Noisy optical detection of chaos-based watermarks

Abstract

In this paper we investigate the limits on optical detection of noisy watermarks that use a chaotic function, the logistic difference equation, in the watermark generation scheme. By varying the function seed, different chaotic sequences exhibiting lowpass and highpass characteristics, can be obtained for the same function, offering an added security advantage over watermarks generated using pseudorandom sequences. Watermark Detection is the process of determining whether an image is watermarked with a certain watermark. In this paper, we model and investigate an optical correlator suitable for watermark detection for certain classes of high-pass or low-pass watermarks. Once in the public domain a watermarked image may be subjected to noise and other attacks, deliberate and unintentional. Additionally,an optical correlator system will also be subject to shot noise. The effects of shot noise on optically transmitted watermarks are modeled in this paper and we examine how the watermark detection scheme performs in such situations. We quantify the degree of noise that may be present in the watermark detection scheme in order to obtain reliable detection or rejection of a watermark using an optical-correlator.