# Stein ICP for Uncertainty Estimation in Point Cloud Matching

arXiv: https://arxiv.org/abs/2106.03287 · HTML: https://mlsanity.com/paper/2106.03287/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 69 references that are in the map.
- First posted on arXiv 7 Jun 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Consistency and fluctuations for stochastic gradient Langevin dynamics](https://mlsanity.com/paper/1409.0578/) (2014)
- [The Newer College Dataset: Handheld LiDAR, Inertial and Vision with Ground Truth](https://mlsanity.com/paper/2003.05691/) (2020)
- [FilterReg: Robust and Efficient Probabilistic Point-Set Registration using Gaussian Filter and Twist Parameterization](https://mlsanity.com/paper/1811.10136/) (2018)
- [PointGMM: a Neural GMM Network for Point Clouds](https://mlsanity.com/paper/2003.13326/) (2020)
- [Stein Variational Gradient Descent With Matrix-Valued Kernels](https://mlsanity.com/paper/1910.12794/) (2019)
- [CELLO-3D: Estimating the Covariance of ICP in the Real World](https://mlsanity.com/paper/1810.01470/) (2018)
- [Rigid and Articulated Point Registration with Expectation Conditional Maximization](https://mlsanity.com/paper/2012.05191/) (2020)
- [A New Approach to 3D ICP Covariance Estimation](https://mlsanity.com/paper/1909.05722/) (2019)
- [Speeding Up Iterative Closest Point Using Stochastic Gradient Descent](https://mlsanity.com/paper/1907.09133/) (2019)
- [Estimating Motion Uncertainty with Bayesian ICP](https://mlsanity.com/paper/2004.07973/) (2020)
- [Invariant EKF Design for Scan Matching-aided Localization](https://mlsanity.com/paper/1503.01407/) (2015)

## Built on by (most cited first, 6 of 6)

- [RANSAC Back to SOTA: A Two-stage Consensus Filtering for Real-time 3D Registration](https://mlsanity.com/paper/2410.15682/) (2024)
- [CHSEL: Producing Diverse Plausible Pose Estimates from Contact and Free Space Data](https://mlsanity.com/paper/2305.08042/) (2023)
- [Stein Variational Evolution Strategies](https://mlsanity.com/paper/2410.10390/) (2024)
- [Constrained Stein Variational Gradient Descent for Robot Perception, Planning, and Identification](https://mlsanity.com/paper/2506.00589/) (2025)
- [Human-Interpretable Uncertainty Explanations for Point Cloud Registration](https://mlsanity.com/paper/2509.18786/) (2025)
- [A dynamic memory assignment strategy for dilation-based ICP algorithm on embedded GPUs](https://mlsanity.com/paper/2512.04996/) (2025)

## Abstract (arXiv)

Quantification of uncertainty in point cloud matching is critical in many tasks such as pose estimation, sensor fusion, and grasping. Iterative closest point (ICP) is a commonly used pose estimation algorithm which provides a point estimate of the transformation between two point clouds. There are many sources of uncertainty in this process that may arise due to sensor noise, ambiguous environment, and occlusion. However, for safety critical problems such as autonomous driving, a point estimate of the pose transformation is not sufficient as it does not provide information about the multiple solutions. Current probabilistic ICP methods usually do not capture all sources of uncertainty and may provide unreliable transformation estimates which can have a detrimental effect in state estimation or decision making tasks that use this information. In this work we propose a new algorithm to align two point clouds that can precisely estimate the uncertainty of ICP's transformation parameters. We develop a Stein variational inference framework with gradient based optimization of ICP's cost function. The method provides a non-parametric estimate of the transformation, can model complex multi-modal distributions, and can be effectively parallelized on a GPU. Experiments using 3D kinect data as well as sparse indoor/outdoor LiDAR data show that our method is capable of efficiently producing accurate pose uncertainty estimates.