# Augmented Equivariant Mesh Networks for Anatomical Segmentation

arXiv: https://arxiv.org/abs/2605.08172 · HTML: https://mlsanity.com/paper/2605.08172/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 27 references that are in the map.
- First posted on arXiv 4 May 2026.

## Builds on (most cited first, 19 of 19)

- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [MeshNet: Mesh Neural Network for 3D Shape Representation](https://mlsanity.com/paper/1811.11424/) (2018)
- [Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs](https://mlsanity.com/paper/2003.05425/) (2020)
- [SpiralNet++: A Fast and Highly Efficient Mesh Convolution Operator](https://mlsanity.com/paper/1911.05856/) (2019)
- [Contrastive Boundary Learning for Point Cloud Segmentation](https://mlsanity.com/paper/2203.05272/) (2022)
- [IntrA: 3D Intracranial Aneurysm Dataset for Deep Learning](https://mlsanity.com/paper/2003.02920/) (2020)
- [A Simple Approach to Intrinsic Correspondence Learning on Unstructured 3D Meshes](https://mlsanity.com/paper/1809.06664/) (2018)
- [E(n) Equivariant Message Passing Simplicial Networks](https://mlsanity.com/paper/2305.07100/) (2023)
- [3DTeethSeg'22: 3D Teeth Scan Segmentation and Labeling Challenge](https://mlsanity.com/paper/2305.18277/) (2023)
- [Boundary Difference Over Union Loss For Medical Image Segmentation](https://mlsanity.com/paper/2308.00220/) (2023)
- [Equivariant Mesh Attention Networks](https://mlsanity.com/paper/2205.10662/) (2022)
- [Using Multiple Vector Channels Improves E(n)-Equivariant Graph Neural Networks](https://mlsanity.com/paper/2309.03139/) (2023)
- [E(3)-Equivariant Mesh Neural Networks](https://mlsanity.com/paper/2402.04821/) (2024)
- [3D Dental Model Segmentation with Geometrical Boundary Preserving](https://mlsanity.com/paper/2503.23702/) (2025)
- [Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning](https://mlsanity.com/paper/2506.19482/) (2025)

## Abstract (arXiv)

Anatomical mesh segmentation requires models that operate directly on irregular surface geometry while remaining robust to changes in coordinate pose across meshes of varying resolution. Existing task-specific mesh and point-cloud methods are not equivariant, and can degrade sharply under test-time perturbation, for example dropping by 28-30 IoU points on 3D-IOSSeg at 40^circ rotation even with matched training augmentation. We present EAMS, an Equivariant Anatomical Mesh Segmentor built on Equivariant Mesh Neural Networks (EMNN), and evaluate it in four dataset settings across three clinical application areas, spanning edge-, vertex-, and face-level supervision. We combine intrinsic mesh descriptors with anatomy-aware priors, including PCA-derived frames for dental arches and liver surfaces, and augment message passing to provide lightweight global context. Across intracranial aneurysm and intraoral segmentation, EAMS variants are competitive with specialized baselines on unperturbed inputs while remaining stable under geometric perturbations, and on liver surfaces they expose a favorable trade-off between canonical-pose accuracy and rotation robustness. These results show that a lightweight (<2M parameters) equivariant framework can deliver robust anatomical mesh segmentation across diverse label types.