Theoretical Framework for Watermark Capacity and Energy Estimation

In this paper, a theoretical framework for image watermark capacity estimation is derived. We present one general watermarking embedding scheme which is based on unitary transforms and adapts the additive watermarking model. In this general frame, simple and elegant formulas about the relationship of robustness and imperceptibility are derived. Hence a direct link between watermark capacity and image quality metrics is established for a given level of perceptual image distortion. The main work of this paper consists of four parts: (1) a general watermark embedding framework, which is based on two basic assumptions (unitary transform and additive watermark embedding model) and also includes the case of using block unitary transformation (such as 8-by-8 block DCT in JPEG and MPEG-1/2); (2) under the above two assumptions, we obtain two important relationships between watermark capacity or energy and image quality measures (one for PSNR and another for HVS-based WPSNR); (3) in addition the paper proves that for block unitary transforms, the above estimated relationships are also held. So it is very helpful for watermark capacity and energy analysis in JPEG and MPEG based watermarking schemes