MeshGuard: Hidden 3D Watermarking in Spectral Space through Laplacian Beltrami Operator and Geometry Fusion

Recent advances in 3D generation and reconstruction enable rapid creation of high-fidelity assets such as point clouds and meshes, increasing the need for reliable intellectual property protection. However, unlike well-studied 2D watermarking, 3D methods remain limited and often embed signals directly into surface geometry, making them vulnerable to distortion and adversarial attacks. We propose a robust mesh watermarking framework based on spectral geometry. Our method leverages the Laplace–Beltrami operator to extract intrinsic spectral representations and embeds watermark signals into mid-band components via eigen-decomposition. The watermark is applied in the spatial domain through predicted vertex-level offsets regressed from updated eigenvectors, achieving imperceptible yet stable embedding. To enhance robustness, we incorporate adversarial training with diverse mesh perturbations, enabling reliable decoding under severe distortions. We further introduce a flexible encoding scheme that converts text or image inputs into binary watermark sequences for fusion and evaluation. Extensive experiments demonstrate improved robustness against a wide range of geometric attacks while preserving high geometric fidelity, outperforming existing approaches by a large margin.