EndoRDH: Constrained Reversible Information Transport over Non-Stationary Endoscopic 3D Gaussian Representations

Dynamic 3D Gaussian Splatting (3DGS) models are increasingly reused as persistent 3D assets, raising the need to embed ownership information without compromising the underlying representation. This is particularly challenging in endoscopic scenes, where clinically sensitive regions restrict admissible modifications and camera-coupled active illumination induces spatially non-stationary spherical harmonic (SH) carriers whose reliability varies across the scene. To address these issues, we introduce EndoRDH, a geometry-aware reversible transport framework that formulates reversible watermarking as constrained information transport over a non-stationary Gaussian representation, allocating information to perceptually low-cost and locally stable carriers while preserving an explicit inverse path to the original host. First, clinically admissible carrier projection restricts watermark updates to a prescribed editable SH subspace while freezing structural Gaussian parameters and excluding protected regions. Second, Riemannian photometric decoupling converts local photometric variation into a carrier-dependent transport geometry without assuming recovery of the underlying illumination physics. Within this geometry, an optimal transport inspired reversible flow adaptively redistributes the watermark payload toward low cost, locally stable carriers while retaining a key conditioned inverse for host recovery. Finally, dual-branch redundant coding distributes error corrected evidence across complementary carrier groups, improving robustness without increasing the per-carrier perturbation budget. Experiments on dynamic endoscopic 3DGS scenes show that EndoRDH achieves a favorable trade-off among representation fidelity, copyright verification, and authorized reversibility, while remaining robust to both rendering-domain and model-domain perturbations. These results suggest that modeling watermark embedding as constrained reversible transport offers a principled alternative to uniform or independently optimized carrier perturbations in non-stationary neural scene representations.