一种抗几何攻击的矢量地图点数据无损水印算法

A Lossless Watermarking Algorithm for Point Layer of Vector Map against Geometric Attack

  • 摘要: 针对矢量地图点数据的版权保护需求,本文提出一种基于存储特征的矢量地图点数据无损水印算法。首先,构建基于矢量地图坐标点的泰森多边形,每个点要素都对应唯一的泰森多边形;其次,根据存储顺序中相邻点要素对应泰森多边形周长的大小关系,确定点要素的存储方向;然后将相邻点要素对应泰森多边形的周长两两求和,再将所有和进行最小-最大值归一化,通过映射函数建立水印与归一化值之间的映射关系;最后,根据水印和对应点要素存储方向之间的关系,调整相邻点要素的存储顺序以嵌入水印。检测水印时,构建含水印矢量地图点数据的泰森多边形,根据相邻点要素的存储方向和映射关系提取水印。实验表明,该算法对平移、缩放和旋转具有良好的鲁棒性;由于水印嵌入过程中未对坐标值进行修改,实现了水印的无损嵌入,不影响高精度地图数据的使用,算法的实用性较强。

     

    Abstract: To address the copyright protection requirements of point data in vector maps, this paper proposes a lossless watermarking algorithm based on storage characteristics. First, Thiessen polygons are constructed from the coordinate points of the vector map, with each point feature corresponding to a unique polygon. Secondly, the ordering of point features is determined according to the magnitude relationship between the perimeters of adjacent polygons. Thirdly, the perimeters of adjacent polygons are summed pairwise and normalized using the min-max method. A mapping function establishes the relationship between the watermark and the normalized values. Finally, the storage order of adjacent point features is adjusted to embed the watermark. For watermark detection, Thiessen polygons are reconstructed, and the watermark is extracted based on the ordering of adjacent point features and the established mapping relationship. Experiments demonstrate that the algorithm is robust against translation, scaling, and rotation. Moreover, since no coordinate values are modified during embedding, the method achieves lossless watermarking, preserves the usability of high-precision map data, and enhances the algorithm’s practicality.

     

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