Accurate ternary polar linear canonical transform domain stereo image zero-watermarking

Stereo images have recently gained considerable attention due to their immersive nature, highlighting an urgent need for robust copyright protection mechanisms. However, most existing zero-watermarking algorithms are tailored for 2D images and do not adequately meet the unique requirements of stereo images. Moreover, current methods for zero-watermarking stereo images often fail to accurately represent and maintain the critical relationship between the left and right views, thereby limiting their effectiveness. To overcome these limitations, this paper proposes an innovative zero-watermarking method specifically designed for stereo images, which leverages an accurate ternary polar linear canonical transform (ATPLCT). We first introduced a new computational technique called the accurate polar linear canonical transform (APLCT) to address the numerical integration problems inherent in the polar linear canonical transform (PLCT). Next, we extend the APLCT using ternary number theory to develop the ATPLCT, which is specifically optimized for capturing stereo image characteristics. Finally, we propose a stereo image zero-watermarking strategy that integrates the ATPLCT with an asymmetric tent map. Comparative experiments and analyses show that our proposed method offers improved performance and greater robustness compared to existing approaches.