Symmetry, Vol. 17, Pages 1849: A High-Precision Verifiable Watermarking Scheme for Vector Geographic Data Using Difference Expansion and Metadata Restoration

Symmetry doi: 10.3390/sym17111849

Authors:
Li-Ming Gao
Qian Wang
Li Zhang

Vector geographic data require strict preservation of coordinate precision and topological integrity. However, their open transmission poses simultaneous challenges for copyright protection and data security. To address these issues, this study proposes a reversible watermarking framework that integrates difference expansion (DE) for lossless coordinate recovery, the Arnold transform for watermark encryption, and a metadata-assisted dual restoration mechanism to ensure geometric and topological consistency after embedding. Experimental evaluations on multiple vector datasets—including administrative boundaries, hydrographic networks, and road layers—demonstrate that the proposed method achieves near-zero distortion (RMSE ≈ 10−16), complete reversibility, and strong robustness against geometric and noise attacks, outperforming conventional DFT- and QIM-based schemes in terms of imperceptibility and restoration accuracy. The approach provides an efficient and verifiable solution for secure sharing and copyright protection of vector geographic data, contributing to reliable data provenance and trustworthy spatial information management.

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Li-Ming Gao www.mdpi.com