Color image watermarking scheme based on quaternion Hadamard transform and Schur decomposition

Based on quaternion Hadamard transform (QHT) and Schur decomposition, a novel color image watermarking scheme is presented. To consider the correlation between different color channels and the significant color information, a new color image processing tool termed as the quaternion Hadamard transform is proposed. Then an efficient method is designed to calculate the QHT of a color image which is represented by quaternion algebra, and the QHT is analyzed for color image watermarking subsequently. With QHT, the host color image is processed in a holistic manner. By use of Schur decomposition, the watermark is embedded into the host color image by modifying the Q matrix. To make the watermarking scheme resistant to geometric attacks, a geometric distortion detection method based upon quaternion Zernike moment is introduced. Thus, all the watermark embedding, the watermark extraction and the geometric distortion parameter estimation employ the color image holistically in the proposed watermarking scheme. By using the detection method, the watermark can be extracted from the geometric distorted color images. Experimental results show that the proposed color image watermarking is not only invisible but also robust against a wide variety of attacks, especially for color attacks and geometric distortions.