A Robust Image Watermarking Scheme Using Local Statistical Distribution in the Contourlet Domain

Data security is a main concern in everyday data transmissions in the Internet. A possible solution to guarantee a secure and legitimate transaction is via hiding a piece of tractable information into the multimedia signal, i.e., watermarking. This brief proposes a new multiplicative image watermarking scheme in the contourlet domain by taking into account the local statistical properties and inter-scale dependencies of the contourlet coefficients of images. Although the contourlet coefficients are non-Gaussian within a sub-band, their local distribution fits the Gaussian distribution very well. In addition, it is known that there exist across-scale dependencies among these coefficients. In view of this, we propose the use of bivariate Gaussian (BVG) distribution to model the distribution of the contourlet coefficients. Motivated by the modeling results, an optimum blind watermark decoder is designed in the contourlet domain using the maximum likelihood method. By means of carrying out a number of experiments, the performance of the proposed decoder is investigated with regard to the bit error rate and compared to other decoders. It will be shown that the proposed decoder built upon the BVG model is superior to other decoders in terms of rate of error. It will also be shown that the proposed decoder provides higher robustness in comparison to other decoders in presence of attacks such as filtering, compression, cropping, scaling, and noise.