Blind Watermarking of Color Medical Images Using Hadamard Transform and Fractional-Order Moments

This paper proposes a new blind, color image watermarking method using fast Walsh–Hadamard transformation (FWHT) and multi-channel fractional Legendre–Fourier moments (MFrLFMs). The input host color image is first split into 4 × 4 non-interfering blocks, and the MFrLFMs are computed for each block, where proper MFrLFMs coefficients are selected and FWHT is applied on the selected coefficients. The scrambled binary watermark has been inserted in the quantized selected MFrLFMs coefficients. The proposed method is a blind extraction, as the original host image is not required to extract the watermark. The proposed method is evaluated over many visual imperceptibility terms such as peak signal-to-noise ratio (PSNR), normalized correlation (NC), and bit error rate. The robustness of the proposed method is tested over several geometrical attacks such as scaling, rotation, cropping, and translation with different parameter values. The most widely recognized image processing attacks are also considered, e.g., compressing and adding noise attacks. A set of combination attacks are also tested to analyze the robustness of the proposed scheme versus several attacks. The proposed model’s experimental and numerical results for invisibility and robustness were superior to the results of similar watermarking methods.

Geometrically Invariant NSCT–GPCET-Based Image Watermarking with Accurate Moment Calculation

Generic polar complex exponential transform (GPCET), as continuous orthogonal moment, has the advantages of computational simplicity, numerical stability, and resistance to geometric transforms, which make it suitable for watermarking. However, errors in kernel function discretization can degrade these advantages. To maximize the GPCET utilization in robust watermarking, this paper proposes a secondary grid-division (SGD)-based moment calculation method that divides each grid corresponding to one pixel into nonoverlapping subgrids and increases the number of sampling points. Using the accurate moment calculation method, a nonsubsampled contourlet transform (NSCT)–GPCET-based watermarking scheme with resistance to image processing and geometrical attacks is proposed. In this scheme, the accurate moment calculation can reduce the numerical error and geometrical error of the traditional methods, which is verified by an image reconstruction comparison. Additionally, NSCT and accurate GPCET are utilized to achieve watermark stability. Subsequent experiments test the proposed watermarking scheme for its invisibility and robustness, and verify that the robustness of the proposed scheme outperforms that of other schemes when its level of invisibility is significantly higher.

New Image Watermarking Algorithm Based on DWT and Pixel Movement Function PMF

In this paper, we propose a new algorithm of image watermarking based on Discrete Wavelet Transform (DWT) including a function for pixels movement. The proposed algorithm uses DWT of two levels in order to compact a higher energy in component LL1, and Contrast Sensitivity Function (CSF) to improve the invisibility and robustness, the new Function of Pixel Movement (PMF) is applied to increase the security properties. Pixel Movement Function (PMF) is a function of N iteration inside each block, this function required a changeable key K calculated in each iteration N for the position of each block. Numerical experiments are performed to demonstrate that the proposed method can improve watermarking quality in terms of imperceptibility of watermark, capacity of insertion and robustness against different attacks such as Joint Photographic Experts Group (JPEG) compression, noise addition and geometrical attacks.