## 5 Conclusions  
Based on mining the geometric statistical information in the spatial domain of vector maps and employing the geometric invariance of the frequency domain transformation \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Attack Mode** & **Scale** & \begin{tabular}{c} **Reference** \\ **[**31**]** \\ \end{tabular} & \begin{tabular}{c} **Reference** \\ **[**32**]** \\ \end{tabular} & \begin{tabular}{c} **Reference** \\ **[**23**]** \\ \end{tabular} & \begin{tabular}{c} **Reference** \\ **[**34**]** \\ \end{tabular} & \begin{tabular}{c} **Reference** \\ **[**40**]** \\ \end{tabular} & \begin{tabular}{c} **Reference** \\ **[**40**]** \\ \end{tabular} & \
\begin{tabular}{c} **The Proposed** \\ \end{tabular} \\ \hline \multirow{3}{*}{Rotation} & \(30^{\circ}\) & \(\surd\) & \(\times\) & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) \\  & \(90^{\circ}\) & \(\surd\) & \(\times\) & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) \\  & \(180^{\circ}\) & \(\surd\) & \(\times\) & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) \\ \hline \multirow{3}{*}{Scaling} & 0.5 times & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\  & 2 times & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\  & 5 times & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline \multirow{3}{*}{Translation} & 10 m & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\  & 20 m & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\  & 50 m & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline \multirow{3}{*}{Cropping} & 20\% & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\  & 25\% & \(\times\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) \\  & 50\% & \(\times\) & \(\times\) & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) \\  & 75\% & \(\times\) & \(\times\) & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) \\ \hline \multirow{3}{*}{Points adding} & 25\% & \(\surd\) & \(\times\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\  & 50\% & \(\surd\) & \(\times\) & \(\surd\) & \(\times\) & \(\surd\) & \(\times\) \\ \cline{1-1}  & 10\% & \(\surd\) & \(\times\) & \(\surd\) & \(\times\) & \(\times\) & \(\times\) \\ \hline \multirow{3}{*}{Points deletion} & 2\% & \(\surd\) & \(\times\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\  & 10\% & \(\times\) & \(\times\) & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) \\ \cline{1-1}  & 20\% & \(\times\) & \(\times\) & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) \\ \hline \multirow{3}{*}{Compression} & 25\% & \(\surd\) & \(\times\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\  & 50\% & \(\surd\) & \(\times\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\  & 75\% & \(\surd\) & \(\times\) & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) \\ \hline \multirow{3}{*}{Coordinate system transform} &
\begin{tabular}{c} Geodetic coordinate \\ system system \\ Projection coordinate \\ system \\ \end{tabular} & \(\surd\) & \(\surd\) & \(\times\) & \(\times\) & \(\surd\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of comparative analysis. coefficients, a robust zero-watermarking scheme for vector maps is presented in this study. In spatial domain information mining, feature points are used to build a CDTN, and the angle values in the CDTN are used to obtain the initial set of features. The extracted angle value sequence is changed using DFT, and the zero watermarks are made using the binary conversion of the phase sequence of DFT as the feature information. The uniqueness of CDTN, the fact that local alterations have no effect globally, and the geometric invariance of DFT transform coefficients provide a solid foundation of robustness for the proposed zero-watermarking scheme.