基于虚拟坐标的矢量地图差值扩展可逆水印方法  

A Differential Expansion Reversible Watermarking Algorithm for Vector Map Based on Virtual Coordinates

作　　者：戴千一 吴柏燕 DAI Qianyi;WU Baiyan(National-Local Joint Engineering Laboratory of Geo-Spatial Information Technology,Hunan University of Science and Technology,Xiangtan 411201;Hunan Provincial Key Laboratory of Geo-Information Engineering in Surveying,Mapping and Remote Sensing,Hunan University of Science and Technology,Xiangtan 411201;School of Earth Sciences and Spatial Information Engineering,Hunan University of Science and Technology,Xiangtan 411201,China)

机构地区：[1]湖南科技大学地理空间信息技术国家地方联合工程实验室,湖南湘潭411201 [2]湖南科技大学测绘遥感信息工程湖南省重点实验室,湖南湘潭411201 [3]湖南科技大学地球科学与空间信息工程学院,湖南湘潭411201

出　　处：《地理与地理信息科学》2024年第1期11-17,25,共8页Geography and Geo-Information Science

基　　金：湖南省自然资源厅科技项目“矢量地图数据云端集中存储管理安全保密技术研究”(20230126XX);湖南省教育厅科研项目“矢量地理空间数据数字水印模型研究”(20C0770);国家自然科学基金项目“地理语义支持的矢量数据高保真水印模型”(41201389)。

摘　　要：传统差值扩展技术受数据相关性限制,直接应用于矢量数据可逆水印方案易导致较低的水印容量和较大的数据失真,对顶点相关性低的矢量地图,水印效果更差。为实现更高的水印容量并控制数据失真,该文针对传统差值扩展技术提出改进:①在顶点坐标之间插入虚拟坐标,以虚拟坐标为参考点计算坐标差值;②将计算得到的坐标差值直方图向左平移,使直方图峰值点与原点重合;③水印以差值扩展的方式嵌入平移后的坐标差值中。实验结果表明:该算法的水印容量为2 bit/点,至少是传统差值扩展水印容量的6倍;与传统差值扩展方法相比,数据失真更小,原始地图坐标与水印地图坐标的RMSE和地图坐标最大改变量Max-R均大幅降低,算法严格可逆且对顶点相关性低的矢量地图水印效果仍然很好。Influenced by the limitations of data correlation,the traditional differential expansion technique applied directly to vector data reversible watermarking schemes is prone to lower watermarking capacity and larger data distortion.For vector maps with low vertex correlation,the watermarking effect is even worse.In order to achieve higher watermarking capacity and control data distortion,two improvement methods are proposed for the traditional difference expansion technique.First,the virtual coordinates are inserted between vertex coordinates and the coordinate difference is calculated with the virtual coordinates as reference points.Second,the histogram of the calculated coordinate differences is shifted to the left,so that the peak point of the histogram coincides with the origin.The watermark is embedded in the shifted coordinate difference by the means of difference expansion.The experimental results show that the improved reversible watermarking algorithm has a watermark capacity of 2 bit/vertex,which is at least 6 times of that of the traditional difference expansion.Compared with the traditional difference expansion algorithms,the proposed algorithm has less data distortion.The RMSE between the original map coordinates and the watermarked map coordinates and the maximum distortion of map coordinates Max-R are both significantly reduced.Moreover,the proposed algorithm is strictly reversible and still works well for watermarking vector maps with low vertex correlation.

关 键 词：矢量地图 可逆水印 差值扩展 虚拟坐标 直方图平移 

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]