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

Recent 4D Gaussian Splatting (4DGS) methods often fail under fast motion with large inter-frame displacements, where Gaussian attributes are poorly learned during training, and fast-moving objects are often lost from the reconstruction. In this work, we introduce Spatiotemporal Position Implicit Network for 4DGS, coined SPIN-4DGS, which learns Gaussian attributes from explicitly collected spatiotemporal positions rather than modeling temporal displacements, thereby enabling more faithful splatting under fast motions with large inter-frame displacements. To avoid the heavy memory overhead of explicitly optimizing attributes across all spatiotemporal positions, we instead predict them with a lightweight feed-forward network trained under a rasterization-based reconstruction loss. Consequently, SPIN-4DGS learns shared representations across Gaussians, effectively capturing spatiotemporal consistency and enabling stable high-quality Gaussian splatting even under challenging motions. Across extensive experiments, SPIN-4DGS consistently achieves higher fidelity under large displacements, with clear improvements in PSNR and SSIM on challenging sports scenes from the CMU Panoptic dataset. For example, SPIN-4DGS notably outperforms the strongest baseline, D3DGS, by achieving +1.83 higher PSNR on the Basketball scene.

Recent progress in 4D Gaussian Splatting (4DGS) has achieved impressive dynamic scene reconstruction results. While these methods demonstrate remarkable performance, the specific factors behind their gains remain underexplored, making a systematic understanding of the underlying principles challenging. In this paper, we perform a comprehensive analysis of these hidden factors to provide a clearer perspective on the 4DGS framework. We first establish a controlled baseline, FreeTimeGS_ours, by formalizing and reproducing the heuristics of the state-of-the-art FreeTimeGS. Using this framework, we examine 4DGS along its fundamental axes and identify practical secrets, including the emergent temporal partitioning driven by Gaussian durations and the decoupling between photometric fidelity and motion behavior. Based on these insights, we propose FreeTimeGS++, a principled method that employs gated marginalization, UFM-guided initialization, and color correction to improve stability and reproducibility. Our approach yields reproducible results with reduced run-to-run variance.

3D Gaussian Splatting (3DGS) has recently redefined the paradigm of 3D reconstruction, striking an unprecedented balance between visual fidelity and computational efficiency. As its adoption proliferates, safeguarding the copyright of explicit 3DGS assets has become paramount. However, existing invisible message embedding frameworks struggle to reconcile secure and high-capacity data embedding with intrinsic asset utility, often disrupting the native rendering pipeline or exhibiting vulnerability to structural perturbations. In this work, we present \textbf{\textit{Splats in Splats++}}, a unified and pipeline-agnostic steganography framework that seamlessly embeds high-capacity 3D/4D content directly within the native 3DGS representation. Grounded in a principled analysis of the frequency distribution of Spherical Harmonics (SH), we propose an importance-graded SH coefficient encryption scheme that achieves imperceptible embedding without compromising the original expressive power. To fundamentally resolve the geometric ambiguities that lead to message leakage, we introduce a \textbf{Hash-Grid Guided Opacity Mapping} mechanism. Coupled with a novel \textbf{Gradient-Gated Opacity Consistency Loss}, our formulation enforces a stringent spatial-attribute coupling between the original and hidden scenes, effectively projecting the discrete attribute mapping into a continuous, attack-resilient latent manifold. Extensive experiments demonstrate that our method substantially outperforms existing approaches, achieving up to \textbf{6.28 db} higher message fidelity, \textbf{3$\times$} faster rendering, and exceptional robustness against aggressive 3D-targeted structural attacks (e.g., GSPure). Furthermore, our framework exhibits remarkable versatility, generalizing seamlessly to 2D image embedding, 4D dynamic scene steganography, and diverse downstream tasks.