Learning SO(3) Equivariant Representations with Spherical CNNs

2017/11/17 by Carlos Esteves, Christine Allen-Blanchette, Esteves, Carlos +5 · 14 citations
Computer Science · Engineering · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Human Pose and Action Recognition #Medical Image Segmentation Techniques #Robotics and Sensor-Based Localization

paper · pdf · doi:10.48550/arxiv.1711.06721

openalex publication_date 2017/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We model 3D data with multi-valued spherical functions and we propose a novel spherical convolutional network that implements exact convolutions on the sphere by realizing them in the spherical harmonic domain. Resulting filters have local symmetry and are localized by enforcing smooth spectra. We apply a novel pooling on the spectral domain and our operations are independent of the underlying spherical resolution throughout the network. We show that networks with much lower capacity and without requiring data augmentation can exhibit performance comparable to the state of the art in standard retrieval and classification benchmarks.

Cited by

• CHyLL: Learning Continuous Neural Representations of Hybrid Systems
• RecruitView: A Multimodal Dataset for Predicting Personality and Interview Performance for Human Resources Applications
• NeuroVascU-Net: A Unified Multi-Scale and Cross-Domain Adaptive Feature Fusion U-Net for Precise 3D Segmentation of Brain Vessels in Contrast-Enhanced T1 MRI
• Unified Spherical Frontend: Learning Rotation-Equivariant Representations of Spherical Images from Any Camera
• Recurrent Equivariant Constraint Modulation: Learning Per-Layer Symmetry Relaxation from Data
• Learning with Category-Equivariant Architectures for Human Activity Recognition
• Explicit Discovery of Nonlinear Symmetries from Dynamic Data
• Learning Generalizable Shape Completion with SIM(3) Equivariance
• FS-KAN: Permutation Equivariant Kolmogorov-Arnold Networks via Function Sharing
• Foveated Retinotopy Improves Classification and Localization in Convolutional Neural Networks
• Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networks
• Local-Canonicalization Equivariant Graph Neural Networks for Sample-Efficient and Generalizable Swarm Robot Control
• Representation Theory of UT₃(\mathbbF₃) and its Applications to Equivariant Decomposition in Neural Architectures
• GradMetaNet: An Equivariant Architecture for Learning on Gradients

Related

• Spin-Weighted Spherical CNNs
• Spherical Convolutional Neural Networks: Stability to Perturbations in SO(3)
• Rotation-Invariant Autoencoders for Signals on Spheres
• Efficient Generalized Spherical CNNs
• SO(3)-Equivariant Neural Networks for Learning from Scalar and Vector Fields on Spheres