A New Double Color Image Watermarking Algorithm Based on the SVD and Arnold Scrambling

Abstract

We propose a new image watermarking scheme based on the real SVD and Arnold scrambling to embed a color watermarking image into a color host image. Before embedding watermark, the color watermark image $W$ with size of $M\times M$ is scrambled by Arnold transformation to obtain a meaningless image $\tilde{W}$. Then, the color host image $A$ with size of $N\times N$ is divided into nonoverlapping $N/M\times N/M$ pixel blocks. In each $(i,j)$ pixel block $A_{i,j}$, we form a real matrix $C_{i,j}$ with the red, green, and blue components of $A_{i,j}$ and perform the SVD of $C_{i,j}$. We then replace the three smallest singular values of $C_{i,j}$ by the red, green, and blue values of ${\tilde{W}}_{ij}$ with scaling factor, to form a new watermarked host image ${\tilde{A}}_{ij}$. With the reserve procedure, we can extract the watermark from the watermarked host image. In the process of the algorithm, we only need to perform real number algebra operations, which have very low computational complexity and are more effective than the one using the quaternion SVD of color image.