In this work, a new quaternion-based method for color image watermarking is proposed. In this method, a
novel set of quaternion radial substituted Chebyshev moments (QRSCMs) is presented for robust geometrically
invariant image watermarking. An efficient computational method is proposed for highly accurate,
fast, and numerically stable QRSCMs in polar coordinates. The proposed watermarking method consists of
three stages. In the first stage, the Arnold transform is used to improve the security of the watermarking
scheme by scrambling the binary watermark. In the second stage, the proposed accurate and stable QRSCMs
of the host color image are computed. In the third stage, the encrypted binary watermark is embedded into
the host image by employing the quantization technique on selected-magnitude QRSCMs where the watermarked
color image is obtained by adding the original host color image to the compensation image. Then,
the binary watermark can be extracted directly without using the original image from the magnitudes of
QRSCMs. Numerical experiments are performed where the performance of proposed method is compared
with the existing quaternion moment-based watermarking methods. The comparison clearly shows that the
proposed method is very efficient in terms of the visual imperceptibility capability and the robustness under
different attacks compared to the existing quaternion moment-based watermarking algorithms.