A new SVM-based image watermarking using Gaussian–Hermite moments

Abstract

Geometric attack 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 attacks. Based on the support vector machine (SVM) and Gaussian–Hermite moments (GHMs), we propose a robust image watermarking algorithm in nonsubsampled contourlet transform (NSCT) domain with good visual quality and reasonable resistance toward geometric attacks in this paper. Firstly, the NSCT is performed on original host image, and corresponding low-pass subband is selected for embedding watermark. Then, the selected low-pass subband is divided into small blocks. Finally, the digital watermark is embedded into host image by modulating adaptively the NSCT coefficients in small block. The main steps of digital watermark detecting procedure include: (1) some low-order Gaussian–Hermite moments of training image are computed, which are regarded as the effective feature vectors; (2) the appropriate kernel function is selected for training, and a SVM training model can be obtained; (3) the watermarked image is corrected with the well trained SVM model; (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, JPEG compression, etc., but also robust against the geometric attacks.