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.

The goal of 3D mesh watermarking is to embed the message in 3D meshes that can withstand various attacks imperceptibly and reconstruct the message accurately from watermarked meshes. The watermarking algorithm is supposed to withstand multiple attacks, and the complexity should not grow significantly with the mesh size. Unfortunately, previous methods are less robust against attacks and lack of adaptability. In this paper, we propose a robust and adaptable deep 3D mesh watermarking Deep3DMark that leverages attention-based convolutions in watermarking tasks to embed binary messages in vertex distributions without texture assistance. Furthermore, our Deep3DMark exploits the property that simplified meshes inherit similar relations from the original ones, where the relation is the offset vector directed from one vertex to its neighbor. By doing so, our method can be trained on simplified meshes but remains effective on large size meshes (size adaptable) and unseen categories of meshes (geometry adaptable). Extensive experiments demonstrate our method remains efficient and effective even if the mesh size is 190× increased. Under mesh attacks, Deep3DMark achieves 10%∼50% higher accuracy than traditional methods, and 2× higher SNR and 8% higher accuracy than previous DNN-based methods.

DNN-based watermarking methods are rapidly developing and delivering impressive performances. Recent advances achieve resolution-agnostic image watermarking by reducing the variant resolution watermarking problem to a fixed resolution watermarking problem. However, such a reduction process can potentially introduce artifacts and low robustness. To address this issue, we propose the first, to the best of our knowledge, Resolution-Agnostic Image WaterMarking (RAIMark) framework by watermarking the implicit neural representation (INR) of image. Unlike previous methods, our method does not rely on the previous reduction process by directly watermarking the continuous signal instead of image pixels, thus achieving resolution-agnostic watermarking. Precisely, given an arbitrary-resolution image, we fit an INR for the target image. As a continuous signal, such an INR can be sampled to obtain images with variant resolutions. Then, we quickly fine-tune the fitted INR to get a watermarked INR conditioned on a binary secret message. A pre-trained watermark decoder extracts the hidden message from any sampled images with arbitrary resolutions. By directly watermarking INR, we achieve resolution-agnostic watermarking with increased robustness. Extensive experiments show that our method outperforms previous methods with significant improvements: averagely improved bit accuracy by 7%~29%. Notably, we observe that previous methods are vulnerable to at least one watermarking attack (e.g. JPEG, Crop, or Resize), while ours are robust against all watermarking attacks.