运用多重频率变换的矢量地图数字水印算法  

Digital watermarking algorithm for vector maps using multiple frequency transformations

作　　者：瞿成意 奚旭 杜景龙 张杰 张新长 QU Chengyi;XI Xu;DU Jinglong;ZHANG Jie;ZHANG Xinchang(College of Geography Science and Geomatics Engineering,Suzhou University of Science and Technology,Suzhou,Jiangsu 215009,China;School of Geographic Science and Remote Sensing,Guangzhou University,Guangzhou 510006,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 [2]广州大学地理科学与遥感学院,广州510006

出　　处：《测绘科学》2023年第7期208-218,共11页Science of Surveying and Mapping

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(SJCX22_1560)。

摘　　要：针对传统基于频率域变换的矢量地图数字水印算法受限于变换系数的稳定性和嵌入位置的随机性,难以同时抵抗旋转、缩放和平移等几何攻击,不可见性也较差,导致其在矢量地图中的应用受到极大的限制的问题。提出一种基于离散傅里叶变换(DFT)和奇异值分解(SVD)多重变换的混合域矢量地图水印方法,采用互补优化策略提升频率域水印算法的性能。该方法对坐标点序列进行DFT变换,再对变换得到的DFT幅度系数进行SVD变换,通过耦合幅度系数与奇异向量的几何不变性可以得到一个具有旋转、缩放、平移不变性的特征不变量序列,并将其作为水印嵌入域;在水印嵌入阶段,对所有特征不变量乘以109,同时采用量化索引调制(QIM)方式将水印信息嵌入至放大后的特征不变量。实验结果显示,水印嵌入造成的误差被控制在非常小的数值范围;在平移、旋转、缩放、裁剪以及组合攻击下,均能提取出完整的水印信息。该文提出的DFT-SVD混合变换域的矢量地图水印算法能够有效提升DFT域水印算法的鲁棒性,并具有良好的不可见性,为提升矢量地图频率域水印算法的实用性提供一种参考方案。The traditional digital watermarking algorithm for vector maps,based on frequency domain transform,has a strong theoretical foundation.However,it is limited by the stability of transform coefficients and the randomness of embedding positions.This limitation makes it difficult to withstand geometric attacks such as rotation,scaling,and translation simultaneously,resulting in poor invisibility.As a result,the application of the algorithms in vector maps is greatly restricted.There is an urgent need to enhance its application capability.To address this problem,a complementary optimization strategy to improve the performance of frequency domain watermarking algorithms is proposed in this study.We introduce a hybrid domain vector map watermarking scheme based on multiple transformations of discrete Fourier transform(DFT)and singular value decomposition(SVD).The proposed scheme involves DFT on the coordinate sequence,followed by an SVD transformation on the obtained DFT magnitude coefficients.By combining the geometric invariance of magnitude coefficients and singular vectors,a sequence of feature invariants with rotation,scaling,and translation invariance can be obtained,which serve as the watermark embedding domain.During the watermark embedding stage,all the feature invariants are multiplied by 109.The quantized index modulation(QIM)method is utilized to embed the watermark information into the scaled feature invariants.Experimental results demonstrate that the watermark embedding process introduces errors within a very small range.Furthermore,the complete watermark information can be extracted under various attacks,including translation,rotation,scaling,cropping,and combination attacks.The proposed vector map watermarking algorithm in the hybrid DFT-SVD transform domain effectively enhances the robustness of the DFT domain watermarking algorithm while maintaining good invisibility.This study provides a reference scheme for improving the practicality of frequency domain watermarking algorithms for vector maps.

关 键 词：数字水印 矢量地图 DFT SVD 混合变换域 

分 类 号：P208[天文地球—地图制图学与地理信息工程]