# Spherical CNNs on Unstructured Grids

arXiv: https://arxiv.org/abs/1901.02039 · HTML: https://mlsanity.com/paper/1901.02039/

## Key facts

- Cited by 79 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jan 2019.

## Built on by (most cited first, 30 of 79)

- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [PanoFormer: Panorama Transformer for Indoor 360 Depth Estimation](https://mlsanity.com/paper/2203.09283/) (2022)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [Bending Reality: Distortion-aware Transformers for Adapting to Panoramic Semantic Segmentation](https://mlsanity.com/paper/2203.01452/) (2022)
- [CSP: Self-Supervised Contrastive Spatial Pre-Training for Geospatial-Visual Representations](https://mlsanity.com/paper/2305.01118/) (2023)
- [Graph-Based Deep Learning for Medical Diagnosis and Analysis: Past, Present and Future](https://mlsanity.com/paper/2105.13137/) (2021)
- [Geometric Deep Learning and Equivariant Neural Networks](https://mlsanity.com/paper/2105.13926/) (2021)
- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
- [Decoding natural image stimuli from fMRI data with a surface-based convolutional network](https://mlsanity.com/paper/2212.02409/) (2022)
- [Both Style and Distortion Matter: Dual-Path Unsupervised Domain Adaptation for Panoramic Semantic Segmentation](https://mlsanity.com/paper/2303.14360/) (2023)
- [Behind Every Domain There is a Shift: Adapting Distortion-aware Vision Transformers for Panoramic Semantic Segmentation](https://mlsanity.com/paper/2207.11860/) (2022)
- [A Survey on Graph-Based Deep Learning for Computational Histopathology](https://mlsanity.com/paper/2107.00272/) (2021)
- [Surround-view Fisheye Camera Perception for Automated Driving: Overview, Survey and Challenges](https://mlsanity.com/paper/2205.13281/) (2022)
- [Elite360D: Towards Efficient 360 Depth Estimation via Semantic- and Distance-Aware Bi-Projection Fusion](https://mlsanity.com/paper/2403.16376/) (2024)
- [Conditional Local Convolution for Spatio-temporal Meteorological Forecasting](https://mlsanity.com/paper/2101.01000/) (2021)
- [SGAT4PASS: Spherical Geometry-Aware Transformer for PAnoramic Semantic Segmentation](https://mlsanity.com/paper/2306.03403/) (2023)
- [Surface Vision Transformers: Attention-Based Modelling applied to Cortical Analysis](https://mlsanity.com/paper/2203.16414/) (2022)
- [Scalable and Equivariant Spherical CNNs by Discrete-Continuous (DISCO) Convolutions](https://mlsanity.com/paper/2209.13603/) (2022)
- [A Survey of Representation Learning, Optimization Strategies, and Applications for Omnidirectional Vision](https://mlsanity.com/paper/2502.10444/) (2025)
- [Scaling Spherical CNNs](https://mlsanity.com/paper/2306.05420/) (2023)
- [HEAL-SWIN: A Vision Transformer On The Sphere](https://mlsanity.com/paper/2307.07313/) (2023)
- [PDO-eS2CNNs: Partial Differential Operator Based Equivariant Spherical CNNs](https://mlsanity.com/paper/2104.03584/) (2021)
- [Flattening-Net: Deep Regular 2D Representation for 3D Point Cloud Analysis](https://mlsanity.com/paper/2212.08892/) (2022)
- [PanelNet: Understanding 360 Indoor Environment via Panel Representation](https://mlsanity.com/paper/2305.09078/) (2023)
- [Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNs](https://mlsanity.com/paper/2102.02828/) (2021)
- [360BEV: Panoramic Semantic Mapping for Indoor Bird's-Eye View](https://mlsanity.com/paper/2303.11910/) (2023)
- [Equivariant Networks for Pixelized Spheres](https://mlsanity.com/paper/2106.06662/) (2021)
- [Panoramic Vision Transformer for Saliency Detection in 360deg Videos](https://mlsanity.com/paper/2209.08956/) (2022)
- [M"obius Convolutions for Spherical CNNs](https://mlsanity.com/paper/2201.12212/) (2022)
- [SphereUFormer: A U-Shaped Transformer for Spherical 360 Perception](https://mlsanity.com/paper/2412.06968/) (2024)

## Abstract (arXiv)

We present an efficient convolution kernel for Convolutional Neural Networks (CNNs) on unstructured grids using parameterized differential operators while focusing on spherical signals such as panorama images or planetary signals. To this end, we replace conventional convolution kernels with linear combinations of differential operators that are weighted by learnable parameters. Differential operators can be efficiently estimated on unstructured grids using one-ring neighbors, and learnable parameters can be optimized through standard back-propagation. As a result, we obtain extremely efficient neural networks that match or outperform state-of-the-art network architectures in terms of performance but with a significantly lower number of network parameters. We evaluate our algorithm in an extensive series of experiments on a variety of computer vision and climate science tasks, including shape classification, climate pattern segmentation, and omnidirectional image semantic segmentation. Overall, we present (1) a novel CNN approach on unstructured grids using parameterized differential operators for spherical signals, and (2) we show that our unique kernel parameterization allows our model to achieve the same or higher accuracy with significantly fewer network parameters.