# Accurate Point Cloud Registration with Robust Optimal Transport

arXiv: https://arxiv.org/abs/2111.00648 · HTML: https://mlsanity.com/paper/2111.00648/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 136 references that are in the map.
- First posted on arXiv 1 Nov 2021.

## Builds on (most cited first, 30 of 55)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [A Large Dataset to Train Convolutional Networks for Disparity, Optical Flow, and Scene Flow Estimation](https://mlsanity.com/paper/1512.02134/) (2015)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [FlowNet3D: Learning Scene Flow in 3D Point Clouds](https://mlsanity.com/paper/1806.01411/) (2018)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)
- [PPFNet: Global Context Aware Local Features for Robust 3D Point Matching](https://mlsanity.com/paper/1802.02669/) (2018)
- [The Perfect Match: 3D Point Cloud Matching with Smoothed Densities](https://mlsanity.com/paper/1811.06879/) (2018)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [SPLATNet: Sparse Lattice Networks for Point Cloud Processing](https://mlsanity.com/paper/1802.08275/) (2018)
- [PRNet: Self-Supervised Learning for Partial-to-Partial Registration](https://mlsanity.com/paper/1910.12240/) (2019)
- [PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local Descriptors](https://mlsanity.com/paper/1808.10322/) (2018)
- [Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures](https://mlsanity.com/paper/1508.07941/) (2015)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [FLOT: Scene Flow on Point Clouds Guided by Optimal Transport](https://mlsanity.com/paper/2007.11142/) (2020)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020)
- [Quicksilver: Fast Predictive Image Registration - a Deep Learning Approach](https://mlsanity.com/paper/1703.10908/) (2017)
- [HPLFlowNet: Hierarchical Permutohedral Lattice FlowNet for Scene Flow Estimation on Large-scale Point Clouds](https://mlsanity.com/paper/1906.05332/) (2019)

## Built on by (most cited first, 30 of 38)

- [textttGradICON: Approximate Diffeomorphisms via Gradient Inverse Consistency](https://mlsanity.com/paper/2206.05897/) (2022)
- [Temporally Consistent Unbalanced Optimal Transport for Unsupervised Action Segmentation](https://mlsanity.com/paper/2404.01518/) (2024)
- [AWT: Transferring Vision-Language Models via Augmentation, Weighting, and Transportation](https://mlsanity.com/paper/2407.04603/) (2024)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Quasi-Monte Carlo for 3D Sliced Wasserstein](https://mlsanity.com/paper/2309.11713/) (2023)
- [Diffeomorphic Image Registration with Neural Velocity Field](https://mlsanity.com/paper/2202.12498/) (2022)
- [Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learning](https://mlsanity.com/paper/2403.01781/) (2024)
- [Brain-ID: Learning Contrast-agnostic Anatomical Representations for Brain Imaging](https://mlsanity.com/paper/2311.16914/) (2023)
- [Joint Self-Supervised Video Alignment and Action Segmentation](https://mlsanity.com/paper/2503.16832/) (2025)
- [Deep learning-driven pulmonary artery and vein segmentation reveals demography-associated vasculature anatomical differences](https://mlsanity.com/paper/2404.07671/) (2024)
- [A Modality-agnostic Multi-task Foundation Model for Human Brain Imaging](https://mlsanity.com/paper/2509.00549/) (2025)
- [Efficient and Accurate Optimal Transport with Mirror Descent and Conjugate Gradients](https://mlsanity.com/paper/2307.08507/) (2023)
- [Unsupervised Cross-Domain Image Retrieval via Prototypical Optimal Transport](https://mlsanity.com/paper/2402.18411/) (2024)
- [Optimal Transport on the Lie Group of Roto-translations](https://mlsanity.com/paper/2402.15322/) (2024)
- [Unraveling Normal Anatomy via Fluid-Driven Anomaly Randomization](https://mlsanity.com/paper/2501.13370/) (2025)
- [Procedure Learning via Regularized Gromov-Wasserstein Optimal Transport](https://mlsanity.com/paper/2507.15540/) (2025)
- [Efficient Transferable Optimal Transport via Min-Sliced Transport Plans](https://mlsanity.com/paper/2511.19741/) (2025)
- [Approximation properties of slice-matching operators](https://mlsanity.com/paper/2310.10869/) (2023)
- [Unsupervised Solution Operator Learning for Mean-Field Games via Sampling-Invariant Parametrizations](https://mlsanity.com/paper/2401.15482/) (2024)
- [React-OT: Optimal Transport for Generating Transition State in Chemical Reactions](https://mlsanity.com/paper/2404.13430/) (2024)
- [APML: Adaptive Probabilistic Matching Loss for Robust 3D Point Cloud Reconstruction](https://mlsanity.com/paper/2509.08104/) (2025)
- [Graph Matching Optimization Network for Point Cloud Registration](https://mlsanity.com/paper/2302.05844/) (2023)
- [Shape-Graph Matching Network (SGM-net): Registration for Statistical Shape Analysis](https://mlsanity.com/paper/2308.06869/) (2023)
- [Partial Transport for Point-Cloud Registration](https://mlsanity.com/paper/2309.15787/) (2023)
- [A denoised Mean Teacher for domain adaptive point cloud registration](https://mlsanity.com/paper/2306.14749/) (2023)
- [Learning signals defined on graphs with optimal transport and Gaussian process regression](https://mlsanity.com/paper/2410.15721/) (2024)
- [PointVoxelFormer -- Reviving point cloud networks for 3D medical imaging](https://mlsanity.com/paper/2412.17390/) (2024)
- [COG: Confidence-aware Optimal Geometric Correspondence for Unsupervised Single-reference Novel Object Pose Estimation](https://mlsanity.com/paper/2603.00493/) (2026)
- [Hierarchical Attention and Graph Neural Networks: Toward Drift-Free Pose Estimation](https://mlsanity.com/paper/2309.09934/) (2023)
- [Interpretable deformable image registration: A geometric deep learning perspective](https://mlsanity.com/paper/2412.13294/) (2024)

## Abstract (arXiv)

This work investigates the use of robust optimal transport (OT) for shape matching. Specifically, we show that recent OT solvers improve both optimization-based and deep learning methods for point cloud registration, boosting accuracy at an affordable computational cost. This manuscript starts with a practical overview of modern OT theory. We then provide solutions to the main difficulties in using this framework for shape matching. Finally, we showcase the performance of transport-enhanced registration models on a wide range of challenging tasks: rigid registration for partial shapes; scene flow estimation on the Kitti dataset; and nonparametric registration of lung vascular trees between inspiration and expiration. Our OT-based methods achieve state-of-the-art results on Kitti and for the challenging lung registration task, both in terms of accuracy and scalability. We also release PVT1010, a new public dataset of 1,010 pairs of lung vascular trees with densely sampled points. This dataset provides a challenging use case for point cloud registration algorithms with highly complex shapes and deformations. Our work demonstrates that robust OT enables fast pre-alignment and fine-tuning for a wide range of registration models, thereby providing a new key method for the computer vision toolbox. Our code and dataset are available online at: https://github.com/uncbiag/robot.