# LSG-CPD: Coherent Point Drift with Local Surface Geometry for Point Cloud Registration

arXiv: https://arxiv.org/abs/2103.15039 · HTML: https://mlsanity.com/paper/2103.15039/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 45 references that are in the map.
- First posted on arXiv 28 Mar 2021.

## Builds on (most cited first, 7 of 7)

- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [FilterReg: Robust and Efficient Probabilistic Point-Set Registration using Gaussian Filter and Twist Parameterization](https://mlsanity.com/paper/1811.10136/) (2018)
- [An Overview of Depth Cameras and Range Scanners Based on Time-of-Flight Technologies](https://mlsanity.com/paper/2012.06772/) (2020)
- [An Adaptive Data Representation for Robust Point-Set Registration and Merging](https://mlsanity.com/paper/1511.04240/) (2015)
- [Rigid and Articulated Point Registration with Expectation Conditional Maximization](https://mlsanity.com/paper/2012.05191/) (2020)
- [Registration of multi-view point sets under the perspective of expectation-maximization](https://mlsanity.com/paper/2002.07464/) (2020)
- [Robust Intrinsic and Extrinsic Calibration of RGB-D Cameras](https://mlsanity.com/paper/1701.05748/) (2017)

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

- [Point Cloud Registration for LiDAR and Photogrammetric Data: a Critical Synthesis and Performance Analysis on Classic and Deep Learning Algorithms](https://mlsanity.com/paper/2302.07184/) (2023)
- [Multi-view Point Cloud Registration based on Evolutionary Multitasking with Bi-Channel Knowledge Sharing Mechanism](https://mlsanity.com/paper/2205.02996/) (2022)
- [GraphReg: Dynamical Point Cloud Registration with Geometry-aware Graph Signal Processing](https://mlsanity.com/paper/2302.01109/) (2023)
- [3D Registration in 30 Years: A Survey](https://mlsanity.com/paper/2412.13735/) (2024)
- [Reasoning and Learning a Perceptual Metric for Self-Training of Reflective Objects in Bin-Picking with a Low-cost Camera](https://mlsanity.com/paper/2503.20207/) (2025)
- [Probabilistic Registration for Gaussian Process 3D shape modelling in the presence of extensive missing data](https://mlsanity.com/paper/2203.14113/) (2022)
- [A General Mobile Manipulator Automation Framework for Flexible Manufacturing in Hostile Industrial Environments](https://mlsanity.com/paper/2302.04486/) (2023)
- [A Multi-modal Garden Dataset and Hybrid 3D Dense Reconstruction Framework Based on Panoramic Stereo Images for a Trimming Robot](https://mlsanity.com/paper/2305.06278/) (2023)
- [UniRiT: Towards Few-Shot Non-Rigid Point Cloud Registration](https://mlsanity.com/paper/2410.22909/) (2024)
- [Gmd: Gaussian mixture descriptor for pair matching of 3D fragments](https://mlsanity.com/paper/2604.21519/) (2026)
- [Sinkhorn-CPD: Robust point cloud registration via unbalanced entropic optimal transport](https://mlsanity.com/paper/2606.16672/) (2026)

## Abstract (arXiv)

Probabilistic point cloud registration methods are becoming more popular because of their robustness. However, unlike point-to-plane variants of iterative closest point (ICP) which incorporate local surface geometric information such as surface normals, most probabilistic methods (e.g., coherent point drift (CPD)) ignore such information and build Gaussian mixture models (GMMs) with isotropic Gaussian covariances. This results in sphere-like GMM components which only penalize the point-to-point distance between the two point clouds. In this paper, we propose a novel method called CPD with Local Surface Geometry (LSG-CPD) for rigid point cloud registration. Our method adaptively adds different levels of point-to-plane penalization on top of the point-to-point penalization based on the flatness of the local surface. This results in GMM components with anisotropic covariances. We formulate point cloud registration as a maximum likelihood estimation (MLE) problem and solve it with the Expectation-Maximization (EM) algorithm. In the E step, we demonstrate that the computation can be recast into simple matrix manipulations and efficiently computed on a GPU. In the M step, we perform an unconstrained optimization on a matrix Lie group to efficiently update the rigid transformation of the registration. The proposed method outperforms state-of-the-art algorithms in terms of accuracy and robustness on various datasets captured with range scanners, RGBD cameras, and LiDARs. Also, it is significantly faster than modern implementations of CPD. The source code is available at https://github.com/ChirikjianLab/LSG-CPD.git.