Robust digital watermarking in PDTDFB domain based on least squares support vector machine

Geometric distortion is known as one of the most difficult attacks to resist, for it can desynchronize the location of the watermark and hence causes incorrect watermark detection. It is a challenging work to design a robust image watermarking scheme against geometric distortions. Based on the least squares support vector machine (LS-SVM) geometric distortions correction, we propose a new image watermarking scheme in shiftable complex directional pyramid (PDTDFB) domain with good visual quality and reasonable resistance toward geometric distortions in this paper. Firstly, the PDTDFB decomposition is performed on the original host image. Then, the corresponding lowpass subband is divided into small blocks. Finally, the digital watermark is embedded into host image by modulating the selected lowpass PDTDFB coefficients in small blocks. The main steps of digital watermark detecting procedure include: (1) the PDTDFB decomposition is performed on the test images, and some low-order Gaussian–Hermite moment energy of highpass subbands are computed, which are regarded as the effective feature vectors; (2) the appropriate kernel function is selected for training, and a LS-SVM training model can be obtained; (3) the watermarked image is corrected with the well trained LS-SVM model; and (4) the digital watermark is extracted from the corrected watermarked image. Experimental results show that the proposed image watermarking is not only invisible and robust against common image processing operations such as filtering, noise adding, and JPEG compression etc, but also robust against the geometrical distortions.