Fast Quaternion Log-Polar Radial Harmonic Fourier Moments for Color Image Zero-Watermarking

As a copyright protection technology, zero-watermarking has received widespread attention in recent years. The zero-watermarking algorithm based on moments has been extensively studied due to its better comprehensive performance and has made great progress. However, three issues of the moments-based zero-watermarking methods should be addressed: first, most of them ignore the analysis and experiment on discriminability, which leads to the high false positive ratio; second, direct computation of the moments from their definition is inefficient, numerically unstable and inaccurate, which severely affects the performances of these moments-based methods; third, most of the algorithms are only suitable for grayscale images, which leads to the limitation of the algorithms in practical applications. In this paper, we present a new color image zero-watermarking using fast quaternion log-polar radial harmonic Fourier moments. This algorithm firstly introduces log-polar coordinates to make traditional RHFMs scale-invariant, secondly improves their speed and accuracy, then introduces the concept of quaternion to make it suitable for color images, and finally applies it to the zero-watermark technology. Theoretical analysis and experimental results show that compared to the existing algorithms, the BER value of the proposed algorithm is 0 under some attacks, which can prove its effectiveness and achieved a good trade-off between discriminability and robustness, and has certain superiority in terms of security, capacity and speed.