A robust zero-watermarking algorithm for lossless copyright protection of medical images

The continuous orthogonal moments of images have become a main tool used in zero-watermarking algorithms in recent years. However, there is a problem that should not be neglected for existing zero-watermarking algorithms, which is known as numerical instability. Because the continuous orthogonal moments used in existing zero-watermarking algorithms are integer-order moments, this problem affects the computational accuracy of such moments and thus affects the performance of zero-watermarking algorithms. Therefore, in this paper, the integer-order radial harmonic Fourier moments (IoRHFMs) are firstly extended to fractional-order radial harmonic Fourier moments (FoRHFMs) to effectively mitigate the problem of numerical instability and improve the computational accuracy of IoRHFMs, and then a FoRHFM-based zero-watermarking algorithm for medical images is proposed to achieve lossless copyright protection of medical images. The experimental results show that this algorithm is highly robust to geometric attacks and common attacks, and is superior to IoRHFM-based and other zero-watermarking algorithms.