<p>The vector map zero-watermarking algorithm constructs a watermark by exploiting feature information from vector maps, with its stability often relying on the inherent invariance of vertices. However, vertices may be altered during map editing, compromising the algorithm’s robustness. To address this issue, this study proposes a vector map zero-watermarking algorithm capable of withstanding geometry attacks and various vertex attacks by leveraging the invariant features of Delaunay triangulation networks (DTN). The algorithm utilizes the Douglas-Peucker algorithm to extract the map's feature points, constructs a DTN from these points, and subsequently computes the circumradius and inradius of each triangle in the DTN. A feature information matrix is derived from the circumradius, and the watermark index is determined based on the inradius combined with the Mersenne Twister algorithm and voting mechanism. Finally, a zero watermark is generated through an XOR operation with the encrypted watermark image, which is scrambled using Logistic. Experimental results demonstrate that the proposed algorithm effectively resists vertex-related attacks, including geometric, point addition, point deletion, precision reduction, compression and noise attacks, while also showing strong resistance to collusion attacks.</p>

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Vertex attack resistant zero-watermarking for vector maps based on geometric feature mining using Delaunay triangulation network

  • Jinglong Du,
  • Yi Wei,
  • Xu Xi,
  • Jie Zhang,
  • Ning Xi

摘要

The vector map zero-watermarking algorithm constructs a watermark by exploiting feature information from vector maps, with its stability often relying on the inherent invariance of vertices. However, vertices may be altered during map editing, compromising the algorithm’s robustness. To address this issue, this study proposes a vector map zero-watermarking algorithm capable of withstanding geometry attacks and various vertex attacks by leveraging the invariant features of Delaunay triangulation networks (DTN). The algorithm utilizes the Douglas-Peucker algorithm to extract the map's feature points, constructs a DTN from these points, and subsequently computes the circumradius and inradius of each triangle in the DTN. A feature information matrix is derived from the circumradius, and the watermark index is determined based on the inradius combined with the Mersenne Twister algorithm and voting mechanism. Finally, a zero watermark is generated through an XOR operation with the encrypted watermark image, which is scrambled using Logistic. Experimental results demonstrate that the proposed algorithm effectively resists vertex-related attacks, including geometric, point addition, point deletion, precision reduction, compression and noise attacks, while also showing strong resistance to collusion attacks.