# S3I-PointHop: SO(3)-Invariant PointHop for 3D Point Cloud Classification

arXiv: https://arxiv.org/abs/2302.11506 · HTML: https://mlsanity.com/paper/2302.11506/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 29 references that are in the map.
- First posted on arXiv 22 Feb 2023.

## Builds on (most cited first, 22 of 22)

- [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)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [PPFNet: Global Context Aware Local Features for Robust 3D Point Matching](https://mlsanity.com/paper/1802.02669/) (2018)
- [PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local Descriptors](https://mlsanity.com/paper/1808.10322/) (2018)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [A Rotation-Invariant Framework for Deep Point Cloud Analysis](https://mlsanity.com/paper/2003.07238/) (2020)
- [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)
- [Leveraging SE(3) Equivariance for Self-Supervised Category-Level Object Pose Estimation](https://mlsanity.com/paper/2111.00190/) (2021)
- [PixelHop++: A Small Successive-Subspace-Learning-Based (SSL-based) Model for Image Classification](https://mlsanity.com/paper/2002.03141/) (2020)
- [Green Learning: Introduction, Examples and Outlook](https://mlsanity.com/paper/2210.00965/) (2022)
- [R-PointHop: A Green, Accurate, and Unsupervised Point Cloud Registration Method](https://mlsanity.com/paper/2103.08129/) (2021)
- [On Supervised Feature Selection from High Dimensional Feature Spaces](https://mlsanity.com/paper/2203.11924/) (2022)
- [PointHop++: A Lightweight Learning Model on Point Sets for 3D Classification](https://mlsanity.com/paper/2002.03281/) (2020)
- [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)
- [GSIP: Green Semantic Segmentation of Large-Scale Indoor Point Clouds](https://mlsanity.com/paper/2109.11835/) (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)

## Built on by (most cited first, 3 of 3)

- [Enhancing Edge Intelligence with Highly Discriminant LNT Features](https://mlsanity.com/paper/2312.14968/) (2023)
- [PointFlowHop: Green and Interpretable Scene Flow Estimation from Consecutive Point Clouds](https://mlsanity.com/paper/2302.14193/) (2023)
- [A Tiny Machine Learning Model for Point Cloud Object Classification](https://mlsanity.com/paper/2303.10898/) (2023)

## Abstract (arXiv)

Many point cloud classification methods are developed under the assumption that all point clouds in the dataset are well aligned with the canonical axes so that the 3D Cartesian point coordinates can be employed to learn features. When input point clouds are not aligned, the classification performance drops significantly. In this work, we focus on a mathematically transparent point cloud classification method called PointHop, analyze its reason for failure due to pose variations, and solve the problem by replacing its pose dependent modules with rotation invariant counterparts. The proposed method is named SO(3)-Invariant PointHop (or S3I-PointHop in short). We also significantly simplify the PointHop pipeline using only one single hop along with multiple spatial aggregation techniques. The idea of exploiting more spatial information is novel. Experiments on the ModelNet40 dataset demonstrate the superiority of S3I-PointHop over traditional PointHop-like methods.