Geometrically invariant image watermarking based on fast Radial Harmonic Fourier Moments

• A fast and precise computing method for Radial Harmonic Fourier Moments (RHFMs) is proposed.
• The proposed method has improved the reconstruction performance and reduced the time complexity significantly.
• The relationship between reconstruction performance and the number of used RHFMs in the reconstruction process is discussed.
• Come up with a new robust image watermarking algorithm by using the proposed method for RHFMs.
• The results show the proposed watermarking algorithm has an outstanding watermark invisibility and robustness.

In order to reduce the time complexity and improve the reconstruction performance of traditional method for Radial Harmonic Fourier Moments (RHFMs), we introduce a fast and precise method by using FFT and based on the which, this paper proposes a novel image watermarking algorithm which is robust to geometric attacks. We firstly compute the RHFMs of the original image by using the proposed method and select the robust RHFMs which are suitable for watermark embedding. Then the watermark is embedded by modifying the magnitudes of RHFMs based on quantization. In the decoder, the watermark can be extracted from the magnitudes of RHFMs directly without using the original image. Simulation results show the proposed algorithm provides an excellent watermark invisibility and can be resilient to geometric attacks and common image processing attacks effectively.