PhysMark: Population-Guided Carrier Learning for Generalizable Physical-Channel Watermarking in 3D Gaussian Splatting

Medical volumes reconstructed with 3D Gaussian Splatting (3DGS) become digital assets for case discussion, teaching, and online sharing. To support provenance and copyright tracking during both digital and physical dissemination, a verifiable message can be embedded into the 3DGS representation. However, most existing 3DGS watermarking methods design carriers for a single asset and do not explicitly exploit cross-asset regularities in carrier reliability, which limits generalization to unseen assets. We observe that the relative reliability of candidate carriers transfers across 3DGS assets: carriers that are relatively reliable on a finite set of seen assets tend to remain relatively reliable on unseen ones. Based on this observation, we propose PhysMark, a generalizable physical-channel 3DGS watermarking framework. PhysMark converts this regularity into a learnable, structured carrier prior: it initializes structured sparse carriers from population-level responses and then refines the carrier representation through the watermark recovery objective, turning asset-specific carrier search into prior-guided cross-asset carrier learning. In addition, PhysMark integrates the print-and-capture process into training, allowing the carrier to adapt to distortions introduced by printing, halftoning, and photographing. Experiments on medical 3DGS assets across multiple message lengths, unseen assets, digital-domain transformations, and real print-and-capture conditions show that the carrier reliability ranking transfers well across assets, that the prior-guided carrier improves recovery stability on unseen assets compared with single-asset carrier design, and that practical detectability is achieved under real printing and photographing.