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%$\sim$29%. Notably, we observe that previous methods are vulnerable to at least one watermarking attack (e.g. JPEG, crop, resize), while ours are robust against all watermarking attacks.

翻译：基于深度神经网络的水印方法正快速发展并展现出卓越性能。近期研究通过将变分辨率水印问题降维为固定分辨率水印问题，实现了分辨率无关的图像水印。然而，这种降维过程可能引入伪影并导致鲁棒性降低。为解决该问题，我们首次提出分辨率无关图像水印框架RAIMark，通过对图像的隐式神经表示进行水印嵌入。与现有方法不同，本方法无需依赖降维过程，直接对连续信号而非图像像素进行水印嵌入，从而实现分辨率无关水印。具体而言，对于任意分辨率的图像，我们拟合其隐式神经表示。作为连续信号，该隐式神经表示可被采样生成不同分辨率的图像。随后，我们快速微调已拟合的隐式神经表示，获得基于二进制密文的条件化水印隐式神经表示。预训练的水印解码器可从任意分辨率采样图像中提取隐藏信息。通过直接对隐式神经表示进行水印嵌入，我们在提升鲁棒性的同时实现了分辨率无关水印。大量实验表明，本方法较现有方法具有显著优势：比特准确率平均提升7%～29%。值得注意的是，我们发现现有方法对至少一种水印攻击（如JPEG压缩、裁剪、缩放）表现脆弱，而本方法对所有水印攻击均具有鲁棒性。