<p>Stereo images have recently attracted substantial attention due to their immersive qualities, leading to an urgent need for effective copyright protection mechanisms. Many current zero-watermarking algorithms designed for image copyright protection are primarily tailored for single, planar images, with few specifically addressing the unique requirements of stereo images. Additionally, existing zero-watermarking techniques for stereo images often face challenges in accurately preserving the critical spatial relationship between the left and right views, which diminishes the effectiveness of these methods. To address these issues, this paper introduces an innovative zero-watermarking technique for stereo images, utilizing accurate ternary generalized Chebyshev–Fourier moments (ATG-CHFMs). First, an accurate computational scheme, termed accurate generalized Chebyshev–Fourier moments (AG-CHFMs), is proposed to mitigate numerical integration errors inherent in traditional generalized Chebyshev–Fourier moments (G-CHFMs). Second, by embedding ternary number theory into the moment formulation, we construct a novel class of ternary generalized Chebyshev–Fourier moments (TG-CHFMs), enhancing structural flexibility and encoding capacity. Third, the TG-CHFM framework is further extended via Gaussian quadrature integration, resulting in ATG-CHFMs that offer improved feature representation for stereo images. Finally, a robust zero-watermarking scheme for stereo images is developed by integrating ATG-CHFMs with an asymmetric tent map, thereby strengthening both watermark security and resistance to geometric distortions. Comparative experiments and analyses with existing methods reveal that the proposed stereo image zero-watermarking approach offers superior performance and enhanced robustness.</p>