# R-PointHop: A Green, Accurate, and Unsupervised Point Cloud Registration Method

arXiv: https://arxiv.org/abs/2103.08129 · HTML: https://mlsanity.com/paper/2103.08129/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 65 references that are in the map.
- First posted on arXiv 15 Mar 2021.

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

- [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)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Green AI](https://mlsanity.com/paper/1907.10597/) (2019)
- [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)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (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)
- [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)
- [3DFeat-Net: Weakly Supervised Local 3D Features for Point Cloud Registration](https://mlsanity.com/paper/1807.09413/) (2018)
- [Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/1908.06297/) (2019)
- [Interpretable Convolutional Neural Networks via Feedforward Design](https://mlsanity.com/paper/1810.02786/) (2018)
- [PointHop: An Explainable Machine Learning Method for Point Cloud Classification](https://mlsanity.com/paper/1907.12766/) (2019)
- [UnsupervisedR&R: Unsupervised Point Cloud Registration via Differentiable Rendering](https://mlsanity.com/paper/2102.11870/) (2021)
- [A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates](https://mlsanity.com/paper/1903.08588/) (2019)
- [PointHop++: A Lightweight Learning Model on Point Sets for 3D Classification](https://mlsanity.com/paper/2002.03281/) (2020)
- [DeepMapping: Unsupervised Map Estimation From Multiple Point Clouds](https://mlsanity.com/paper/1811.11397/) (2018)
- [Unsupervised Point Cloud Registration via Salient Points Analysis (SPA)](https://mlsanity.com/paper/2009.01293/) (2020)
- [Unsupervised Feedforward Feature (UFF) Learning for Point Cloud Classification and Segmentation](https://mlsanity.com/paper/2009.01280/) (2020)
- [Iterative Transformer Network for 3D Point Cloud](https://mlsanity.com/paper/1811.11209/) (2018)
- [CORSAIR: Convolutional Object Retrieval and Symmetry-AIded Registration](https://mlsanity.com/paper/2103.06911/) (2021)
- [Evaluating Local Geometric Feature Representations for 3D Rigid Data Matching](https://mlsanity.com/paper/1907.00233/) (2019)

## Built on by (most cited first, 26 of 26)

- [Green Learning: Introduction, Examples and Outlook](https://mlsanity.com/paper/2210.00965/) (2022)
- [AnomalyHop: An SSL-based Image Anomaly Localization Method](https://mlsanity.com/paper/2105.03797/) (2021)
- [Overlap-guided Gaussian Mixture Models for Point Cloud Registration](https://mlsanity.com/paper/2210.09836/) (2022)
- [E-PixelHop: An Enhanced PixelHop Method for Object Classification](https://mlsanity.com/paper/2107.02966/) (2021)
- [TGHop: An Explainable, Efficient and Lightweight Method for Texture Generation](https://mlsanity.com/paper/2107.04020/) (2021)
- [GSIP: Green Semantic Segmentation of Large-Scale Indoor Point Clouds](https://mlsanity.com/paper/2109.11835/) (2021)
- [DefakeHop++: An Enhanced Lightweight Deepfake Detector](https://mlsanity.com/paper/2205.00211/) (2022)
- [PAGER: Progressive Attribute-Guided Extendable Robust Image Generation](https://mlsanity.com/paper/2206.00162/) (2022)
- [Bridging Gap between Image Pixels and Semantics via Supervision: A Survey](https://mlsanity.com/paper/2107.13757/) (2021)
- [GreenPCO: An Unsupervised Lightweight Point Cloud Odometry Method](https://mlsanity.com/paper/2112.04054/) (2021)
- [PCRP: Unsupervised Point Cloud Object Retrieval and Pose Estimation](https://mlsanity.com/paper/2202.07843/) (2022)
- [GENHOP: An Image Generation Method Based on Successive Subspace Learning](https://mlsanity.com/paper/2210.03689/) (2022)
- [Design of Supervision-Scalable Learning Systems: Methodology and Performance Benchmarking](https://mlsanity.com/paper/2206.09061/) (2022)
- [S3I-PointHop: SO(3)-Invariant PointHop for 3D Point Cloud Classification](https://mlsanity.com/paper/2302.11506/) (2023)
- [Enhancing Edge Intelligence with Highly Discriminant LNT Features](https://mlsanity.com/paper/2312.14968/) (2023)
- [RoCNet: 3D Robust Registration of Point-Clouds using Deep Learning](https://mlsanity.com/paper/2303.07963/) (2023)
- [LoGDesc: Local geometric features aggregation for robust point cloud registration](https://mlsanity.com/paper/2410.02420/) (2024)
- [3D Registration in 30 Years: A Survey](https://mlsanity.com/paper/2412.13735/) (2024)
- [The Z-axis, X-axis, Weight and Disambiguation Methods for Constructing Local Reference Frame in 3D Registration: An Evaluation](https://mlsanity.com/paper/2204.08024/) (2022)
- [PointFlowHop: Green and Interpretable Scene Flow Estimation from Consecutive Point Clouds](https://mlsanity.com/paper/2302.14193/) (2023)
- [Green Steganalyzer: A Green Learning Approach to Image Steganalysis](https://mlsanity.com/paper/2306.04008/) (2023)
- [NPNet: A Non-Parametric Network with Adaptive Gaussian-Fourier Positional Encoding for 3D Classification and Segmentation](https://mlsanity.com/paper/2602.00542/) (2026)
- [Accurate Ground-Truth Depth Image Generation via Overfit Training of Point Cloud Registration using Local Frame Sets](https://mlsanity.com/paper/2207.07016/) (2022)
- [A Tiny Machine Learning Model for Point Cloud Object Classification](https://mlsanity.com/paper/2303.10898/) (2023)
- [GWPT: A Green Word-Embedding-based POS Tagger](https://mlsanity.com/paper/2401.07475/) (2024)
- [Rethinking Rotation-Invariant Recognition of Fine-grained Shapes from the Perspective of Contour Points](https://mlsanity.com/paper/2503.10992/) (2025)

## Abstract (arXiv)

Inspired by the recent PointHop classification method, an unsupervised 3D point cloud registration method, called R-PointHop, is proposed in this work. R-PointHop first determines a local reference frame (LRF) for every point using its nearest neighbors and finds local attributes. Next, R-PointHop obtains local-to-global hierarchical features by point downsampling, neighborhood expansion, attribute construction and dimensionality reduction steps. Thus, point correspondences are built in hierarchical feature space using the nearest neighbor rule. Afterwards, a subset of salient points with good correspondence is selected to estimate the 3D transformation. The use of the LRF allows for invariance of the hierarchical features of points with respect to rotation and translation, thus making R-PointHop more robust at building point correspondence, even when the rotation angles are large. Experiments are conducted on the 3DMatch, ModelNet40, and Stanford Bunny datasets, which demonstrate the effectiveness of R-PointHop for 3D point cloud registration. R-PointHop's model size and training time are an order of magnitude smaller than those of deep learning methods, and its registration errors are smaller, making it a green and accurate solution. Our codes are available on GitHub.