanity.com/paper/2303.12384/) (2023)
- [Robust Outlier Rejection for 3D Registration with Variational Bayes](https://mlsanity.com/paper/2304.01514/) (2023)
- [Point-TTA: Test-Time Adaptation for Point Cloud Registration Using Multitask Meta-Auxiliary Learning](https://mlsanity.com/paper/2308.16481/) (2023)
- [Robust Multiview Point Cloud Registration with Reliable Pose Graph Initialization and History Reweighting](https://mlsanity.com/paper/2304.00467/) (2023)
- [PARE-Net: Position-Aware Rotation-Equivariant Networks for Robust Point Cloud Registration](https://mlsanity.com/paper/2407.10142/) (2024)
- [FastMAC: Stochastic Spectral Sampling of Correspondence Graph](https://mlsanity.com/paper/2403.08770/) (2024)
- [Deep Graph-based Spatial Consistency for Robust Non-rigid Point Cloud Registration](https://mlsanity.com/paper/2303.09950/) (2023)
- [Extend Your Own Correspondences: Unsupervised Distant Point Cloud Registration by Progressive Distance Extension](https://mlsanity.com/paper/2403.03532/) (2024)
- [TurboReg: TurboClique for Robust and Efficient Point Cloud Registration](https://mlsanity.com/paper/2507.01439/) (2025)
- [Learning Accurate Template Matching with Differentiable Coarse-to-Fine Correspondence Refinement](https://mlsanity.com/paper/2303.08438/) (2023)
- [RANSAC Back to SOTA: A Two-stage Consensus Filtering for Real-time 3D Registration](https://mlsanity.com/paper/2410.15682/) (2024)
- [UTOPIC: Uncertainty-aware Overlap Prediction Network for Partial Point Cloud Registration](https://mlsanity.com/paper/2208.02712/) (2022)
- [PointDifformer: Robust Point Cloud Registration With Neural Diffusion and Transformer](https://mlsanity.com/paper/2404.14034/) (2024)
- [Efficient and Deterministic Search Strategy Based on Residual Projections for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/2305.11716/) (2023)
- [Deep Semantic Graph Matching for Large-scale Outdoor Point Clouds Registration](https://mlsanity.com/paper/2308.05314/) (2023)
- [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)
- [Adaptive Multi-step Refinement Network for Robust Point Cloud Registration](https://mlsanity.com/paper/2312.03053/) (2023)
- [ML-SemReg: Boosting Point Cloud Registration with Multi-level Semantic Consistency](https://mlsanity.com/paper/2407.09862/) (2024)
- [Unsupervised Point Cloud Registration with Self-Distillation](https://mlsanity.com/paper/2409.07558/) (2024)
- [A Consistency-Aware Spot-Guided Transformer for Versatile and Hierarchical Point Cloud Registration](https://mlsanity.com/paper/2410.10295/) (2024)
- [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)
- [Let-It-Flow: Simultaneous Optimization of 3D Flow and Object Clustering](https://mlsanity.com/paper/2404.08363/) (2024)
- [CLIP-Clique: Graph-based Correspondence Matching Augmented by Vision Language Models for Object-based Global Localization](https://mlsanity.com/paper/2410.03054/) (2024)
- [RegFormer++: An Efficient Large-Scale 3D LiDAR Point Registration Network with Projection-Aware 2D Transformer](https://mlsanity.com/paper/2603.14290/) (2026)
- [SphereNet: Learning a Noise-Robust and General Descriptor for Point Cloud Registration](https://mlsanity.com/paper/2307.09351/) (2023)
- [Shape-Graph Matching Network (SGM-net): Registration for Statistical Shape Analysis](https://mlsanity.com/paper/2308.06869/) (2023)
- [Q-REG: End-to-End Trainable Point Cloud Registration with Surface Curvature](https://mlsanity.com/paper/2309.16023/) (2023)

## Abstract (arXiv)

In this paper, we present a second order spatial compatibility (SC2) measure based method for efficient and robust point cloud registration (PCR), called SC2-PCR. Firstly, we propose a second order spatial compatibility (SC2) measure to compute the similarity between correspondences. It considers the global compatibility instead of local consistency, allowing for more distinctive clustering between inliers and outliers at early stage. Based on this measure, our registration pipeline employs a global spectral technique to find some reliable seeds from the initial correspondences. Then we design a two-stage strategy to expand each seed to a consensus set based on the SC2 measure matrix. Finally, we feed each consensus set to a weighted SVD algorithm to generate a candidate rigid transformation and select the best model as the final result. Our method can guarantee to find a certain number of outlier-free consensus sets using fewer samplings, making the model estimation more efficient and robust. In addition, the proposed SC2 measure is general and can be easily plugged into deep learning based frameworks. Extensive experiments are carried out to investigate the performance of our method. Code will be available at urlhttps://github.com/ZhiChen902/SC2-PCR.