Two Images Watermarking by using Exponent Fourier Moments

[Purposes] Most of the existing image watermarking schemes are designed to embed the watermark into independent images. Embedding a watermark into two images at one time is suggested to improve the efficiency of the watermarking procedure. [Methods] First, the two original images were combined together through complex representation, then the watermark was embedded by quantizing the magnitudes of the Exponent Fourier moments of the combined image, and the watermarked combined image was obtained by adding the combined image with the compensation image the was generated by reconstructing image from the modified Exponent Fourier moments. At last, the watermarked combined image was decomposed to obtain two watermarked images. Most importantly, it was impossible to extract watermarks without the access of both watermarked images. [Results] Experimental results have demonstrated the feasibility of the proposed scheme as well as its robustness to various attacks. In comparision with the excellent PCET-based method, with the attack situations of 5×5 median filter, 5×5 average filter, Gaussian noise with variance of 0.03, salt and pepper noise with noise density of 0.03, and JPEG compression factor of 10, the BER values of the proposed method decrease by 36%, 44%, 45%, 59%, and 29%, respectively. Moreover, when extracting watermarks, the extraction time is reduced by 50% compared with processing two images separately.