# Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration

arXiv: https://arxiv.org/abs/1605.03344 · HTML: https://mlsanity.com/paper/1605.03344/

## Key facts

- Cited by 159 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 May 2016.

## Built on by (most cited first, 30 of 159)

- [Robust Point Cloud Registration Framework Based on Deep Graph Matching](https://mlsanity.com/paper/2103.04256/) (2021)
- [Lepard: Learning partial point cloud matching in rigid and deformable scenes](https://mlsanity.com/paper/2111.12591/) (2021)
- [A comprehensive survey on point cloud registration](https://mlsanity.com/paper/2103.02690/) (2021)
- [3D Registration with Maximal Cliques](https://mlsanity.com/paper/2305.10854/) (2023)
- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [FS6D: Few-Shot 6D Pose Estimation of Novel Objects](https://mlsanity.com/paper/2203.14628/) (2022)
- [Full-Body Articulated Human-Object Interaction](https://mlsanity.com/paper/2212.10621/) (2022)
- [You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptors](https://mlsanity.com/paper/2109.00182/) (2021)
- [LCDNet: Deep Loop Closure Detection and Point Cloud Registration for LiDAR SLAM](https://mlsanity.com/paper/2103.05056/) (2021)
- [Deep Hough Voting for Robust Global Registration](https://mlsanity.com/paper/2109.04310/) (2021)
- [HRegNet: A Hierarchical Network for Large-scale Outdoor LiDAR Point Cloud Registration](https://mlsanity.com/paper/2107.11992/) (2021)
- [Accurate Point Cloud Registration with Robust Optimal Transport](https://mlsanity.com/paper/2111.00648/) (2021)
- [3D Face Reconstruction with the Geometric Guidance of Facial Part Segmentation](https://mlsanity.com/paper/2312.00311/) (2023)
- [Globally-Optimal Contrast Maximisation for Event Cameras](https://mlsanity.com/paper/2206.05127/) (2022)
- [Green Learning: Introduction, Examples and Outlook](https://mlsanity.com/paper/2210.00965/) (2022)
- [MULLS: Versatile LiDAR SLAM via Multi-metric Linear Least Square](https://mlsanity.com/paper/2102.03771/) (2021)
- [R-PointHop: A Green, Accurate, and Unsupervised Point Cloud Registration Method](https://mlsanity.com/paper/2103.08129/) (2021)
- [SSC: Semantic Scan Context for Large-Scale Place Recognition](https://mlsanity.com/paper/2107.00382/) (2021)
- [ReAgent: Point Cloud Registration using Imitation and Reinforcement Learning](https://mlsanity.com/paper/2103.15231/) (2021)
- [Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization](https://mlsanity.com/paper/2109.03349/) (2021)
- [PCAM: Product of Cross-Attention Matrices for Rigid Registration of Point Clouds](https://mlsanity.com/paper/2110.01269/) (2021)
- [A Single Correspondence Is Enough: Robust Global Registration to Avoid Degeneracy in Urban Environments](https://mlsanity.com/paper/2203.06612/) (2022)
- [FastMAC: Stochastic Spectral Sampling of Correspondence Graph](https://mlsanity.com/paper/2403.08770/) (2024)
- [Scalable 3D Registration via Truncated Entry-wise Absolute Residuals](https://mlsanity.com/paper/2404.00915/) (2024)
- [KISS-Matcher: Fast and Robust Point Cloud Registration Revisited](https://mlsanity.com/paper/2409.15615/) (2024)
- [ARCS: Accurate Rotation and Correspondence Search](https://mlsanity.com/paper/2203.14493/) (2022)
- [DeepMapping2: Self-Supervised Large-Scale LiDAR Map Optimization](https://mlsanity.com/paper/2212.06331/) (2022)
- [Accelerating Globally Optimal Consensus Maximization in Geometric Vision](https://mlsanity.com/paper/2304.05156/) (2023)
- [Multiway Point Cloud Mosaicking with Diffusion and Global Optimization](https://mlsanity.com/paper/2404.00429/) (2024)
- [MatchNorm: Learning-based Point Cloud Registration for 6D Object Pose Estimation in the Real World](https://mlsanity.com/paper/2203.15309/) (2022)

## Abstract (arXiv)

The Iterative Closest Point (ICP) algorithm is one of the most widely used methods for point-set registration. However, being based on local iterative optimization, ICP is known to be susceptible to local minima. Its performance critically relies on the quality of the initialization and only local optimality is guaranteed. This paper presents the first globally optimal algorithm, named Go-ICP, for Euclidean (rigid) registration of two 3D point-sets under the L2 error metric defined in ICP. The Go-ICP method is based on a branch-and-bound (BnB) scheme that searches the entire 3D motion space SE(3). By exploiting the special structure of SE(3) geometry, we derive novel upper and lower bounds for the registration error function. Local ICP is integrated into the BnB scheme, which speeds up the new method while guaranteeing global optimality. We also discuss extensions, addressing the issue of outlier robustness. The evaluation demonstrates that the proposed method is able to produce reliable registration results regardless of the initialization. Go-ICP can be applied in scenarios where an optimal solution is desirable or where a good initialization is not always available.