Fragile watermark based on the Gaussian mixture model in the wavelet domain for image authentication

In this paper, a new fragile watermarking method based on statistical analysis in the wavelet domain is developed for image authentication. A two component Gaussian mixture model is developed to describe the statistical characteristics of images in the wavelet domain. Each wavelet subspace of the original image is divided into a watermarking block and a reference block. A Gaussian mixture model is then applied to both blocks to obtain their respective model parameters by an EM (expectation-maximization) algorithm. By slightly changing the wavelet coefficients (adding watermark) in the watermark block, we can adjust its model parameter to the same value as that of the reference block for authentication purposes, which constitutes the fragile watermark. Any change in the fragile-watermarked image will break the relationship of the statistical models between the watermarking block and reference block. The authentication procedure needs only a simple comparison between the model parameters of the two blocks in the watermarked image and no information about the original image. The preliminary experimental results indicate that the new watermarking scheme conforms with human perception characteristics and provides a perceptually invisible fragile watermark with fewer image data modified, compared with some other conventional fragile watermarking methods.