Abstract

All digital images are band-limited to a degree that is determined by a spatial extent of the point spread function; the bandwidth of the image being determined by the optical transfer function. In the printing industry, the limit is determined by the resolution of the printed material. By band limiting the digital image in such away that the printed document maintains its fidelity, it is possible to use the out-of-band frequency space to introduce low amplitude coded data that remains hidden in the image. In this way, a covert signature can be embedded into an image to provide a digital watermark, which is sensitive to reproduction. In this paper a high frequency fractal noise is used as a low amplitude signal. A statistically robust solution to the authentication of printed material using high-fractal noise is proposed here which is based on cross-entropy metrics to provide a statistical confidence test. The fractal watermark is based on application of self-affine fields, which is suitable for documents containing high degree of texture. In principle, this new approach will allow batch tracking to be performed using coded data that has been embedded into the high frequency components of the image whose statistical characteristics are dependent on the printer/scanner technology. The details of this method as well as experimental results are presented.