Double Medical Images Zero-Watermarking Algorithm Based on the Chaotic System and Ternary Accurate Polar Complex Exponential Transform

Different from the traditional watermarking schemes, zero-watermarking schemes are lossless embedding methods, which are applicable to be used in medical, military, remote sensing and other fields requiring high-integrity image copyright protection. However, most of the existing zero-watermarking schemes only provide copyright protection for one image at a time, which has certain limitations. This paper proposes a novel zero-watermarking scheme for protecting the copyright of two similar medical images simultaneously. Firstly, an accurate polar complex exponential transform (APCET) is designed using Gaussian numerical integration (GNI) method, which effectively improves the computation accuracy of polar complex exponential transform (PCET). Then, ternary accurate polar complex exponential transform (TAPCET) is constructed based on ternary number theory and APCET, which describes two similar medical images simultaneously. Finally, a robust zero-watermarking algorithm for two similar medical images is proposed based on TAPCET and chaotic mapping. The experimental results show that the proposed scheme can resist common image processing attacks and geometric attacks, and is superior to other zero-watermarking algorithms, being applicable for the copyright protection of two similar medical images simultaneously.