# CLIPPER+: A Fast Maximal Clique Algorithm for Robust Global Registration

arXiv: https://arxiv.org/abs/2402.15464 · HTML: https://mlsanity.com/paper/2402.15464/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 50 references that are in the map.
- First posted on arXiv 23 Feb 2024.

## Builds on (most cited first, 19 of 19)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [The Perfect Match: 3D Point Cloud Matching with Smoothed Densities](https://mlsanity.com/paper/1811.06879/) (2018)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [Graph-Cut RANSAC](https://mlsanity.com/paper/1706.00984/) (2017)
- [Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection](https://mlsanity.com/paper/1909.08605/) (2019)
- [3D Registration with Maximal Cliques](https://mlsanity.com/paper/2305.10854/) (2023)
- [Guaranteed Outlier Removal for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/1711.10209/) (2017)
- [ROBIN: a Graph-Theoretic Approach to Reject Outliers in Robust Estimation using Invariants](https://mlsanity.com/paper/2011.03659/) (2020)
- [DOOR-SLAM: Distributed, Online, and Outlier Resilient SLAM for Robotic Teams](https://mlsanity.com/paper/1909.12198/) (2019)
- [CLIPPER: A Graph-Theoretic Framework for Robust Data Association](https://mlsanity.com/paper/2011.10202/) (2020)
- [A Practical Maximum Clique Algorithm for Matching with Pairwise Constraints](https://mlsanity.com/paper/1902.01534/) (2019)
- [Parallel Maximum Clique Algorithms with Applications to Network Analysis and Storage](https://mlsanity.com/paper/1302.6256/) (2013)
- [CLEAR: A Consistent Lifting, Embedding, and Alignment Rectification Algorithm for Multi-View Data Association](https://mlsanity.com/paper/1902.02256/) (2019)
- [Solving the Maximum Clique Problem with Symmetric Rank-One Nonnegative Matrix Approximation](https://mlsanity.com/paper/1505.07077/) (2015)
- [GraffMatch: Global Matching of 3D Lines and Planes for Wide Baseline LiDAR Registration](https://mlsanity.com/paper/2212.12745/) (2022)
- [View-Invariant Localization using Semantic Objects in Changing Environments](https://mlsanity.com/paper/2209.14426/) (2022)
- [MIXER: Multiattribute, Multiway Fusion of Uncertain Pairwise Affinities](https://mlsanity.com/paper/2210.08360/) (2022)

## Built on by (most cited first, 5 of 5)

- [BUFFER-X: Towards Zero-Shot Point Cloud Registration in Diverse Scenes](https://mlsanity.com/paper/2503.07940/) (2025)
- [Toward Zero-Shot Point Cloud Registration Across Diverse Scales, Scenes, and Sensor Setups](https://mlsanity.com/paper/2601.02759/) (2026)
- [DualReg: Dual-Space Filtering and Reinforcement for Rigid Registration](https://mlsanity.com/paper/2508.17034/) (2025)
- [Robust 3D Alignment of Generative Reconstructions via Partial Monocular Observations](https://mlsanity.com/paper/2607.00498/) (2026)
- [PARTE: Plane-Assisted Robust Transformation Estimation for Point Cloud Registration](https://mlsanity.com/paper/2609.25375/) (2026)

## Abstract (arXiv)

We present CLIPPER+, an algorithm for finding maximal cliques in unweighted graphs for outlier-robust global registration. The registration problem can be formulated as a graph and solved by finding its maximum clique. This formulation leads to extreme robustness to outliers; however, finding the maximum clique is an NP-hard problem, and therefore approximation is required in practice for large-size problems. The performance of an approximation algorithm is evaluated by its computational complexity (the lower the runtime, the better) and solution accuracy (how close the solution is to the maximum clique). Accordingly, the main contribution of CLIPPER+ is outperforming the state-of-the-art in accuracy while maintaining a relatively low runtime. CLIPPER+ builds on prior work (CLIPPER [1] and PMC [2]) and prunes the graph by removing vertices that have a small core number and cannot be a part of the maximum clique. This will result in a smaller graph, on which the maximum clique can be estimated considerably faster. We evaluate the performance of CLIPPER+ on standard graph benchmarks, as well as synthetic and real-world point cloud registration problems. These evaluations demonstrate that CLIPPER+ has the highest accuracy and can register point clouds in scenarios where over 99% of associations are outliers. Our code and evaluation benchmarks are released at https://github.com/ariarobotics/clipperp.