# Concentric Spherical GNN for 3D Representation Learning

arXiv: https://arxiv.org/abs/2103.10484 · HTML: https://mlsanity.com/paper/2103.10484/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 17 references that are in the map.
- First posted on arXiv 18 Mar 2021.

## Builds on (most cited first, 13 of 13)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/1908.06297/) (2019)
- [Spherical CNNs on Unstructured Grids](https://mlsanity.com/paper/1901.02039/) (2019)
- [DeepSphere: a graph-based spherical CNN](https://mlsanity.com/paper/2012.15000/) (2020)
- [VV-Net: Voxel VAE Net with Group Convolutions for Point Cloud Segmentation](https://mlsanity.com/paper/1811.04337/) (2018)
- [Effective Rotation-invariant Point CNN with Spherical Harmonics kernels](https://mlsanity.com/paper/1906.11555/) (2019)
- [SRINet: Learning Strictly Rotation-Invariant Representations for Point Cloud Classification and Segmentation](https://mlsanity.com/paper/1911.02163/) (2019)
- [Pointwise Rotation-Invariant Network with Adaptive Sampling and 3D Spherical Voxel Convolution](https://mlsanity.com/paper/1811.09361/) (2018)

## Built on by (most cited first, 2 of 2)

- [Geometric Deep Learning and Equivariant Neural Networks](https://mlsanity.com/paper/2105.13926/) (2021)
- [Nonlinearities in Steerable SO(2)-Equivariant CNNs](https://mlsanity.com/paper/2109.06861/) (2021)

## Abstract (arXiv)

Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional architecture for learning over concentric spherical feature maps, of which the single sphere representation is a special case. Our hierarchical architecture is based on alternatively learning to incorporate both intra-sphere and inter-sphere information. We show the applicability of our method for two different types of 3D inputs, mesh objects, which can be regularly sampled, and point clouds, which are irregularly distributed. We also propose an efficient mapping of point clouds to concentric spherical images, thereby bridging spherical convolutions on grids with general point clouds. We demonstrate the effectiveness of our approach in improving state-of-the-art performance on 3D classification tasks with rotated data.