A High‐Capacity and Robust Reversible Watermarking Method for Vector Maps via Coarse‐To‐Fine Polar Grid Embedding

ABSTRACT

As the primary spatial data format in geographic information systems (GIS), vector maps demand exact coordinate reversibility for copyright protection. However, vector maps encode geographic features as irregularly distributed floating‐point coordinates with limited redundancy. This lack of redundancy forces algorithms to perturb coordinates, creating a trade‐off among capacity, geometric robustness, and exact reversibility. We propose CFPG‐RW, a Coarse‐to‐Fine Polar Grid Reversible Watermarking method built on three mechanisms. First, a triplet‐defined local polar coordinate system provides embedding carriers invariant to rotation, scaling, and translation (RST): differential angle and distance ratio. Second, a coarse‐to‐fine polar grid encodes multi‐bit watermarks per‐vertex, lifting capacity beyond 1–2 bpv schemes. Third, a center‐referenced offset contraction strategy guarantees exact reversibility by shrinking and inverting vertex offsets. On real‐world OpenStreetMap‐derived datasets, CFPG‐RW achieves 6.99 bpv, recovers coordinates with errors at the degree level, and remains robust against RST attacks, cropping, and vertex‐editing attacks, outperforming existing methods.