Augmented Equivariant Mesh Networks for Anatomical Segmentation

TL;DR

This paper introduces EAMS, an equivariant mesh segmentation model that operates directly on irregular surface geometry, demonstrating robustness to pose and mesh variations across multiple clinical tasks.

Contribution

The paper presents a lightweight, equivariant mesh neural network framework that improves robustness and accuracy in anatomical segmentation without task-specific architectures.

Findings

EAMS achieves competitive accuracy on unperturbed data.

EAMS remains stable under geometric perturbations.

EAMS balances pose accuracy and rotation robustness on liver surfaces.

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 $40^\circ$ 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 ($<2$M parameters) equivariant framework can deliver robust anatomical mesh segmentation across diverse supervision types without task-specific architectures.