Dual color images watermarking scheme with geometric correction based on quaternion FrOOFMMs and LS-SVR

To better describe the features of a color image, the quaternion fractional-order orthogonal Fourier-Mellin moments (QFrOOFMMs) are defined. By combining QFrOOFMMs with least square support vector regression, a dual color images watermarking scheme is investigated based on geometric correction. The original color watermark is encrypted by 3D sine map to enhance watermark security. A pure quaternion matrix can be obtained by performing the lifting wavelet transform, block division and the discrete cosine transform on the original color cover image. The robustness of the watermarking scheme is enhanced by executing the quaternion discrete Fourier transform on the quaternion matrix. Subsequently, the singular value matrix of the watermarked image with embedding operation is yielded by performing the quaternion singular value decomposition on the encryption watermark and the processed cover image. Before extracting the watermark, geometric distortion parameters to realize geometric correction are estimated by the least square support vector regression with the low-order QFrOOFMMs. Experimental results illustrate that the designed dual color images watermarking algorithm performs well in terms of imperceptibility and robustness, where the average PSNR value of the watermarked cover images is 61.6929 dB, and most of the NC values of the extracted watermarks are above 0.8500.