A new locally optimum watermark detection using vector-based hidden Markov model in wavelet domain

- The vector-based HMM is used to model the wavelet coefficients of images.
- A new watermark detector using vector-based HMM is proposed.
- Closed-form expression for test statistic is derived and experimentally validated.
- The proposed vector-based HMM detector outperforms other existing detectors.
- The vector-based HMM detector is highly robust against various kinds of attacks.

Watermark detection is a way of verifying the existence of a watermark in a watermarking scheme used for copyright protection of digital data. Statistical modeling of wavelet subband coefficients has been extensively used in watermark detection. The effectiveness of a watermarking scheme depends directly on how the wavelet coefficients are modeled. It is known that the vector-based hidden Markov model (HMM) is a very powerful statistical model for describing the distribution of the wavelet coefficients, since it is capable of capturing the subband marginal distribution as well as the inter-scale and cross orientation dependencies of the wavelet coefficients. In this paper, it is shown that modeling using the vector-based HMM gives a better fit for the empirical data in comparison to modeling with Cauchy, Bessel-K form (BKF) and generalized Gaussian (GG) distributions. In view of this, we propose a locally-optimum blind watermark detector using the vector-based HMM in the wavelet domain. In a Bayesian framework, closed-form expressions for the mean and variance of a test statistic are derived, experimentally validated and used in evaluating the performance of the proposed detector. Using a number of test images, the performance of the proposed detector is evaluated. It is shown that the proposed detector provides a detection rate higher than that provided by other detectors designed based on the Cauchy, Gaussian, BKF or GG distributions for the wavelet coefficients. The proposed detector is also shown to be highly robust against various kinds of attacks.