The advances in the Neural Radiance Fields (NeRF) research offer extensive applications in diverse domains, but protecting their copyrights has not yet been researched in depth. Recently, NeRF watermarking has been considered one of the pivotal solutions for safely deploying NeRF-based 3D representations. However, existing methods are designed to apply only to implicit or explicit NeRF representations. In this work, we introduce an innovative watermarking method that can be employed in both representations of NeRF. This is achieved by fine-tuning NeRF to embed binary messages in the rendering process. In detail, we propose utilizing the discrete wavelet transform in the NeRF space for watermarking. Furthermore, we adopt a deferred back-propagation technique and introduce a combination with the patch-wise loss to improve rendering quality and bit accuracy with minimum trade-offs. We evaluate our method in three different aspects: capacity, invisibility, and robustness of the embedded watermarks in the 2D-rendered images. Our method achieves state-of-the-art performance with faster training speed over the compared state-of-the-art methods.

翻译：神经辐射场（NeRF）研究的进展为多个领域提供了广泛的应用，但其版权保护尚未得到深入研究。近年来，NeRF水印技术被认为是安全部署基于NeRF的三维表示的关键解决方案之一。然而，现有方法仅适用于隐式或显式的NeRF表示。在本工作中，我们提出了一种创新的水印方法，可同时应用于NeRF的两种表示形式。该方法通过微调NeRF，在渲染过程中嵌入二进制信息来实现。具体而言，我们提出利用NeRF空间中的离散小波变换进行水印嵌入。此外，我们采用延迟反向传播技术，并结合块级损失函数，以最小化性能折损的同时提升渲染质量与比特精度。我们从容量、不可见性和鲁棒性三个维度评估了所嵌入水印在二维渲染图像中的表现。实验表明，本方法在训练速度更快的同时，性能优于当前最先进的方法。