As 3D Gaussian Splatting~(3D-GS) gains significant attention and its commercial usage increases, the need for watermarking technologies to prevent unauthorized use of the 3D-GS models and rendered images has become increasingly important. In this paper, we introduce a robust watermarking method for 3D-GS that secures ownership of both the model and its rendered images. Our proposed method remains robust against distortions in rendered images and model attacks while maintaining high rendering quality. To achieve these objectives, we present Frequency-Guided Densification~(FGD), which removes 3D Gaussians based on their contribution to rendering quality, enhancing real-time rendering and the robustness of the message. FGD utilizes Discrete Fourier Transform to split 3D Gaussians in high-frequency areas, improving rendering quality. Furthermore, we employ a gradient mask for 3D Gaussians and design a wavelet-subband loss to enhance rendering quality. Our experiments show that our method embeds the message in the rendered images invisibly and robustly against various attacks, including model distortion. Our method achieves state-of-the-art performance. Project page: https://kuai-lab.github.io/3dgsw2024/

翻译：随着3D高斯泼溅（3D-GS）获得显著关注及其商业应用日益增多，为防止3D-GS模型及其渲染图像被未经授权使用，水印技术的需求变得愈发重要。本文提出了一种针对3D-GS的鲁棒水印方法，旨在保护模型及其渲染图像的所有权。所提方法在保持高渲染质量的同时，能够有效抵抗渲染图像失真和模型攻击。为实现这些目标，我们提出了频率引导致密化（FGD），该方法根据3D高斯对渲染质量的贡献度移除部分高斯，从而增强实时渲染能力并提升消息的鲁棒性。FGD利用离散傅里叶变换对高频区域的3D高斯进行分割，以改善渲染质量。此外，我们为3D高斯采用了梯度掩码，并设计了小波子带损失以进一步提升渲染质量。实验表明，我们的方法能够将消息不可见且鲁棒地嵌入到渲染图像中，并能有效抵抗包括模型失真在内的多种攻击。本方法实现了最先进的性能。项目页面：https://kuai-lab.github.io/3dgsw2024/