A multiscale fragile watermark based on the Gaussian mixture model in the wavelet domain

The wavelet coefficients in 2D discrete wavelet transform (DWT) subspaces have a peaky, heavy-tailed marginal distribution that can be well described by a Gaussian mixture statistical model. In this paper, a multiscale implementation of fragile watermarks based on the Gaussian mixture model is presented. The presented new method can embed a message bit stream, such as personal signatures or copyright logos, into a host image. With the embedded message bits spreading over the whole image area, the new method can detect and localize any image tampering since it will inevitably destroy a certain message bits. Compared with some other fragile watermark techniques, the statistical model based method modifies only a very small amount of image data to embed watermarks and the modification is hardly perceived by human vision because it occurs at texture edges. Besides, the multiscale implementation of fragile watermarks based on the presented method can help distinguish some normal image operations such as compression from malicious attacks, which is meaningful in terms of semi-fragile watermarking applications.