False Negative and Positive Models of Dither Modulation Watermarking

False negative and positive probabilities are two important performances of watermarking systems. In the existing literature, results are known for studying the false negative and positive probabilities of the systems based on correlation detectors. Instead, in this paper, we study the false negative and positive probability models of dither modulation system which doesn't use correlation detector. We derive the false negative and positive probability models for dither modulation from the detection principle of the detectors. Expressions are derived both for the case of Gaussian noise and of no noise. The theoretical results are compared with the experimental results obtained in the case of random work and watermark, and the comparison validates the accuracy of the established models, and it also shows that random work and watermark have little influence on the false negative and positive probabilities, and this is different from the systems based on correlation detection.