KEYWORDS: Digital watermarking, Fractal analysis, Printing, Scanners, Linear filtering, Signal to noise ratio, Sensors, Image filtering, Interference (communication), Image processing
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.
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