Truncated Robust Natural Watermarking with Hungarian Optimization

Over the past two decades, spread spectrum (SS) embedding has been widely used in digital watermarking due to its competitive performance in robustness and security. However, the robustness of existing secure SS embedding methods, such as natural watermarking (NW) and robust-NW (RNW), is still weak. In this paper, we propose a new secure SS embedding method named truncated-RNW (TRNW), which improves the robustness of RNW while maintaining the same security level. The main idea of TRNW is to move RNW-watermarked correlations within an origin-centered sphere onto the spherical surface along the radial direction. Moreover, Hungarian algorithm is used to reduce embedding distortion, and the optimized method is called Hungarian-TRNW (HTRNW). A theoretical analysis and extensive experiments are conducted to validate the effectiveness of the proposed method. The results show that HTRNW achieves the same security level as RNW and a significant improvement over existing representative secure SS embeddings in terms of robustness.