Multiscale Fragile Watermarking Based on the Gaussian Mixture Model

Abstract

In this paper, a new multiscale fragile watermarking scheme based on the Gaussian mixture model (GMM) is presented. First, a GMM is developed to describe the statistical characteristics of images in the wavelet domain and an expectation-maximization algorithm is employed to identify GMM model parameters. With wavelet multiscale subspaces being divided into watermarking blocks, the GMM model parameters of different watermarking blocks are adjusted to form certain relationships, which are employed for the presented new fragile watermarking scheme for authentication. An optimal watermark embedding method is developed to achieve minimum watermarking distortion. A secret embedding key is designed to securely embed the fragile watermarks so that the new method is robust to counterfeiting, even when the malicious attackers are fully aware of the watermark embedding algorithm. It is shown that the presented new method can securely embed a message bit stream, such as personal signatures or copyright logos, into a host image as fragile watermarks. Compared with conventional fragile watermark techniques, this new statistical model based method modifies only a small amount of image data such that the distortion on the host image is imperceptible. Meanwhile, with the embedded message bits spreading over the entire image area through the statistical model, the new method can detect and localize image tampering. Besides, the new multiscale implementation of fragile watermarks based on the presented method can help distinguish some normal image operations such as JPEG compression from malicious image attacks and, thus, can be used for semi-fragile watermarking.