# Mesh Variational Autoencoders with Edge Contraction Pooling

arXiv: https://arxiv.org/abs/1908.02507 · HTML: https://mlsanity.com/paper/1908.02507/

## Key facts

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

## Built on by (most cited first, 14 of 14)

- [3D Shape Variational Autoencoder Latent Disentanglement via Mini-Batch Feature Swapping for Bodies and Faces](https://mlsanity.com/paper/2111.12448/) (2021)
- [Learning Feature Aggregation for Deep 3D Morphable Models](https://mlsanity.com/paper/2105.02173/) (2021)
- [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)
- [Mesh Convolutional Autoencoder for Semi-Regular Meshes of Different Sizes](https://mlsanity.com/paper/2110.09401/) (2021)
- [3D Generative Model Latent Disentanglement via Local Eigenprojection](https://mlsanity.com/paper/2302.12798/) (2023)
- [DiffSurf: A Transformer-based Diffusion Model for Generating and Reconstructing 3D Surfaces in Pose](https://mlsanity.com/paper/2408.14860/) (2024)
- [MeshMamba: State Space Models for Articulated 3D Mesh Generation and Reconstruction](https://mlsanity.com/paper/2507.15212/) (2025)
- [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)
- [3D Generation for Embodied AI and Robotic Simulation: A Survey](https://mlsanity.com/paper/2604.26509/) (2026)
- [MeshCNN Fundamentals: Geometric Learning through a Reconstructable Representation](https://mlsanity.com/paper/2105.13277/) (2021)
- [Deep Spectral Meshes: Multi-Frequency Facial Mesh Processing with Graph Neural Networks](https://mlsanity.com/paper/2402.10365/) (2024)
- [Mat'ern Noise for Triangulation-Agnostic Flow Matching on Meshes](https://mlsanity.com/paper/2605.19305/) (2026)

## Abstract (arXiv)

3D shape analysis is an important research topic in computer vision and graphics. While existing methods have generalized image-based deep learning to meshes using graph-based convolutions, the lack of an effective pooling operation restricts the learning capability of their networks. In this paper, we propose a novel pooling operation for mesh datasets with the same connectivity but different geometry, by building a mesh hierarchy using mesh simplification. For this purpose, we develop a modified mesh simplification method to avoid generating highly irregularly sized triangles. Our pooling operation effectively encodes the correspondence between coarser and finer meshes in the hierarchy. We then present a variational auto-encoder structure with the edge contraction pooling and graph-based convolutions, to explore probability latent spaces of 3D surfaces. Our network requires far fewer parameters than the original mesh VAE and thus can handle denser models thanks to our new pooling operation and convolutional kernels. Our evaluation also shows that our method has better generalization ability and is more reliable in various applications, including shape generation, shape interpolation and shape embedding.