4D-GSW: Kinematic-Aware Spatio-Temporal Consistent Watermarking for 4D Gaussian Splatting

2026-05-21

AI Summary

This work addresses temporal flickering and non-physical artifacts in 4D Gaussian splatting dynamic content watermarking, which arise from neglecting the kinematic manifold. To resolve these issues, we propose a kinematics-aware watermarking framework that identifies temporally salient frames via a spatio-temporal curvature (STC) metric, synchronizes watermark phases across space and time using a joint Hidden Markov Model–Markov Random Field (HMM-MRF) energy formulation, and decouples watermark embedding from photometric reconstruction through anisotropic gradient routing. The proposed method achieves robust watermark imperceptibility under various attacks while preserving high rendering fidelity and strong spatio-temporal consistency. It effectively mitigates Frechet Video Distance (FVD) collapse and temporal flicker, thereby significantly enhancing the physical plausibility and visual authenticity of dynamic content for copyright protection.

Abstract

While 4D Gaussian Splatting (4DGS) has revolutionized high-fidelity dynamic reconstruction, safeguarding the intellectual property of these assets remains an open challenge. Conventional steganographic techniques often neglect the underlying kinematic manifolds, triggering non-physical artifacts such as severe temporal flickering and "FVD collapse". To address this, we propose \textbf{4D-GSW}, a kinematic-aware watermarking framework designed to embed robust copyright information while preserving high spatio-temporal consistency. Unlike prior 4D steganography that primarily focuses on opacity-guided invisibility, our approach explicitly addresses the physical coherence of motion trajectories. We introduce a \textbf{Spatio-Temporal Curvature (STC)} metric to identify "Dynamic Instants," adaptively gating watermark gradient injection to shield critical motion manifolds from non-physical perturbations. To ensure global coherence across complex deformations, we formulate a joint \textbf{HMM-MRF energy minimization} model that synchronizes watermark phases within both temporal trajectories and spatial neighborhoods. Furthermore, an \textbf{anisotropic gradient routing} mechanism ensures that watermark embedding remains strictly decoupled from photometric reconstruction fidelity. Extensive experiments have demonstrated the superior performance of our method in robustly hiding watermarks while resisting various attacks and maintaining high rendering quality and spatiotemporal consistency.

Problem

• 4D Gaussian Splatting
• watermarking
• spatio-temporal consistency
• kinematic manifold
• intellectual property protection

Innovation

• 4D Gaussian Splatting
• kinematic-aware watermarking
• spatio-temporal consistency
• HMM-MRF energy minimization
• anisotropic gradient routing