distortion can be reduced by selecting appropriate
watermark embedding parameters. For example, it
was found that using π=1 and π
ξ¬Ά
=0.5, makes it
possible to achieve the absolute watermark extraction
accuracy for π£πππ’π < 0.5.
Thus, we can conclude that the proposed
watermark embedding method can be configured to
be highly robust to distortions 1-4 for any π£πππ’π and
to distortions 5-6 with an average level of π£πππ’ππ .
Such results make the proposed method very
attractive for practical use.
5 CONCLUSIONS
In this paper, we proposed a watermarking method to
protect geodata in the Mapbox Vector Tile (MVT)
format against theft. Despite its popularity in web
mapping services due to its efficient storage and fast
rendering, the vector nature of the MVT format
makes it vulnerable to theft by attackers. The method
proposed in the paper protected MVT data with a
digital watermark that was based on the re-
quantization of point coordinates of object geometry.
The method could be adjusted using several
parameters to balance the robustness of the digital
watermark to map distortions and the error introduced
when embedding.
A series of experiments were performed to test the
robustness of the method against various distortions,
including the removal of objects and layers, reduction
in the number of points, adding new objects, and
shifting some points in the tile geometry. We found
that with a proper choice of watermark parameters,
the proposed method could achieve a 100%
watermark extraction accuracy for all bits of the built-
in watermark, even with a reasonable level of the
listed distortions that did not lead to a loss of
significance of the protected geodata.
Planned areas for further work include further
improvement and deeper investigation of the
proposed method.
ACKNOWLEDGEMENTS
This study was supported by Russian Science
Foundation, project 22-71-10097. https://rscf.ru/en/
project/22-71-10097/.
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