Color image triple zero-watermarking using decimal-order polar harmonic transforms and chaotic system

Abstract Existing zero-watermarking algorithms basically construct single zero-watermark information for the entire image and hence their efficiency is relatively low. In this paper, a color image triple zero-watermarking algorithm based on decimal-order polar harmonic transforms (DoPHTs) and chaotic system is proposed to achieve triple color image copyright protection, which is robust to geometric attacks. Firstly, the traditional integer-order polar harmonic transforms (IoPHTs) are extended to the decimal-order to construct DoPHTs, which effectively improve the performance of IoPHTs. Secondly, the three forms of DoPHTs, namely, decimal-order polar complex exponential transform (DoPCET), decimal-order polar cosine transform (DoPCT) and decimal-order polar sine transform (DoPST), are used to construct triple zero-watermark information. This algorithm uses geometrically invariant DoPHTs to improve its robustness to geometric attacks and uses the chaotic system to scramble logo image and feature images to enhance its security. The experimental results show that the proposed algorithm is highly robust to common image processing attacks and geometric attacks and is superior to other algorithms.