In this paper, a spread-spectrum-like discrete cosine transform (DCT) domain watermarking technique for copyright protection of still digital images is analyzed. The DCT is applied in blocks of 8x8 pixels, as in the JPEG algorithm. The watermark can encode information to track illegal misuses. For flexibility purposes, the original image is not necessary during the ownership verification process, so it must be modeled by noise. Two tests are involved in the ownership verification stage: watermark decoding, in which the message carried by the watermark is extracted, and watermark detection, which decides whether a given image contains a watermark generated with a certain key. We apply generalized Gaussian distributions to statistically model the DCT coefficients of the original image and show how the resulting detector structures lead to considerable improvements in performance with respect to the correlation receiver, which has been widely considered in the literature and makes use of the Gaussian noise assumption. As a result of our work, analytical expressions for performance measures, such as the probability of errors in watermark decoding and the probabilities of false alarms and of detection in watermark detection, are derived and contrasted with experimental results.

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A considerable amount of attention has been lately payed to a number of data hiding methods based in quantization, seeking to achieve in practice the results predicted by Costa for a channel with side information at the encoder. With the objective of filling a gap in the literature, this paper supplies a fair comparison between significant representatives of both this family of methods and the former spread-spectrum approaches that make use of near-optimal ML decoding; the comparison is based on measuring their probabilities of decoding error in the presence of channel distortions. Accurate analytical expressions and tight bounds for the probability of decoding error are given and validated by means of Monte Carlo simulations. For Dithered Modulation (DM) a novel technique that allows to obtain tighter bounds to the probability of error is presented. Within the new framework, the strong points and weaknesses of both methods are distinctly displayed. This comparative study allows us to propose a new technique named "Quantized Projection" (QP), which by adequately combining elements of those previous approaches, produces gains in performance.

A novel quantization-based data-hiding method, called Rational Dither Modulation (RDM), is presented. This method retains most of the simplicity of the conventional dither modulation (DM) scheme, which is largely vulnerable to amplitude scalings and modifies it in such a way that the result becomes invariant to gain attacks. RDM is based on using a gain-invariant adaptive quantization step-size at both embedder and decoder. This causes the watermarked signal to be asymptotically stationary. Mathematical tools are used to determine the stationary probability density function, which is later used to assess the performance of RDM in Gaussian channels. It is also shown that by increasing the memory of the system, it is possible to asymptotically approach the performance of DM, still keeping invariance against gain attacks. RDM is compared with improved spread-spectrum methods, showing that the former can achieve much higher rates for the same bit error probability. Experimental results confirm the validity of the theoretical analyses given in the paper. Finally, a broader class of methods, that extends gain-in- variance to quantization index modulation (QIM) methods, is also presented

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In this paper a watermarking scheme for copyright protection of still images is modeled and analyzed. In this scheme a signal following a key-dependent two-dimensional multipulse modulation is added to the image for ownership enforcement purposes. The main contribution of this paper is the introduction of an analytical point of view to the estimation of performance measurements. Two topics are covered in the analysis: the ownership verification process, also called watermark detection test, and the data-hiding process. In the first case, bounds and approximations to the receiver operating characteristic are derived. These results can be used to determine the threshold associated to a required probability of false alarm and the corresponding probability of detection. The data-hiding process is modeled as a communications system and approximations for the bit error rate are derived. Finally, analytical expressions are contrasted with experimental results.

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