# Utility of Equivariant Message Passing in Cortical Mesh Segmentation

arXiv: https://arxiv.org/abs/2206.03164 · HTML: https://mlsanity.com/paper/2206.03164/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 41 references that are in the map.
- First posted on arXiv 7 Jun 2022.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (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)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [Swin-Unet: Unet-like Pure Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2105.05537/) (2021)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations](https://mlsanity.com/paper/1707.03237/) (2017)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [TransFuse: Fusing Transformers and CNNs for Medical Image Segmentation](https://mlsanity.com/paper/2102.08005/) (2021)
- [Equivariant Flows: sampling configurations for multi-body systems with symmetric energies](https://mlsanity.com/paper/1910.00753/) (2019)
- [Spherical U-Net on Cortical Surfaces: Methods and Applications](https://mlsanity.com/paper/1904.00906/) (2019)
- [Cortical surface registration using unsupervised learning](https://mlsanity.com/paper/2004.04617/) (2020)
- [Geometric Convolutional Neural Network for Analyzing Surface-Based Neuroimaging Data](https://mlsanity.com/paper/1708.00587/) (2017)
- [Graph Domain Adaptation for Alignment-Invariant Brain Surface Segmentation](https://mlsanity.com/paper/2004.00074/) (2020)

## Abstract (arXiv)

The automated segmentation of cortical areas has been a long-standing challenge in medical image analysis. The complex geometry of the cortex is commonly represented as a polygon mesh, whose segmentation can be addressed by graph-based learning methods. When cortical meshes are misaligned across subjects, current methods produce significantly worse segmentation results, limiting their ability to handle multi-domain data. In this paper, we investigate the utility of E(n)-equivariant graph neural networks (EGNNs), comparing their performance against plain graph neural networks (GNNs). Our evaluation shows that GNNs outperform EGNNs on aligned meshes, due to their ability to leverage the presence of a global coordinate system. On misaligned meshes, the performance of plain GNNs drop considerably, while E(n)-equivariant message passing maintains the same segmentation results. The best results can also be obtained by using plain GNNs on realigned data (co-registered meshes in a global coordinate system).