A hybrid domain-based watermarking for vector maps utilizing a complementary advantage of discrete fourier transform and singular value decomposition

Digital watermarking plays a crucial role in the copyright protecting of vector maps. Due to its solid theoretical foundation, Discrete Fourier transform (DFT) is frequently used in the construction of watermarking scheme for diverse electronic data. However, when applied to vector maps, DFT is particularly vulnerable to local changes in coordinate points, posing challenges in surviving coordinate point attacks and limiting its practicality. Furthermore, its resistance against geometric attacks is quite weak. To address these issues, we propose an algorithmic complementary strategy that enhances the performance of DFT-based vector map watermarking scheme. The proposed scheme is founded upon a hybrid transform domain consisting of DFT and singular value decomposition (SVD). The first step is to extract feature points using the Douglas Peucker algorithm, with the distance threshold set to a relative value to ensure synchronization of feature points throughout scaling. The feature points are then subjected to DFT to obtain magnitude coefficients, which are then further transformed using SVD. By combining the geometric invariance of magnitude coefficients with the singular vectors of SVD, an invariant with rotation, scaling, and translation invariance can be generated. For watermark embedding, the invariant serves as an embedding domain and are multiplied to minimize the impact on the host vector maps. The experimental results reveal that the proposed vector map watermarking has very low disturbance, substantially lower than the comparing algorithms, deriving in excellent invisibility. The scheme can extract watermark images with a normalized correlation value of 1 under a variety of attacks, including rotation, scaling, translation, vertex addition, simplification, and map cropping, and it can even extract identifiable copyright information under a 10% vertex deletion, demonstrating very comprehensive robustness.