# Mesh Convolutional Autoencoder for Semi-Regular Meshes of Different Sizes

arXiv: https://arxiv.org/abs/2110.09401 · HTML: https://mlsanity.com/paper/2110.09401/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 18 Oct 2021.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs](https://mlsanity.com/paper/2003.05425/) (2020)
- [Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation](https://mlsanity.com/paper/1905.02876/) (2019)
- [Variational Autoencoders for Deforming 3D Mesh Models](https://mlsanity.com/paper/1709.04307/) (2017)
- [MeshCNN: A Network with an Edge](https://mlsanity.com/paper/1809.05910/) (2018)
- [Subdivision-Based Mesh Convolution Networks](https://mlsanity.com/paper/2106.02285/) (2021)
- [Geodesic Convolutional Shape Optimization](https://mlsanity.com/paper/1802.04016/) (2018)
- [Mesh Variational Autoencoders with Edge Contraction Pooling](https://mlsanity.com/paper/1908.02507/) (2019)
- [HexagDLy - Processing hexagonally sampled data with CNNs in PyTorch](https://mlsanity.com/paper/1903.01814/) (2019)
- [Analysis and Prediction of Deforming 3D Shapes using Oriented Bounding Boxes and LSTM Autoencoders](https://mlsanity.com/paper/2009.03782/) (2020)

## Built on by (most cited first, 8 of 8)

- [Deep Structural Causal Shape Models](https://mlsanity.com/paper/2208.10950/) (2022)
- [What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives](https://mlsanity.com/paper/2211.06009/) (2022)
- [3D-QAE: Fully Quantum Auto-Encoding of 3D Point Clouds](https://mlsanity.com/paper/2311.05604/) (2023)
- [Transfer Learning using Spectral Convolutional Autoencoders on Semi-Regular Surface Meshes](https://mlsanity.com/paper/2212.05810/) (2022)
- [WrappingNet: Mesh Autoencoder via Deep Sphere Deformation](https://mlsanity.com/paper/2308.15413/) (2023)
- [Unsupervised Representation Learning for Diverse Deformable Shape Collections](https://mlsanity.com/paper/2310.18141/) (2023)
- [Squeeze3D: Extreme Neural Compression with Latent Space Bridging](https://mlsanity.com/paper/2506.07932/) (2025)
- [A 3D mesh convolution-based autoencoder for geometry compression](https://mlsanity.com/paper/2603.02125/) (2026)

## Abstract (arXiv)

The analysis of deforming 3D surface meshes is accelerated by autoencoders since the low-dimensional embeddings can be used to visualize underlying dynamics. But, state-of-the-art mesh convolutional autoencoders require a fixed connectivity of all input meshes handled by the autoencoder. This is due to either the use of spectral convolutional layers or mesh dependent pooling operations. Therefore, the types of datasets that one can study are limited and the learned knowledge cannot be transferred to other datasets that exhibit similar behavior. To address this, we transform the discretization of the surfaces to semi-regular meshes that have a locally regular connectivity and whose meshing is hierarchical. This allows us to apply the same spatial convolutional filters to the local neighborhoods and to define a pooling operator that can be applied to every semi-regular mesh. We apply the same mesh autoencoder to different datasets and our reconstruction error is more than 50% lower than the error from state-of-the-art models, which have to be trained for every mesh separately. Additionally, we visualize the underlying dynamics of unseen mesh sequences with an autoencoder trained on different classes of meshes.