RST and Noise Attack Resistant Zero‐Watermarking Algorithm for Vector Maps Based on Frequency Ratio's Invariance of <scp>DWT</scp>

ABSTRACT Current vector map zero‐watermarking algorithms primarily rely on features such as angles, distances, or vertex counts, which are highly sensitive to noise. While frequency‐domain coefficients offer greater stability and a promising alternative, existing frequency‐domain algorithms remain vulnerable to rotation, scaling, and translation attacks. To overcome these limitations, this study proposes a novel zero‐watermarking algorithm for vector maps based on the ratio invariance in the discrete wavelet transform (DWT) domain. The proposed algorithm first employs the Douglas–Peucker algorithm to simplify objects, enhancing robustness against changes in the vertex count. Subsequently, the horizontal and vertical coordinates of the feature points are separated, and their DWT high‐frequency coefficients are calculated. A rotation‐ and scale‐invariant geometric ratio domain is progressively constructed by leveraging the translation invariance of these coefficients. The ratio sequence is then binarized against its median to enhance resistance to vertex noise. Finally, the resulting binary sequences are superimposed to form the final feature matrix. Experimental results demonstrate that the proposed algorithm maintains significant uniqueness while exhibiting outstanding robustness, enabling stable watermark extraction under various attacks, including vertex simplification, vertex addition, noise perturbation, translation, rotation, and scaling.