Robust watermarking is an effective method and a promising solution for securing and
protecting the copyright of digital images. Moments and moment invariants have become
popular tools for robust watermarking due to their geometric invariance and favorable
capability of image description. Many moments-based robust watermarking schemes
have been proposed. However, there is a challenging problem of these schemes that
should be addressed. One of these problems is to improve both imperceptibility and
robustness. In contrast, the other problem, most of these schemes used inefficient,
traditional computation methods of the moments, resulting in an inaccurate and inefficient
performance of the watermarking schemes. To overcome these challenges, in this paper,
we propose a novel robust color image-watermarking algorithm based on new multiple
fractional multi-channel orthogonal moments, fractional-order exponent moments
(MFrEMs), fractional-order polar harmonic transforms (MFrPHTs), and fractional-order
radial harmonic Fourier moments (MFrRHFMs). Firstly, highly accurate fractional new
multi-channel orthogonal moments are computed for the host color images. Then, more
stable and accurate coefficients of fractional new multi-channel orthogonal moments are
selected. Finally, a robust color image watermarking approach for multiple watermarks
images is proposed based on MFrEMs, MFrPHTs, and MFrRHFMs using a 1D Sine
chaotic map. The experimental results demonstrate that the proposed approach provides
robustness against various attacks and better imperceptibility than the existing methods.