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. Traditional methods are less robust against attacks. Recent DNN-based methods either introduce excessive distortions or fail to embed the watermark without the help of texture information. However, embedding the watermark in textures is insecure because replacing the texture image can completely remove the watermark. In this paper, we propose a robust deep 3D mesh watermarking WM-NET, which leverages attention-based convolutions in watermarking tasks to embed binary messages in vertex distributions without texture assistance. Furthermore, our WM-NET 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(limited data) but remains effective on large-sized meshes (size adaptable) and unseen categories of meshes (geometry adaptable). Extensive experiments demonstrate our method brings 50% fewer distortions and 10% higher bit accuracy compared to previous work. Our watermark WM-NET is robust against various mesh attacks, e.g. Gauss, rotation, translation, scaling, and cropping.

翻译：三维网格水印的目标是向三维网格中嵌入信息，使其能够以不可察觉的方式抵御多种攻击，并能从含水印的网格中准确重建消息。传统方法对攻击的鲁棒性较弱。近期基于深度神经网络的方法要么引入过多失真，要么在缺乏纹理信息辅助时无法成功嵌入水印。然而，将水印嵌入纹理并不安全，因为替换纹理图像可完全去除水印。本文提出鲁棒深度三维网格水印WM-NET，该网络利用水印任务中的注意力卷积机制，在无纹理辅助条件下将二进制信息嵌入顶点分布中。此外，WM-NET利用简化网格继承原始网格相似关系的特性（该关系指顶点指向其邻域的偏移向量）。通过此设计，我们的方法可在简化网格（有限数据）上训练，却仍能有效处理大规模网格（尺寸自适应）与未见过的网格类别（几何自适应）。大量实验表明，与先前工作相比，本方法失真减少50%，比特准确率提升10%。我们的WM-NET水印对高斯、旋转、平移、缩放及裁剪等多种网格攻击均具有鲁棒性。