目的 传统基于频率域的矢量地图水印算法往往通过直接修改变换系数实现水印嵌入，嵌入位置随机，且嵌入强度难以控制，实用能力受限。为此，本文挖掘了离散小波变换（discrete wavelet transform，DWT）和复数奇异值分解（complex singular value decomposition，CSVD）系数比值作为新的水印嵌入域，融合系数放大法和量化索引调制（quantization index modulation，QIM）提出了一种嵌入强度可控的鲁棒性矢量地图水印算法。方法 利用道格拉斯—普克算法提取矢量地图特征点，并基于特征点构建复数序列，对复数序列进行二层 DWT，得到二层低频系数和二层高频系数。在此基础上，利用 CSVD 分别计算二层低频和高频系数的奇异值，并以奇异值比值作为水印嵌入域。在水印嵌入阶段，对系数比值放大合适倍数，通过调制放大后的奇异值比值来控制水印嵌入误差，并实现水印信息的盲提取。结果 与最新的 3 种方法进行比较，本文算法从平移、旋转和缩放的组合攻击中提取的水印图像的归一化相关性系数（normalized correlation，NC）值从低于 0. 6 提升至 1。此外，在裁剪、简化和几何攻击的任意组合攻击中，本文算法均能够提取出 NC 值为 1 的水印图像，相较于对比方法，鲁棒性更加全面。在不可见性方面，本文算法表现优势，水印嵌入造成的误差被控制在毫米级。结论 本文所提的矢量地图水印算法挖掘了多重频率域变换的比值作为水印嵌入域，具有良好的安全性和稳健性，可以为矢量地图的版权保护提供技术参考。

Objective Traditional frequency domain-based vector map watermarking algorithms often embed watermarks by directly modifying transform coefficients, resulting in limited practicality due to unpredictable embedding locations and difficult-to-control embedding strengths. To address this issue, this paper explores the ratio of coefficients between discrete wavelet transform （DWT） and complex singular value decomposition （CSVD） as a new watermark embedding domain and proposes a robust vector map watermarking algorithm with controllable embedding strength by integrating coefficient amplification and quantization index modulation （QIM）. Through the development of watermark embedding domain mining and watermark embedding method, the overall performance of the frequency domain watermarking for vector maps is enhanced, hence improving the practical utility of watermarking in vector maps.Method In the process of data preprocessing, the watermarking scheme uses the Douglas-Peucker algorithm to extract feature points from the vector map and constructs a complex sequence based on the feature points. The complex sequence is then subjected to a two-level DWT to obtain low-frequency coefficients （AC2） and high-frequency coefficients （DC2）. On the basis of this approach, the singular values of AC2 and DC2 are calculated using CSVD, and the ratio of singular values is used as the watermark embedding domain. Theoretical analysis determined that the ratio can remain unaffected by geometric transformations of rotation, translation, and scaling, and has a high degree of robustness； likewise, the singular value is relatively stable and insensitive to changes in a few coordinate points. In the watermark embedding stage, the coefficient ratio is appropriately amplified （the amplified coefficient is 10⁶ in this study）, and the QIM method （the interval step size in QIM is set as 10 in this study） is used to modulate the amplified ratio of singular values to control the embedding error and achieve blind extraction of watermark information.Result We compared the proposed watermarking with three state-of-the-art saliency schemes, namely, DWT-CSVD mixed watermarking algorithm, single watermarking algorithm based on DWT, and the mixed watermarking algorithm based on discrete Fourier-transform frequency domain and spatial domain. After watermark information is embedded into various datasets with different watermarking algorithms, watermarked datasets are subjected to different degrees of geometric attacks, coordinate point attacks, clipping attacks, and combination attacks, and watermark information are extracted under various attack modes. Experimental results show that the proposed algorithm has good invisibility and comprehensive robustness. The difference between the original datasets and the watermarked datasets is difficult to perceive with the naked eye, and the greatest coordinate disturbance induced by watermark embedding is less than 3.92×10^-3, indicating a solid error control effect. Under various degrees of common geometric attacks, cropping, simplification, and coordinate point editing, the proposed watermarking algorithm can always extract the watermark images with an NC value of 1. Even under multiple attack modes involving multiple random combinations, the proposed algorithm is able to extract clearly identifiable watermark images. With the traditional frequency domain vector map watermarking approach, achieving such high performance would be challenging.Conclusion The proposed vector map watermarking algorithm exploits the ratio of multiple frequency transforms as the watermark embedding domain, which is secure and robust and can provide a technical reference for copyright protection of vector maps.