Statistical analysis of watermarking schemes for copyright protection of images

In this paper, we address the problem of the performance analysis of image watermarking systems that do not require the availability of the original image during ownership verification. We focus on a statistical approach to obtain models that can serve as a basis for the application of decision theory to the design of efficient detector structures. Special attention is paid to the possible nonexistence of a statistical description of the original image. Different modeling approaches are proposed for the cases when such a statistical characterization is known and when it is not. Watermarks may encode a message, and the performance of the watermarking system is evaluated using as a measure the probability of false alarm, the probability of detection when the presence of the watermark is tested, and the probability of error when the information that it carries is extracted. Finally, the modeling techniques studied are applied to the analysis of two watermarking schemes, one of them defined in the spatial domain, and the other in the direct cosine transform (DCT) domain. The theoretical results are contrasted with empirical data obtained through experimentation covering several cases of interest. We show how choosing an appropriate statistical model for the original image can lead to considerable improvements in performance.