Improved Color Image Watermarking Using Logistic Maps and Quaternion Legendre-Fourier Moments

In this chapter, an improved color image watermarking method is presented where the logistic maps were utilized with the quaternion Legendre-Fourier moments (Logistic maps–QLFMs). An exact, highly accurate, fast and numerically stable method is used to compute the Logistic maps–QLFMs in polar coordinates. In the Logistic maps–QLFMs method, the radial and angular kernels are computed over circular pixels by using analytical integration. Based on the geometric invariance of QLFMs, the robustness of the Logistic maps–QLFMs method is improved against geometric attacks, and the logistic mapping is used to randomly select QLFMs coefficients. Therefore, selected QLFMs are quantized to embed the binary digital watermark in the host color image. Moreover, the Logistic maps–QLFMs watermarking method is compared with quaternion Legendre-Fourier moments and existing quaternion methods. The QLFMs method is computed by using the same computation of the Logistic maps–QLFMs method. Utilizing an efficient computational method, the radial kernels of existing quaternion are computed using the accurate Gaussian quadrature method while the angular kernel is computed using analytical integration with the same as Logistic maps–QLFMs and QLFMs methods. Numerical experiments are performed where the performance of Logistic maps–QLFMs method is compared with the existing quaternion moment-based watermarking methods in terms of visual imperceptibility and robustness against different attacks. The comparison clearly shows that the Logistic maps–QLFMs is outperformed than existing quaternion moment-based watermarking methods.