Robust Watermarking Scheme for Vector Geographic Data Based on the Ratio Invariance of DWT–CSVD Coefficients

Abstract

Traditional frequency-domain watermarking algorithms for vector geographic data suffer from disadvantages such as the random watermark embedding position, unpredictable embedding strength, and difficulty in resisting multiple attacks at the same time. To address these problems, we propose a novel watermarking algorithm based on the geometric invariance of the ratios of discrete wavelet transform (DWT) and complex singular value decomposition (CSVD) coefficients, which embeds the watermark information in a new embedding domain. The proposed scheme first extracts feature points from the original vector geographic data using the Douglas–Peucker algorithm, and then constructs a complex sequence based on the feature points set. The two-level DWT is then performed on the complex sequence to obtain the low frequency coefficients (L2) and high frequency coefficients (H2). On this premise, the CSVD algorithm is utilized to calculate the singular values of L2 and H2, and the ratio of the singular values of L2 and H2 is acquired as the watermark embedding domain. During the watermark embedding process, a new watermark sequence is created by the fusion of the original watermark index value and bits value to improve the recognition of the watermark information, and the decimal part at different positions of the ratio is altered by the new watermark sequence to control the watermark embedding strength. The experimental results show that the proposed watermarking algorithm is not only robust to common attacks such as geometric, cropping, simplification, and coordinate point editing, but also can extract watermark images with a high probability under random multiple attacks.