Mesh Watermark Removal Attack and Mitigation: A Novel Perspective of Function Space

Mesh watermark embeds secret messages in 3D meshes and decodes the message from watermarked meshes for ownership verification. Current watermarking methods directly hide secret messages in vertex and face sets of meshes. However, mesh is a discrete representation that uses vertex and face sets to describe a continuous signal, which can be discretized in other discrete representations with different vertex and face sets. This raises the question of whether the watermark can still be verified on the different discrete representations of the watermarked mesh. We conduct this research in an attack-then-defense manner by proposing a novel function space mesh watermark removal attack FuncEvade and then mitigating it through function space mesh watermarking FuncMark. In detail, FuncEvade generates a different discrete representation of a watermarked mesh by extracting it from the signed distance function of the watermarked mesh. We observe that the generated mesh can evade ALL previous watermarking methods. FuncMark mitigates FuncEvade by watermarking signed distance function through message-guided deformation. Such deformation can survive isosurfacing and thus be inherited by the extracted meshes for further watermark decoding. Extensive experiments demonstrate that FuncEvade achieves 100% evasion rate among all previous watermarking methods while achieving only 0.3% evasion rate on FuncMark. Besides, our FuncMark performs similarly on other metrics compared to state-of-the-art mesh watermarking methods.