Ternary radial harmonic Fourier moments based robust stereo image zero-watermarking algorithm

With the development and popularization of computer network technology, the copyright protection of stereo images is a serious problem to be solved. Based on ternary number theory and radial harmonic Fourier moments (RHFM), ternary radial harmonic Fourier moments (TRHFM) is proposed to deal with stereo images in a holistic manner, and based on this moment, this paper proposes a robust stereo image zero-watermarking algorithm. We first compute the TRHFM of the original stereo image, and we randomly select TRHFMs using logistic mapping; then, we obtain a binary feature image using the magnitudes of the selected TRHFMs, and finally, we apply a bitwise exclusive-or operation on permuted logo image and binary feature image to obtain the zero-watermark image. Experimental results indicate that the proposed stereo image zero-watermarking algorithm is strongly robust to various asymmetric and symmetric attacks and has superiority compared with other zero-watermarking algorithms.