A New Geometric-Transformation Robust and Practical Embedding Scheme for Watermarking 2D Vector Maps in the Graph Spectral Domain

In this paper, we first analyze the geometric-transformation robustness and computing performance of the previous watermarking algorithms for vector maps in the graph spectral domain, and propose that translation of a vector map affects only the first graph spectral coefficient, the watermarks embedded in the graph spectral coefficients can´t remain invariant to scaling and rotation. In succession, we present a new watermark embedding scheme for vector map polygonal lines. In the scheme, feature points of a polygonal line are selected firstly, a star tree of feature points is constructed instead of using Delaunay triangulation mesh, and a vector map polygonal line is watermarked via modifying both the magnitudes and the phases of the star-tree spectral coefficients except the first one. Adopted practical map datum, computing results show that watermarks generated by this technique are robust to geometric transformation and simplification, and the algorithm is efficient and practical