Augmented Equivariant Mesh Networks for Anatomical Segmentation

2026-05-04

AI Summary

Existing anatomical mesh segmentation methods lack geometric equivariance under variations in patient pose and mesh resolution, leading to significant performance degradation. To address this limitation, this work proposes EAMS—a general-purpose segmentation framework based on equivariant mesh neural networks—which, for the first time, applies a lightweight equivariant architecture to multi-class anatomical structure segmentation. EAMS integrates intrinsic geometric descriptors, an anatomy-aware coordinate system constructed via PCA, and an enhanced message-passing mechanism, enabling unified supervision across edges, vertices, and faces. Experiments demonstrate that EAMS achieves performance on par with specialized models on standard datasets for intracranial aneurysm, intraoral scan, and liver surface segmentation, while maintaining robustness under geometric perturbations—all with fewer than two million parameters.

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.

Problem

• anatomical mesh segmentation
• equivariance
• geometric perturbations
• mesh resolution variation
• patient pose

Innovation

• equivariant mesh networks
• anatomical segmentation
• mesh neural networks
• geometric robustness
• lightweight architecture