# RIConv++: Effective Rotation Invariant Convolutions for 3D Point Clouds Deep Learning

arXiv: https://arxiv.org/abs/2202.13094 · HTML: https://mlsanity.com/paper/2202.13094/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 58 references that are in the map.
- First posted on arXiv 26 Feb 2022.

## Builds on (most cited first, 30 of 35)

- [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)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [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)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [Relation-Shape Convolutional Neural Network for Point Cloud Analysis](https://mlsanity.com/paper/1904.07601/) (2019)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (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)
- [Volumetric and Multi-View CNNs for Object Classification on 3D Data](https://mlsanity.com/paper/1604.03265/) (2016)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [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)
- [Pointwise Convolutional Neural Networks](https://mlsanity.com/paper/1712.05245/) (2017)
- [ShellNet: Efficient Point Cloud Convolutional Neural Networks using Concentric Shells Statistics](https://mlsanity.com/paper/1908.06295/) (2019)
- [Polar Transformer Networks](https://mlsanity.com/paper/1709.01889/) (2017)
- [Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/1908.06297/) (2019)
- [TI-POOLING: transformation-invariant pooling for feature learning in Convolutional Neural Networks](https://mlsanity.com/paper/1604.06318/) (2016)
- [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)
- [O-CNN: Octree-based Convolutional Neural Networks for 3D Shape Analysis](https://mlsanity.com/paper/1712.01537/) (2017)
- [Equivariant Multi-View Networks](https://mlsanity.com/paper/1904.00993/) (2019)
- [Quaternion Equivariant Capsule Networks for 3D Point Clouds](https://mlsanity.com/paper/1912.12098/) (2019)
- [Rotation-Invariant Local-to-Global Representation Learning for 3D Point Cloud](https://mlsanity.com/paper/2010.03318/) (2020)
- [Rotational Projection Statistics for 3D Local Surface Description and Object Recognition](https://mlsanity.com/paper/1304.3192/) (2013)

## Built on by (most cited first, 29 of 29)

- [Benchmarking the Robustness of LiDAR Semantic Segmentation Models](https://mlsanity.com/paper/2301.00970/) (2023)
- [Unlearnable 3D Point Clouds: Class-wise Transformation Is All You Need](https://mlsanity.com/paper/2410.03644/) (2024)
- [RI-MAE: Rotation-Invariant Masked AutoEncoders for Self-Supervised Point Cloud Representation Learning](https://mlsanity.com/paper/2409.00353/) (2024)
- [Registration is a Powerful Rotation-Invariance Learner for 3D Anomaly Detection](https://mlsanity.com/paper/2510.16865/) (2025)
- [RISurConv: Rotation Invariant Surface Attention-Augmented Convolutions for 3D Point Cloud Classification and Segmentation](https://mlsanity.com/paper/2408.06110/) (2024)
- [Rotation-Adaptive Point Cloud Domain Generalization via Intricate Orientation Learning](https://mlsanity.com/paper/2502.02247/) (2025)
- [MaskLRF: Self-supervised Pretraining via Masked Autoencoding of Local Reference Frames for Rotation-invariant 3D Point Set Analysis](https://mlsanity.com/paper/2403.00206/) (2024)
- [ShapeEmbed: a self-supervised learning framework for 2D contour quantification](https://mlsanity.com/paper/2507.01009/) (2025)
- [PatchMixer: Rethinking network design to boost generalization for 3D point cloud understanding](https://mlsanity.com/paper/2307.15692/) (2023)
- [FoV-Net: Rotation-Invariant CAD B-rep Learning via Field-of-View Ray Casting](https://mlsanity.com/paper/2602.24084/) (2026)
- [General Rotation Invariance Learning for Point Clouds via Weight-Feature Alignment](https://mlsanity.com/paper/2302.09907/) (2023)
- [Self-supervised Learning of Rotation-invariant 3D Point Set Features using Transformer and its Self-distillation](https://mlsanity.com/paper/2308.04725/) (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)
- [REGRACE: A Robust and Efficient Graph-based Re-localization Algorithm using Consistency Evaluation](https://mlsanity.com/paper/2503.03599/) (2025)
- [Rotation-Invariant Completion Network](https://mlsanity.com/paper/2308.11979/) (2023)
- [RIDE: Boosting 3D Object Detection for LiDAR Point Clouds via Rotation-Invariant Analysis](https://mlsanity.com/paper/2408.15643/) (2024)
- [HFBRI-MAE: Handcrafted Feature Based Rotation-Invariant Masked Autoencoder for 3D Point Cloud Analysis](https://mlsanity.com/paper/2504.14132/) (2025)
- [Robust Point Cloud Reinforcement Learning via PCA-Based Canonicalization](https://mlsanity.com/paper/2510.20974/) (2025)
- [Evaluating 3D Shape Analysis Methods for Robustness to Rotation Invariance](https://mlsanity.com/paper/2305.18557/) (2023)
- [DRIP: Discriminative Rotation-Invariant Pole Landmark Descriptor for 3D LiDAR Localization](https://mlsanity.com/paper/2406.11266/) (2024)
- [Enhancing Robustness to Noise Corruption for Point Cloud Recognition via Spatial Sorting and Set-Mixing Aggregation Module](https://mlsanity.com/paper/2407.10806/) (2024)
- [Rotation Perturbation Robustness in Point Cloud Analysis: A Perspective of Manifold Distillation](https://mlsanity.com/paper/2411.01748/) (2024)
- [Rethinking Rotation-Invariant Recognition of Fine-grained Shapes from the Perspective of Contour Points](https://mlsanity.com/paper/2503.10992/) (2025)
- [SHREC 2025: Protein surface shape retrieval including electrostatic potential](https://mlsanity.com/paper/2509.12976/) (2025)
- [Beyond Random Masking: A Dual-Stream Approach for Rotation-Invariant Point Cloud Masked Autoencoders](https://mlsanity.com/paper/2509.14975/) (2025)
- [REVNET: Rotation-Equivariant Point Cloud Completion via Vector Neuron Anchor Transformer](https://mlsanity.com/paper/2601.08558/) (2026)
- [RI-Mamba: Rotation-Invariant Mamba for Robust Text-to-Shape Retrieval](https://mlsanity.com/paper/2602.11673/) (2026)
- [Learning Coordinate-based Convolutional Kernels for Continuous SE(3) Equivariant and Efficient Point Cloud Analysis](https://mlsanity.com/paper/2603.17538/) (2026)

## Abstract (arXiv)

3D point clouds deep learning is a promising field of research that allows a neural network to learn features of point clouds directly, making it a robust tool for solving 3D scene understanding tasks. While recent works show that point cloud convolutions can be invariant to translation and point permutation, investigations of the rotation invariance property for point cloud convolution has been so far scarce. Some existing methods perform point cloud convolutions with rotation-invariant features, existing methods generally do not perform as well as translation-invariant only counterpart. In this work, we argue that a key reason is that compared to point coordinates, rotation-invariant features consumed by point cloud convolution are not as distinctive. To address this problem, we propose a simple yet effective convolution operator that enhances feature distinction by designing powerful rotation invariant features from the local regions. We consider the relationship between the point of interest and its neighbors as well as the internal relationship of the neighbors to largely improve the feature descriptiveness. Our network architecture can capture both local and global context by simply tuning the neighborhood size in each convolution layer. We conduct several experiments on synthetic and real-world point cloud classifications, part segmentation, and shape retrieval to evaluate our method, which achieves the state-of-the-art accuracy under challenging rotations.