Abstract
Watermarking plays an import role in digital copyright protection. It enables copyright owners to embed invisible watermarks within copies of data before distribution. However, most existing watermarking algorithms for 2D vector maps use either spatial domain methods, e.g., the Least Significant Bit or frequency domain methods, e.g., discrete Fourier transform (DFT), and very few algorithms combine the two domains. In order to improve the robustness of watermarks to against more common attacks, a novel algorithm using a combination of spatial and frequency domains is presented. Both the spatial domain and the frequency domain can be used for watermark embedding. Obviously, the advantages of each method are retained and the disadvantages of each method are offset by complementation. The watermark was also shuffled before embedding. A one-way hash function was used to map the watermark and 2D vector map. By using two different methods, one part of the watermark was embedded into the spatial domain first and another part of the watermark was embedded into the DFT domain. Additionally, the watermark was embedded multiple times. No original map data are required for the watermark extraction procedure. Analysis shows that the distortions of the watermarked data are extremely small, and the algorithm is more robust than methods using a single domain. It can resist the most common attacks, such as vertex insertion and removal, cropping, compression, reordering, and data format conversion attacks. It is also robust against rotation scaling and translation attacks.
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Acknowledgments
This work is funded by the Natural Science Foundation Committee, China (No. 41761080, and No. 41671447), Talent Innovation Venture Science and Technology Program of Lanzhou, No. 2016-RC-59, and Industrial Support and Guidance Project of Gansu Colleges and Universities, No. 2019C-04.
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L. Zhang conceived, designed, and performed the experiments and also wrote the manuscript; H. Yan and R. Zhu supervised the study; H. Yan offered helpful suggestions and reviewed the manuscript. R. Zhu and P. Du analyzed and evaluated the results.
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The code and the test vector map data associated with this paper can be found at https://github.com/diylife/Combinational-Watermarking-Algorithm.git.
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Zhang, L., Yan, H., Zhu, R. et al. Combinational spatial and frequency domains watermarking for 2D vector maps. Multimed Tools Appl 79, 31375–31387 (2020). https://doi.org/10.1007/s11042-020-09573-3
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DOI: https://doi.org/10.1007/s11042-020-09573-3