A digital watermark is a visible, or preferably invisible, identification code that is permanently embedded in digital media, to prove owner authentication thereby providing a level of document protection. In this paper, we review several approaches for the generation of watermarks using chaotic functions, and in particular, the logistic chaotic function. Using this function, in conjunction with seed management, it is possible to generate chaotic sequences that may be used to create highpass or lowpass digital watermarks. A slight change in the initial conditions will quickly lead to a significant change in the subsequent states of the system, and thus will generate substantially different watermarks. This technique has been shown to offer an added security advantage over the more traditionally generated watermarks created from pseudorandom sequences, in that only the function seed needs to be stored. It also has the advantage that, through examination of the theoretical properties of the function, it is possible to choose seeds that lead to robust, lowpass watermarks. We review various detection techniques including correlation and statistical methods, and present an analysis of the impact of noise present in a model optical detector. The logistic function presented in this paper is ill defined for certain seed values and has not been fully investigated for the purpose of watermark generation. We consider the impact of the theoretical properties of the logistic function for several chaos-based watermark generation techniques, in particular, their highpass and lowpass properties, which when embedded in digital media, are suitable for correlation and statistical based detection methods.
A digital watermark is a visible, or preferably invisible,
identification code that is permanently embedded in digital media,
to prove owner authentication and provide protection for security
or defence documents. In this paper, we present an approach for
the generation of watermarks using a logistic chaotic function.
Using this function, in conjunction with seed management, it is
possible to generate chaotic sequences that may be used to create
highpass or lowpass digital watermarks. A slight change in the
initial conditions will quickly lead to a significant change in
the subsequent states of the system, and thus will generate
substantially different watermarks. This technique has been shown
to offer an added security advantage over the more traditionally
generated watermarks created from pseudorandom sequences, in that
only the function seed needs to be stored. We have previously
presented a study where an optical correlator was suitable for the
detection of chaotically generated watermarks. We have also
studied the impact of shot noise present in an optical detector
for watermarks generated using the logistic function. The logistic
function presented in this paper is ill-defined for certain seed
values and has not been fully investigated for the purpose of
watermark generation. We consider the impact of the theoretical
properties of the logistic function on watermark generation and
their highpass and lowpass properties, which when embedded in
digital media, are suitable for optical detection.
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.
A digital watermark is a visible, or preferably invisible, identification code that is permanently embedded in some digital data to prove owner authentication and provide protection of that document. In this paper we utilize a watermark generation technique based on the use of chaotic functions and the motivation for using these functions is presented. The technique used for watermark embedding is also described, together with a watermark detection scheme based on an optical Matched Filter correlator. We provide results of optical simulations of the watermark detection scheme and show that correlation-based detection is an excellent method for detecting chaotically-generated watermarks embedded in the Fourier domain using multiplicative embedding. We also show that it is possible to detect chaotically-generated watermarks in images that have been subjected to noise.
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