Augmented Equivariant Mesh Networks for Anatomical Mesh Segmentation (ICML 2026 Workshops) [R]

Paper: https://arxiv.org/abs/2605.08172

Workshops: AI for Science & Structured Data for Health at ICML 2026

Abstract:

Anatomical mesh segmentation requires models that operate directly on irregular surface geometry while remaining robust to arbitrary patient pose and mesh resolution variation. Existing task-specific mesh and point-cloud methods are not equivariant, and can degrade sharply under test-time perturbation, for example dropping by 25-26 IoU points on intraoral scan segmentation at 40^o tilt. We present EAMS, an Equivariant Anatomical Mesh Segmentor built on Equivariant Mesh Neural Networks (EMNN), and evaluate it across four clinically distinct tasks 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 supervision types without task-specific architectures.

Hi everyone

I’m excited to share my solo paper "Augmented Equivariant Mesh Networks for Anatomical Mesh Segmentation" which has been accepted for poster presentations at the ICML 2026 workshops on AI for Science and Structured Data for Health.

The project stemmed from my parallel research on structural encoders for biomolecules where enforcing roto-translational equivariance is standard. In this work, I wanted to extend those principles directly to various 3D medical meshes. While current anatomical mesh segmentation methods are highly disjoint and anatomy-specific, we present a unified framework built on EMNN. By augmenting standard local message passing to incorporate a lightweight global context, and using a descriptive feature set incorporating intrinsic surface descriptors (HKS) and anatomical frames derived from an area-weighted PCA, we successfully benchmarked this single architecture across clinically distinct tasks spanning vertex-, edge-, and face-level supervision.

Equivariance trade-off

One of the more interesting findings from the experiments is that strict equivariance isn't always better. In fact, the inductive biases of the equivariant architecture occasionally performed worse than standard, non-equivariant baselines.

For instance, on our liver dataset, the target anatomical landmarks are highly subtle creases. Standard baselines can "cheat" by using raw coordinates to easily resolve the left-right and front-back ambiguity. Because the equivariant network is mathematically blind to absolute space, it struggled with these subtle, asymmetric features.

Future directions

To fix this without losing the generalization benefits of geometric deep learning, I’m currently exploring relaxed constraints like learned canonicalization and frame-averaging (soft equivariance).

As this is a solo project, I would appreciate any feedback!

Also, I'll be heading to Seoul for ICML 2026 to present these workshop posters. if you're working on geometric DL for medical/biological applications, feel free to connect!