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Rethinking Mesh Watermark: Towards Highly Robust and Adaptable Deep 3D Mesh Watermarking
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Proposes Deep3DMark, a GAT-based end-to-end 3D mesh watermarking method that embeds 8-bit messages in vertex coordinates using relation-based offsets, trained on simplified meshes for size and geometry adaptability.
Problem
Robust and adaptable 3D mesh watermarking: embedding messages in vertex distributions that survive attacks (noise, rotation, scaling, translation, cropping, compression) while staying imperceptible and working across mesh sizes and unseen geometry categories.
Approach
Uses graph attention networks whose attention weights are MLPs over relative vertex offsets (relations), which are preserved under mesh simplification, so a model trained on simplified meshes generalizes to larger and unseen meshes; adds an attack layer for adversarial-style robustness and a learnable channel-coding message autoencoder (NECST) for redundancy.
Key results
- Under attacks, the method achieves 10%-50% higher bit accuracy than traditional methods and 1%-8% higher than prior DNN-based methods, with about 2x the SNR of the DNN baseline (Wang).
- Trained on simplified m500 meshes, it still reaches 81.81% accuracy on ModelNet meshes with up to 100,000 vertices (about 190x increase).
- On ShapeNet unseen categories, the m2500 model achieves 93.48% average bit accuracy with 0.0248 L1 vertex difference.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Deep3DMark instead of Wang | Mesh watermarking · Mesh test set, translation attack | bit accuracy (%): 90.22 -> 98.17 | Helped |
| Use Deep3DMark instead of Wang | Mesh watermarking · Mesh test set, cropping attack | bit accuracy (%): 70.21 -> 78.90 | Helped |
| Use Deep3DMark instead of Wang | Mesh watermarking · Mesh test set | SNR: 15.04 -> 30.84 | Helped |
| Train on simplified meshes with 2500 rather than 500 vertices | Deep3DMark · ShapeNet, average | bit accuracy: 0.8863 -> 0.9348 | Helped |
| Train on simplified meshes with 2500 rather than 500 vertices | Deep3DMark · ModelNet, vertex counts [80000,100000) | bit accuracy: 0.8181 -> 0.8708 | Helped |
| Add adversarially generated mesh perturbations during training | Deep3DMark · Multiple mesh attacks | robustness | Helped |
Surprising findings
- Traditional LSB/MSB-based methods such as Peng and TTsai fail under Gaussian noise or rotation/scaling respectively, despite high mesh quality.
- Accuracy drops as training mesh size decreases, so the m500 model is less adaptable than m2500.
Limitations
- Accuracy degrades with larger distortions such as strong cropping (65.81% at c=0.9) and strong Laplacian smoothing.
- Lower SNR than traditional methods (about 30.8 dB vs 36-47 dB), with visible quality concerns.
- Adaptability decreases when the training mesh size is smaller.
Experimental setup
Datasets: ModelNet40 ShapeNet GraspNet ScanNet Hands
Benchmarks: ModelNet40 ShapeNet GraspNet ScanNet Hands
Metrics: bit accuracy Hausdorff distance L1 vertex difference SNR running time
Baselines: Jiang Spectral Peng PPeng Tsai TTsai Hou Wang Yoo
Builds on: graph attention network NECST CGAL
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