Exploring Accurate Invariants on Polar Harmonic Fourier Moments in Polar Coordinates for Robust Image Watermarking

In moment-based watermarking schemes, the accuracy of the moments is crucial for constructing robust watermarking schemes. The robustness of the watermarking scheme relies heavily on the proper representation of the moments. Despite the importance, current theoretical research on accuracy is very limited in watermarking techniques. To this end, we propose a novel robust image watermarking scheme based on accurate polar harmonic Fourier moments (PHFMs). Specifically, the accurate PHFMs computation based on polar pixel tiling with nearest neighbor interpolation (PPTN) is designed. This computation is general and used for embedder and extractor. This ingenious design eliminates geometric and numerical integration errors and also avoids the distortion interaction caused by watermarks. Also, an improved quantization strategy is applied to the embedding process, and satisfactory imperceptibility is obtained. The watermark is extracted without the host image. The experimental results show the excellent robustness of the proposed watermarking scheme to common image processing attacks, geometric attacks, and some kinds of compound attacks. The proposed scheme is superior to the state-of-the-art image watermarking schemes.