  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.
