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 190x increased. Under mesh attacks, Deep3DMark achieves 10%~50% higher accuracy than traditional methods, and 2x higher SNR and 8% higher accuracy than previous DNN-based methods.

翻译：3D网格水印的目标是将信息以不可感知的方式嵌入3D网格中，使其能够抵御多种攻击，并从含水印的网格中准确重建信息。水印算法应能抵御多重攻击，且其复杂度不应随网格尺寸显著增长。然而，以往的方法在抗攻击方面鲁棒性不足，且缺乏适应性。本文提出了一种鲁棒且自适应的深度3D网格水印方法Deep3DMark，该方法利用注意力机制卷积在水印任务中，将二进制信息嵌入无需纹理辅助的顶点分布中。此外，Deep3DMark利用了简化网格继承原始网格相似关系的特性，该关系是从一个顶点指向其邻接顶点的偏移向量。通过这一方式，我们的方法可在简化网格上训练，但仍能有效作用于大尺寸网格（尺寸自适应）和未见过的网格类别（几何自适应）。大量实验表明，即使网格尺寸增大190倍，我们的方法依然保持高效与有效性。在网格攻击下，Deep3DMark相比传统方法准确率提高10%~50%，相比先前基于深度神经网络的方法信噪比提高2倍，准确率提高8%。