Vertex Attack Resistant Watermarking Scheme for Vector Maps Based on Virtual Vertices and Frequency Coefficient Ratios of DWT

Frequency-domain watermarking is highly effective in copyright authentication for various forms of multimedia data, including but not limited to images, videos, and audios. However, it faces vulnerability to vertex attacks, such as map cropping and vertex deletion, when applied to vector maps. To enhance the robustness of frequency-domain watermarking for vector maps, this study proposes a new scheme based on virtual vertices (VVs) and frequency coefficient ratios. Prior to watermark embedding, VVs are inserted between each pair of adjacent vertices. Next, the discrete wavelet transform is employed to decompose x- and y-coordinates sequences, which include both actual and virtual coordinates. The ratios between high frequency coefficients of the x- and y-coordinates sequences are computed and selected as the embedding domain. To minimize distortion from watermark embedding, the ratios are amplified and modulated to conceal the watermark information. Furthermore, a watermark correction method is devised to address VVs inconsistency, further enhancing robustness. Experimental results demonstrate that the proposed watermark correction method improves robustness performance by up to 35% compared to the uncorrected baseline. The proposed scheme also exhibits remarkable robustness against vertex deletion, vertex addition, and map cropping, achieving bit error rate ranging from 0% to 9.65%. Furthermore, the watermark’s visibility is well controlled, with error statistics approaching 0, thereby ensuring its imperceptibility.