# Joint Alignment of Multiple Point Sets with Batch and Incremental Expectation-Maximization

arXiv: https://arxiv.org/abs/1609.01466 · HTML: https://mlsanity.com/paper/1609.01466/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2016.

## Built on by (most cited first, 19 of 19)

- [Unsupervised Deep Probabilistic Approach for Partial Point Cloud Registration](https://mlsanity.com/paper/2303.13290/) (2023)
- [Overlap-guided Gaussian Mixture Models for Point Cloud Registration](https://mlsanity.com/paper/2210.09836/) (2022)
- [Robust Multi-view Registration of Point Sets with Laplacian Mixture Model](https://mlsanity.com/paper/2110.13744/) (2021)
- [Multi-view Point Cloud Registration based on Evolutionary Multitasking with Bi-Channel Knowledge Sharing Mechanism](https://mlsanity.com/paper/2205.02996/) (2022)
- [Correspondence-Free SE(3) Point Cloud Registration in RKHS via Unsupervised Equivariant Learning](https://mlsanity.com/paper/2407.20223/) (2024)
- [3D Registration in 30 Years: A Survey](https://mlsanity.com/paper/2412.13735/) (2024)
- [A Comprehensive Survey for Real-World Industrial Defect Detection: Challenges, Approaches, and Prospects](https://mlsanity.com/paper/2507.13378/) (2025)
- [3DMNDT:3D multi-view registration method based on the normal distributions transform](https://mlsanity.com/paper/2103.11084/) (2021)
- [Online Learning of a Probabilistic and Adaptive Scene Representation](https://mlsanity.com/paper/2103.16832/) (2021)
- [Incremental Multiview Point Cloud Registration](https://mlsanity.com/paper/2407.05021/) (2024)
- [SGBA: Semantic Gaussian Mixture Model-Based LiDAR Bundle Adjustment](https://mlsanity.com/paper/2410.01618/) (2024)
- [Multiview Point Cloud Registration via Optimization in an Autoencoder Latent Space](https://mlsanity.com/paper/2504.21467/) (2025)
- [Multiview point cloud registration with anisotropic and space-varying localization noise](https://mlsanity.com/paper/2201.00708/) (2022)
- [Robust Motion Averaging for Multi-view Registration of Point Sets Based Maximum Correntropy Criterion](https://mlsanity.com/paper/2208.11327/) (2022)
- [Attention-guided reference point shifting for Gaussian-mixture-based partial point set registration](https://mlsanity.com/paper/2512.02496/) (2025)
- [GeGS-PCR: Effective and Robust 3D Point Cloud Registration with Two-Stage Color-Enhanced Geometric-3DGS Fusion](https://mlsanity.com/paper/2604.17721/) (2026)
- [Structured Analytic Coherent Point Drift for Non-Rigid Point Set Registration](https://mlsanity.com/paper/2605.00934/) (2026)
- [A Holistic Method for Superquadric Fitting Using Unsupervised Clustering Analysis](https://mlsanity.com/paper/2605.16779/) (2026)
- [Spectral Consistency-Guided Multiview Point Cloud Registration for Low-Overlap Scenes](https://mlsanity.com/paper/2609.12417/) (2026)

## Abstract (arXiv)

This paper addresses the problem of registering multiple point sets. Solutions to this problem are often approximated by repeatedly solving for pairwise registration, which results in an uneven treatment of the sets forming a pair: a model set and a data set. The main drawback of this strategy is that the model set may contain noise and outliers, which negatively affects the estimation of the registration parameters. In contrast, the proposed formulation treats all the point sets on an equal footing. Indeed, all the points are drawn from a central Gaussian mixture, hence the registration is cast into a clustering problem. We formally derive batch and incremental EM algorithms that robustly estimate both the GMM parameters and the rotations and translations that optimally align the sets. Moreover, the mixture's means play the role of the registered set of points while the variances provide rich information about the contribution of each component to the alignment. We thoroughly test the proposed algorithms on simulated data and on challenging real data collected with range sensors. We compare them with several state-of-the-art algorithms, and we show their potential for surface reconstruction from depth data.