# PRIN/SPRIN: On Extracting Point-wise Rotation Invariant Features

arXiv: https://arxiv.org/abs/2102.12093 · HTML: https://mlsanity.com/paper/2102.12093/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 55 references that are in the map.
- First posted on arXiv 24 Feb 2021.

## Builds on (most cited first, 30 of 37)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filters](https://mlsanity.com/paper/1803.11527/) (2018)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1706.01307/) (2017)
- [SO-Net: Self-Organizing Network for Point Cloud Analysis](https://mlsanity.com/paper/1803.04249/) (2018)
- [The Perfect Match: 3D Point Cloud Matching with Smoothed Densities](https://mlsanity.com/paper/1811.06879/) (2018)
- [SPLATNet: Sparse Lattice Networks for Point Cloud Processing](https://mlsanity.com/paper/1802.08275/) (2018)
- [Point Convolutional Neural Networks by Extension Operators](https://mlsanity.com/paper/1803.10091/) (2018)
- [Escape from Cells: Deep Kd-Networks for the Recognition of 3D Point Cloud Models](https://mlsanity.com/paper/1704.01222/) (2017)
- [PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local Descriptors](https://mlsanity.com/paper/1808.10322/) (2018)
- [Point2Sequence: Learning the Shape Representation of 3D Point Clouds with an Attention-based Sequence to Sequence Network](https://mlsanity.com/paper/1811.02565/) (2018)
- [Rotation-invariant convolutional neural networks for galaxy morphology prediction](https://mlsanity.com/paper/1503.07077/) (2015)
- [Recurrent Slice Networks for 3D Segmentation of Point Clouds](https://mlsanity.com/paper/1802.04402/) (2018)
- [Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/1908.06297/) (2019)
- [A Rotation-Invariant Framework for Deep Point Cloud Analysis](https://mlsanity.com/paper/2003.07238/) (2020)
- [Effective Rotation-invariant Point CNN with Spherical Harmonics kernels](https://mlsanity.com/paper/1906.11555/) (2019)
- [Spherical Kernel for Efficient Graph Convolution on 3D Point Clouds](https://mlsanity.com/paper/1909.09287/) (2019)

## Built on by (most cited first, 15 of 15)

- [CPPF: Towards Robust Category-Level 9D Pose Estimation in the Wild](https://mlsanity.com/paper/2203.03089/) (2022)
- [USEEK: Unsupervised SE(3)-Equivariant 3D Keypoints for Generalizable Manipulation](https://mlsanity.com/paper/2209.13864/) (2022)
- [General Place Recognition Survey: Towards Real-World Autonomy](https://mlsanity.com/paper/2405.04812/) (2024)
- [ACR-Pose: Adversarial Canonical Representation Reconstruction Network for Category Level 6D Object Pose Estimation](https://mlsanity.com/paper/2111.10524/) (2021)
- [RI-MAE: Rotation-Invariant Masked AutoEncoders for Self-Supervised Point Cloud Representation Learning](https://mlsanity.com/paper/2409.00353/) (2024)
- [RPR-Net: A Point Cloud-based Rotation-aware Large Scale Place Recognition Network](https://mlsanity.com/paper/2108.12790/) (2021)
- [Key-Grid: Unsupervised 3D Keypoints Detection using Grid Heatmap Features](https://mlsanity.com/paper/2410.02237/) (2024)
- [Rotation-Adaptive Point Cloud Domain Generalization via Intricate Orientation Learning](https://mlsanity.com/paper/2502.02247/) (2025)
- [CRIN: Rotation-Invariant Point Cloud Analysis and Rotation Estimation via Centrifugal Reference Frame](https://mlsanity.com/paper/2303.03101/) (2023)
- [Learning 3D Scene Analogies with Neural Contextual Scene Maps](https://mlsanity.com/paper/2503.15897/) (2025)
- [SelfGeo: Self-supervised and Geodesic-consistent Estimation of Keypoints on Deformable Shapes](https://mlsanity.com/paper/2408.02291/) (2024)
- [Evaluating 3D Shape Analysis Methods for Robustness to Rotation Invariance](https://mlsanity.com/paper/2305.18557/) (2023)
- [DEMOS: Dynamic Environment Motion Synthesis in 3D Scenes via Local Spherical-BEV Perception](https://mlsanity.com/paper/2403.01740/) (2024)
- [Rotation Perturbation Robustness in Point Cloud Analysis: A Perspective of Manifold Distillation](https://mlsanity.com/paper/2411.01748/) (2024)
- [Leveraging a Statistical Shape Model for Efficient Generation of Annotated Training Data: A Case Study on Liver Landmarks Segmentation](https://mlsanity.com/paper/2603.13969/) (2026)

## Abstract (arXiv)

Point cloud analysis without pose priors is very challenging in real applications, as the orientations of point clouds are often unknown. In this paper, we propose a brand new point-set learning framework PRIN, namely, Point-wise Rotation Invariant Network, focusing on rotation invariant feature extraction in point clouds analysis. We construct spherical signals by Density Aware Adaptive Sampling to deal with distorted point distributions in spherical space. Spherical Voxel Convolution and Point Re-sampling are proposed to extract rotation invariant features for each point. In addition, we extend PRIN to a sparse version called SPRIN, which directly operates on sparse point clouds. Both PRIN and SPRIN can be applied to tasks ranging from object classification, part segmentation, to 3D feature matching and label alignment. Results show that, on the dataset with randomly rotated point clouds, SPRIN demonstrates better performance than state-of-the-art methods without any data augmentation. We also provide thorough theoretical proof and analysis for point-wise rotation invariance achieved by our methods. Our code is available on https://github.com/qq456cvb/SPRIN.