Capacity issues in digital image watermarking

We study certain aspects of the problem of watermarking images, not for the classical example of ownership identification, but instead for embedding a unique identifier that can act as a "serial number" for the image in which it is embedded. In this context, two fundamental questions are: (a) what is the maximum number of different watermarks that can be distinguished reliably? and (b) what are good design techniques for watermarking methods to approximate that maximum? Under the assumption that attacks can be modeled as additive noise, we provide answers to both questions. To answer (a), we first show how the process of inserting a watermark is analogous to that of storing bits in certain devices, and then we compute the storage capacity of these devices. To answer (b), we present a specific design of a modulator to store information in those devices. Numerical simulations reveal that although strongly suboptimal in the number of bits they can effectively store in an image, simple and very low complexity modulator designs are able to pack enough bits in an image to be useful in practice.