Design Principles for Orthogonal Moments in Video Watermarking

In watermarking schemes, deriving the geometric invariants of the multimedia content is crucial for modern watermarking against geometric deformations. The invariants based on orthogonal moments can effectively describe the semantic content of multimedia due to their excellent mathematical properties. Modulating watermarked signals into these invariants can yield satisfactory geometric robustness. However, with the emerging risks posed by generative large models, the current theoretical analysis of the relationship between invariants and watermarking is still limited, and the intrinsic connection between them is neglected to varying degrees when designing moments-based watermarking schemes. To bridge this gap, we propose a set of design principles, including the texture complexity priority principle, uniform zeros distribution priority principle, and invariants conjugation priority principle, and reveal the critical influence of the mathematical properties of moments on video watermarking. Based on the above principles, we also propose a texture-aware adaptive video watermarking scheme based on orthogonal moments. Extensive experiments show that the proposed video watermarking scheme outperforms state-of-the-art watermarking algorithms regarding imperceptibility, robustness, and computational complexity.