# Surface Networks via General Covers

arXiv: https://arxiv.org/abs/1812.10705 · HTML: https://mlsanity.com/paper/1812.10705/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Dec 2018.

## Built on by (most cited first, 22 of 22)

- [Deep Learning on Implicit Neural Representations of Shapes](https://mlsanity.com/paper/2302.05438/) (2023)
- [Subdivision-Based Mesh Convolution Networks](https://mlsanity.com/paper/2106.02285/) (2021)
- [Neural Surface Maps](https://mlsanity.com/paper/2103.16942/) (2021)
- [MeshMAE: Masked Autoencoders for 3D Mesh Data Analysis](https://mlsanity.com/paper/2207.10228/) (2022)
- [Equivariance versus Augmentation for Spherical Images](https://mlsanity.com/paper/2202.03990/) (2022)
- [HEAL-SWIN: A Vision Transformer On The Sphere](https://mlsanity.com/paper/2307.07313/) (2023)
- [Flattening-Net: Deep Regular 2D Representation for 3D Point Cloud Analysis](https://mlsanity.com/paper/2212.08892/) (2022)
- [Field Convolutions for Surface CNNs](https://mlsanity.com/paper/2104.03916/) (2021)
- [Laplacian2Mesh: Laplacian-Based Mesh Understanding](https://mlsanity.com/paper/2202.00307/) (2022)
- [DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds](https://mlsanity.com/paper/2111.08799/) (2021)
- [PolyNet: Polynomial Neural Network for 3D Shape Recognition with PolyShape Representation](https://mlsanity.com/paper/2110.07882/) (2021)
- [Dynamic 3D Point Cloud Sequences as 2D Videos](https://mlsanity.com/paper/2403.01129/) (2024)
- [Generalizable Local Feature Pre-training for Deformable Shape Analysis](https://mlsanity.com/paper/2303.15104/) (2023)
- [Dense Graph Convolutional Neural Networks on 3D Meshes for 3D Object Segmentation and Classification](https://mlsanity.com/paper/2106.15778/) (2021)
- [Interpolated SelectionConv for Spherical Images and Surfaces](https://mlsanity.com/paper/2210.10123/) (2022)
- [InfoGNN: End-to-end deep learning on mesh via graph neural networks](https://mlsanity.com/paper/2503.02414/) (2025)
- [CageNet: A Meta-Framework for Learning on Wild Meshes](https://mlsanity.com/paper/2505.18772/) (2025)
- [A Hypertoroidal Covering for Perfect Color Equivariance](https://mlsanity.com/paper/2603.04256/) (2026)
- [MeshCNN Fundamentals: Geometric Learning through a Reconstructable Representation](https://mlsanity.com/paper/2105.13277/) (2021)
- [U-mesh: Human Correspondence Matching with Mesh Convolutional Networks](https://mlsanity.com/paper/2108.06695/) (2021)
- [Gaussian map predictions for 3D surface feature localisation and counting](https://mlsanity.com/paper/2112.03736/) (2021)
- [MME: Mixture of Mesh Experts with Random Walk Transformer Gating](https://mlsanity.com/paper/2603.00828/) (2026)

## Abstract (arXiv)

Developing deep learning techniques for geometric data is an active and fruitful research area. This paper tackles the problem of sphere-type surface learning by developing a novel surface-to-image representation. Using this representation we are able to quickly adapt successful CNN models to the surface setting. The surface-image representation is based on a covering map from the image domain to the surface. Namely, the map wraps around the surface several times, making sure that every part of the surface is well represented in the image. Differently from previous surface-to-image representations, we provide a low distortion coverage of all surface parts in a single image. Specifically, for the use case of learning spherical signals, our representation provides a low distortion alternative to several popular spherical parameterizations used in deep learning. We have used the surface-to-image representation to apply standard CNN architectures to 3D models as well as spherical signals. We show that our method achieves state of the art or comparable results on the tasks of shape retrieval, shape classification and semantic shape segmentation.