Fast image reconstruction method using radial harmonic Fourier moments and its application in digital watermarking

The Radial Harmonic Fourier Moments(RHFMs) is a kind of continuous orthogonal moments with good performance of image representation and reconstruction. Most of existing methods focused on improving the computation of RHFMs, and ignored the research about the reconstruction. Therefore, a fast reconstruction method based on RHFMs by using inverse fast Fourier transform(IFFT) is proposed in this paper. The time cost of reconstruction is greatly decreased. Then, the fast computation method is extend to the quaternion radial harmonic Fourier moments(QRHFMs) by using quaternion theory, which is suitable for the color image representation. Finally, a color image watermarking scheme based on the QRHFMs is conducted. During the embedding process, considering the association between QRHFMs and quaternion discrete Fourier transform(QDFT), the watermark is embedded in the magnitude of QRHFMs symmetrically. The center area of cover image is ignored in order to improve the quality of watermarked image. Experiments denote that proposed watermarking algorithm has low computation complexity and good robust against geometric attacks and common attacks.