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Augmented Equivariant Mesh Networks for Anatomical Segmentation

NeurIPS 2026 · Point clouds › Point cloud classification · approach: Equivariant point cloud networks · 0 citations (OpenAlex)

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Proposes EAMS, a lightweight (<2M params) equivariant mesh segmentor built on EMNN with anatomy-aware PCA frames and multi-token global context (soft regional aggregators, virtual nodes), evaluated on liver, intraoral, and intracranial aneurysm mesh segmentation.

Problem

Anatomical mesh segmentation must be robust to arbitrary patient pose and varying mesh resolution, but existing mesh and point-cloud methods are not equivariant and degrade sharply under rotation.

Approach

Build segmentation on an equivariant mesh network (EMNN) augmented with intrinsic descriptors (HKS, dihedral angles), PCA-derived anatomy-relative cylindrical coordinates, and multi-token global context via soft regional aggregators or virtual nodes with auxiliary regularizers.

Key results

• On 3D-IOSSeg at 40° rotation, the strongest baseline falls from 81.05% to 52.33% IoU while VN+EAMS goes from 79.74% to 80.09%.
• On IntrA at 40° rotation, aneurysm Dice is 93.59–95.81% for EAMS variants versus 81.75% for the strongest baseline (DGCNN).
• VN+EAMS with 1.9M parameters approaches Fast-TGCN (19.8M) on 3D-IOSSeg and Teeth3DS, e.g. 83.16% vs 84.31% Average IoU on Teeth3DS baseline.

Surprising findings

• On liver surfaces, baselines outperform EAMS on unperturbed meshes (e.g. ligament Dice 44.13% for MeshGraphCNN vs 20.46% for EAMS), trading canonical accuracy for rotation robustness.
• Pose-sensitive raw-XYZ inputs help liver and dental segmentation but hurt IntrA.

Limitations

• Liver segmentation has a canonical-accuracy vs rotation-robustness trade-off, with lower ligament Dice for EAMS variants at high curvature.
• Dental PCA frame retains an unresolved (X,Z) sign ambiguity, leading to upper-tail sensitivity under rotation.
• Targeted pose and component diagnostics cover only one fold; augmented models incur runtime overhead.

Experimental setup

Datasets: IntrA 3D-IOSSeg Teeth3DS liver surface dataset (3Dircadb, LiTS, Amos)

Benchmarks: IntrA 3D-IOSSeg Teeth3DS liver surface segmentation dataset

Metrics: Dice IoU Average IoU Chamfer distance Hausdorff distance

Baselines: DGCNN PTv3 Fast-TGCN PointNet++ MeshGraphCNN

Builds on: EMNN EGNN Heat Kernel Signature Point Transformer V3 DGCNN

Closest papers by meaning

• CARL: A Framework for Equivariant Image Registration (CVPR 2025 · similarity 0.84)
• EffiDec3D: An Optimized Decoder for High-Performance and Efficient 3D Medical Image Segmentation (CVPR 2025 · similarity 0.84)
• Why Invariance is Not Enough for Biomedical Domain Generalization and How to Fix It (NeurIPS 2026 · similarity 0.83)
• E2ENet: Dynamic Sparse Feature Fusion for Accurate and Efficient 3D Medical Image Segmentation (NeurIPS 2024 · similarity 0.83)
• Point2SSM: Learning Morphological Variations of Anatomies from Point Clouds (ICLR 2024 · similarity 0.83)
• Uncertainty Estimation for Pretrained Medical Image Registration Models via Transformation Equivariance (NeurIPS 2026 · similarity 0.83)