Deformable Digital Watermarking for Copyright Protection of 3D Gaussian Splatting

While the deformation technology of 3D Gaussian Splatting （3DGS） expands modeling capabilities， it also introduces new security risks： malicious users can tamper with model content through deformation operations and then illegally claim ownership. Existing 3DGS watermarking methods can only cope with simple image-level perturbations or 3D operations and struggle to provide effective protection against complex geometric deformations. To address this challenge， this paper proposes DeformDefender—a deformable 3D watermarking method specifically designed to resist unauthorized deformation attacks. This method innovatively introduces a dual-layer deformable watermark embedding strategy. By systematically analyzing the impact mechanisms of 3DGS deformation operations on the model at both the parameter and rendering levels， a targeted watermark injection scheme is designed to ensure that the watermark maintains its integrity and extractability， even after the model undergoes deformation. Furthermore， a deformation-robust watermark extractor is developed， capable of reliably recovering the watermark information from rendered images subjected to severe geometric distortion. Experimental results demonstrate that DeformDefender can effectively resist malicious deformations and protect copyright without compromising the visual quality or rendering performance of the 3DGS model. Compared to existing methods， the watermark embedded by DeformDefender has minimal impact on the model’s visual quality and exhibits superior robustness against various 2D and 3D perturbations. Additionally， our method requires adjustments to the existing model parameters only for watermark embedding， avoiding extensive modifications to the model structure， thereby maintaining good adaptability to different 3DGS model variants. This research provides a viable and scalable solution for 3D model copyright protection in response to the growing prevalence of deformation techniques.