# Effective Rotation-invariant Point CNN with Spherical Harmonics kernels

arXiv: https://arxiv.org/abs/1906.11555 · HTML: https://mlsanity.com/paper/1906.11555/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2019.

## Built on by (most cited first, 30 of 57)

- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Equivariance with Learned Canonicalization Functions](https://mlsanity.com/paper/2211.06489/) (2022)
- [You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptors](https://mlsanity.com/paper/2109.00182/) (2021)
- [Leveraging SE(3) Equivariance for Self-Supervised Category-Level Object Pose Estimation](https://mlsanity.com/paper/2111.00190/) (2021)
- [RIConv++: Effective Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/2202.13094/) (2022)
- [Advancements in Point Cloud Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2308.12113/) (2023)
- [Deep Learning-based 3D Point Cloud Classification: A Systematic Survey and Outlook](https://mlsanity.com/paper/2311.02608/) (2023)
- [Unified Fourier-based Kernel and Nonlinearity Design for Equivariant Networks on Homogeneous Spaces](https://mlsanity.com/paper/2206.08362/) (2022)
- [Understanding and Improving Features Learned in Deep Functional Maps](https://mlsanity.com/paper/2303.16527/) (2023)
- [VectorAdam for Rotation Equivariant Geometry Optimization](https://mlsanity.com/paper/2205.13599/) (2022)
- [PRIN/SPRIN: On Extracting Point-wise Rotation Invariant Features](https://mlsanity.com/paper/2102.12093/) (2021)
- [Field Convolutions for Surface CNNs](https://mlsanity.com/paper/2104.03916/) (2021)
- [Few-shot Class-incremental Learning for 3D Point Cloud Objects](https://mlsanity.com/paper/2205.15225/) (2022)
- [ART-Point: Improving Rotation Robustness of Point Cloud Classifiers via Adversarial Rotation](https://mlsanity.com/paper/2203.03888/) (2022)
- [Non-Rigid Shape Registration via Deep Functional Maps Prior](https://mlsanity.com/paper/2311.04494/) (2023)
- [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024)
- [A Simple and Universal Rotation Equivariant Point-cloud Network](https://mlsanity.com/paper/2203.01216/) (2022)
- [DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds](https://mlsanity.com/paper/2111.08799/) (2021)
- [LPF-Defense: 3D Adversarial Defense based on Frequency Analysis](https://mlsanity.com/paper/2202.11287/) (2022)
- [Point-DAE: Denoising Autoencoders for Self-supervised Point Cloud Learning](https://mlsanity.com/paper/2211.06841/) (2022)
- [Test-Time Adaptation of 3D Point Clouds via Denoising Diffusion Models](https://mlsanity.com/paper/2411.14495/) (2024)
- [Generalizable Local Feature Pre-training for Deformable Shape Analysis](https://mlsanity.com/paper/2303.15104/) (2023)
- [Improving Shift Invariance in Convolutional Neural Networks with Translation Invariant Polyphase Sampling](https://mlsanity.com/paper/2404.07410/) (2024)
- [AtomSurf : Surface Representation for Learning on Protein Structures](https://mlsanity.com/paper/2309.16519/) (2023)
- [An intuitive multi-frequency feature representation for SO(3)-equivariant networks](https://mlsanity.com/paper/2405.04537/) (2024)
- [RISurConv: Rotation Invariant Surface Attention-Augmented Convolutions for 3D Point Cloud Classification and Segmentation](https://mlsanity.com/paper/2408.06110/) (2024)
- [SO(3)-Pose: SO(3)-Equivariance Learning for 6D Object Pose Estimation](https://mlsanity.com/paper/2208.08338/) (2022)
- [Designing Rotationally Invariant Neural Networks from PDEs and Variational Methods](https://mlsanity.com/paper/2108.13993/) (2021)
- [Nonlinearities in Steerable SO(2)-Equivariant CNNs](https://mlsanity.com/paper/2109.06861/) (2021)
- [Learning a Task-specific Descriptor for Robust Matching of 3D Point Clouds](https://mlsanity.com/paper/2210.14899/) (2022)

## Abstract (arXiv)

We present a novel rotation invariant architecture operating directly on point cloud data. We demonstrate how rotation invariance can be injected into a recently proposed point-based PCNN architecture, at all layers of the network, achieving invariance to both global shape transformations, and to local rotations on the level of patches or parts, useful when dealing with non-rigid objects. We achieve this by employing a spherical harmonics based kernel at different layers of the network, which is guaranteed to be invariant to rigid motions. We also introduce a more efficient pooling operation for PCNN using space-partitioning data-structures. This results in a flexible, simple and efficient architecture that achieves accurate results on challenging shape analysis tasks including classification and segmentation, without requiring data-augmentation, typically employed by non-invariant approaches.