# Deep Positional and Relational Feature Learning for Rotation-Invariant Point Cloud Analysis

arXiv: https://arxiv.org/abs/2011.09080 · HTML: https://mlsanity.com/paper/2011.09080/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2020.

## Built on by (most cited first, 22 of 22)

- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptors](https://mlsanity.com/paper/2109.00182/) (2021)
- [Frame Averaging for Equivariant Shape Space Learning](https://mlsanity.com/paper/2112.01741/) (2021)
- [The Devil is in the Pose: Ambiguity-free 3D Rotation-invariant Learning via Pose-aware Convolution](https://mlsanity.com/paper/2205.15210/) (2022)
- [RI-MAE: Rotation-Invariant Masked AutoEncoders for Self-Supervised Point Cloud Representation Learning](https://mlsanity.com/paper/2409.00353/) (2024)
- [SVNet: Where SO(3) Equivariance Meets Binarization on Point Cloud Representation](https://mlsanity.com/paper/2209.05924/) (2022)
- [Local-consistent Transformation Learning for Rotation-invariant Point Cloud Analysis](https://mlsanity.com/paper/2403.11113/) (2024)
- [RPR-Net: A Point Cloud-based Rotation-aware Large Scale Place Recognition Network](https://mlsanity.com/paper/2108.12790/) (2021)
- [Rethinking Rotation Invariance with Point Cloud Registration](https://mlsanity.com/paper/2301.00149/) (2022)
- [CRIN: Rotation-Invariant Point Cloud Analysis and Rotation Estimation via Centrifugal Reference Frame](https://mlsanity.com/paper/2303.03101/) (2023)
- [Open-Pose 3D Zero-Shot Learning: Benchmark and Challenges](https://mlsanity.com/paper/2312.07039/) (2023)
- [Stable and Consistent Prediction of 3D Characteristic Orientation via Invariant Residual Learning](https://mlsanity.com/paper/2306.11406/) (2023)
- [A Simple Strategy to Provable Invariance via Orbit Mapping](https://mlsanity.com/paper/2209.11916/) (2022)
- [General Rotation Invariance Learning for Point Clouds via Weight-Feature Alignment](https://mlsanity.com/paper/2302.09907/) (2023)
- [A general framework for rotation invariant point cloud analysis](https://mlsanity.com/paper/2402.01331/) (2024)
- [Efficient Continuous Group Convolutions for Local SE(3) Equivariance in 3D Point Clouds](https://mlsanity.com/paper/2502.07505/) (2025)
- [SPE-Net: Boosting Point Cloud Analysis via Rotation Robustness Enhancement](https://mlsanity.com/paper/2211.08250/) (2022)
- [Cloud-RAIN: Point Cloud Analysis with Reflectional Invariance](https://mlsanity.com/paper/2305.07814/) (2023)
- [RIDE: Boosting 3D Object Detection for LiDAR Point Clouds via Rotation-Invariant Analysis](https://mlsanity.com/paper/2408.15643/) (2024)
- [Revisiting Transformation Invariant Geometric Deep Learning: An Initial Representation Perspective](https://mlsanity.com/paper/2112.12345/) (2021)
- [Hierarchical Direction Perception via Atomic Dot-Product Operators for Rotation-Invariant Point Clouds Learning](https://mlsanity.com/paper/2511.08240/) (2025)
- [Attention-guided reference point shifting for Gaussian-mixture-based partial point set registration](https://mlsanity.com/paper/2512.02496/) (2025)

## Abstract (arXiv)

In this paper we propose a rotation-invariant deep network for point clouds analysis. Point-based deep networks are commonly designed to recognize roughly aligned 3D shapes based on point coordinates, but suffer from performance drops with shape rotations. Some geometric features, e.g., distances and angles of points as inputs of network, are rotation-invariant but lose positional information of points. In this work, we propose a novel deep network for point clouds by incorporating positional information of points as inputs while yielding rotation-invariance. The network is hierarchical and relies on two modules: a positional feature embedding block and a relational feature embedding block. Both modules and the whole network are proven to be rotation-invariant when processing point clouds as input. Experiments show state-of-the-art classification and segmentation performances on benchmark datasets, and ablation studies demonstrate effectiveness of the network design.