Geometric Properties of Watermarking Schemes

A variety of image watermarking schemes have been proposed using orthogonal transformations, projections, and coding techniques to embed imperceptible watermarks into images. Analytical studies of the watermarking problem have typically been based on studying the performance limits of these known algorithms. In contrast, this paper formalizes the watermarking problem in an “algorithm independent” framework, representing any watermarking algorithm as a partition of the image space into a collection of sets, and defining requirements of these sets that must be met by any solution to the watermarking problem. Specifically, these requirements define and constrain the falsealarm ratio, distortion, robustness and security of a watermarking system. Using this formalism, we first characterize common features of algorithms that solve the watermarking problem. We show how the requirements defined earlier force important differences between watermarking signal sets and classical communication systems signal sets. Next, we show how common components of existing watermarking algorithms (e.g. transformations, projections, and coding) can be associated with specific requirements of the watermarking definition. Finally, we show how our new formalism of the watermarking problem provides a procedure for optimal design of watermarking systems to target specified false-alarm, distortion, and robustness objectives.