# Rigid and Articulated Point Registration with Expectation Conditional Maximization

arXiv: https://arxiv.org/abs/2012.05191 · HTML: https://mlsanity.com/paper/2012.05191/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2020.

## Built on by (most cited first, 11 of 11)

- [LSG-CPD: Coherent Point Drift with Local Surface Geometry for Point Cloud Registration](https://mlsanity.com/paper/2103.15039/) (2021)
- [Self-supervised 3D Human Mesh Recovery from Noisy Point Clouds](https://mlsanity.com/paper/2107.07539/) (2021)
- [Stein ICP for Uncertainty Estimation in Point Cloud Matching](https://mlsanity.com/paper/2106.03287/) (2021)
- [GraphReg: Dynamical Point Cloud Registration with Geometry-aware Graph Signal Processing](https://mlsanity.com/paper/2302.01109/) (2023)
- [Correspondence-Free SE(3) Point Cloud Registration in RKHS via Unsupervised Equivariant Learning](https://mlsanity.com/paper/2407.20223/) (2024)
- [A Comprehensive Survey for Real-World Industrial Defect Detection: Challenges, Approaches, and Prospects](https://mlsanity.com/paper/2507.13378/) (2025)
- [3D Shape Registration Using Spectral Graph Embedding and Probabilistic Matching](https://mlsanity.com/paper/2106.11166/) (2021)
- [SGBA: Semantic Gaussian Mixture Model-Based LiDAR Bundle Adjustment](https://mlsanity.com/paper/2410.01618/) (2024)
- [Improved Algorithm for the Network Alignment Problem with Application to Binary Diffing](https://mlsanity.com/paper/2112.15336/) (2021)
- [Multiview point cloud registration with anisotropic and space-varying localization noise](https://mlsanity.com/paper/2201.00708/) (2022)
- [Structured Analytic Coherent Point Drift for Non-Rigid Point Set Registration](https://mlsanity.com/paper/2605.00934/) (2026)

## Abstract (arXiv)

This paper addresses the issue of matching rigid and articulated shapes through probabilistic point registration. The problem is recast into a missing data framework where unknown correspondences are handled via mixture models. Adopting a maximum likelihood principle, we introduce an innovative EM-like algorithm, namely the Expectation Conditional Maximization for Point Registration (ECMPR) algorithm. The algorithm allows the use of general covariance matrices for the mixture model components and improves over the isotropic covariance case. We analyse in detail the associated consequences in terms of estimation of the registration parameters, and we propose an optimal method for estimating the rotational and translational parameters based on semi-definite positive relaxation. We extend rigid registration to articulated registration. Robustness is ensured by detecting and rejecting outliers through the addition of a uniform component to the Gaussian mixture model at hand. We provide an in-depth analysis of our method and we compare it both theoretically and experimentally with other robust methods for point registration.