Modelling the false alarm and missed

Theoretical modeling of watermarks allow prediction of the detector reliability and facilitates the development of more reliable systems. In particular, mathematical evaluation is relevant to estimate the rate at which \false alarms" occur. In this paper, the probability of incorrect detection (missed detection or false alarm) is expressed in terms of the watermark-energy-to-image-luminance-variance ratio. We present some counterintuitive results which show for instance that the reliability of detection signiicantly depends on spatial correlation in watermark. Moreover we nd that a small but uncompensated random DC component in the watermark can have a signiicant eeect on the reliability. I Background New multi-media networks and services facilitate the dissemination of audio and video content, but at the same time make illegal copying and copyright piracy simple. This has created a need to embed copyright data in the content in an indelible way. Particularly if watermark detection is part of an active copy control concept on Consumer Electronics (CE) and PC platforms, typical requirements include: 1], 2], 3], 4], 5], and 6] 1. Erasing or altering the watermark should be diicult. 2. The watermarking scheme should be robust against typical transmission and storage imperfections (such as lossy compression, noise addition, format conversion , bit errors) and signal processing artefacts (noise reduction, ltering), even if such operations are intended to erase the watermark. 3. It should be robust against typical attacks, e.g. those described in 5]. 4. False alarms, i.e., positive responses for content that does not contain a watermark should not occur (orders of magnitude) more often than electronic or mechanical product failures. CE devices or PC-s should not fail to work due to an erroneously triggered watermark detector. 5. The watermark should be unobtrusive, and not be annoying to bona-de users. The "low false alarm" requirement appears to be too stringent to determine the error rates only by experiments. This has been our motivation to develop a mathematical model for the reliability of watermark detectors.