Fast optimum decoding for nonadditive readable watermarking

Watermarking algorithms for copyright protection are usually classified as belonging to one of two classes: detectable and readable. The aim of this paper is to present a possible approach for transforming an optimum, detectable technique previously proposed by the authors into a readable one. Similarly to what has been done previously by other authors we embed multiple copies of the watermark into the image, letting their relative positions in the frequency domain to be related to the informative message. The main drawback of this approach is that all copies of the watermark have to be detected without knowing their positions, i.e. all possible positions (many tenth thousands in our case) have to be tested, which is a prohibitive task from the point of view of the computational cost. Correlation based watermark detectors can overcome this problem by exploiting the Fast Fourier Transform (FFT) algorithm, but they are not optimum in the case of non additive watermarks. In this paper we demonstrate how the formula of the optimum watermark detector can be re-conducted to a correlation structure, thus allowing us to use the FFT for testing the watermark presence at all possible positions: in this way a fast optimum decoding system is obtained.