基于虚拟区间映射和扰动可控的矢量地图可逆水印算法  

A Reversible Watermarking Algorithm for Vector Maps Based on Virtual Interval Mapping and Controllable Perturbation

作　　者：吴明康 奚旭 杜景龙 康苏蒙 WU Mingkang;XI Xu;DU Jinglong;KANG Sumeng(School of Geography Science and Geomatics Engineering,Suzhou University of Science and Technology,Suzhou 215009,China)

机构地区：[1]苏州科技大学地理科学与测绘工程学院,江苏苏州215009

出　　处：《地理与地理信息科学》2024年第6期21-29,共9页Geography and Geo-Information Science

基　　金：国家自然科学基金项目(42101420);江苏省研究生科研与实践创新计划项目(SJCX24_1911)。

摘　　要：在大多数矢量地图可逆水印算法中,水印的宿主顶点之间往往存在强关联性,致使算法对顶点增删类的攻击不具有鲁棒性。针对上述问题,该文以量化索引调制为基础思想,结合伪随机映射算法,设计一种鲁棒性强且扰动可控的矢量地图可逆水印算法。首先,根据数据的精度容差构建虚拟区间作为水印的隐藏域,并利用容差限制顶点的移动范围;其次,利用要素内相邻顶点的参考距离作为伪随机种子,生成一个伪随机数计算水印信息,以此降低顶点间的相关性;最后,通过设置嵌入强度定义多个子区间,根据水印信息调制坐标点的子区间位置,实现大容量水印嵌入,并计算所有顶点的平均坐标值作为密钥,以确保水印可逆提取的准确性。实验结果显示,该算法对顶点增删、要素增删及地图裁剪、简化、平移、缩放等攻击具有很好的抵抗性,同时能确保扰动程度处于可控范围内。In the majority of vector map reversible watermarking algorithms,there is significant correlation between the watermarked vertices.This correlation weakens the algorithms′resistance to vertex editing attacks and limits its practical effectiveness.Therefore,this paper proposes a robust and perturbation-controlled reversible watermarking algorithm for vector maps.The algorithm is designed based on the concepts of quantized index modulation and pseudo-random mapping.Firstly,a virtual interval is created as the concealed domain of the watermark based on the precision tolerance of the data,and the tolerance is employed to restrict the range of movement of the vertices.Secondly,the proximity of the adjacent vertices inside the feature is employed as a pseudo-random seed,generating a pseudo-random integer to calculate the watermark information.This process effectively reduces the correlation among the vertices.Finally,the embedding strength is used to define multiple subintervals.The position of the vertex within these subintervals is then adjusted based on the watermark information.This process allows for the embedding of a high-capacity watermark and improves the algorithm′s suitability for small-scale data.Once the watermark embedding process is finished,the average value of all vertices is computed as the key to guarantee the precision of watermark extraction.The experimental results demonstrate that the proposed watermarking algorithm exhibits strong resistance against vertex addition and deletion,feature addition and deletion,cropping,simplification,translation,scaling,and other related manipulations.Additionally,it ensures that the level of disturbance remains within a manageable range.

关 键 词：矢量地图 可逆水印 虚拟区间映射 扰动控制 信息编码 

分 类 号：P208[天文地球—地图制图学与地理信息工程] TP309.7[天文地球—测绘科学与技术]