## 4 Results and Discussion  
### Watermark Capacity  
Table 3 compares the watermark capacity for different schemes, of which four schemes designed for large-capacity are selected from literature for comparisons. The method in [PERSON] et al. [34] conforms to the basic capacity of the reversible watermark, which reaches 1 bit/vertex. The methods in both [35] and [36] add the embedding algorithms, which increase the average capacity to 1.97187 bit/vertex and 3.9978 bit/vertex, respectively. The zero-watermarking scheme developed in [55] could reach an average watermark capacity of 1 bit/vertex, nearly as high as the reversible watermarking. The watermark capacities in the above-mentioned schemes are at the high-end of methods in the literature. By comparison, the watermark capacity of our developed scheme could reach 3.50316 Bit/vertex on average, which is approximately 3.5 times that in [34; 55], 1.8 times that of [PERSON]'s method, and only slightly lower than that of [PERSON]'s method.  
The watermark capacity directly affects the watermark robustness. In general, the larger the watermark capacity, the lower the robustness, but in our repeat embedding scheme, more capacity can promote a higher chance of the complete watermark information retained under attacks. For the coordinate-domain and frequency-domain watermarking algorithms, the more information the embedded watermark contains, the easier the map accuracies could change. As such, the watermark capacities for both the coordinate-domain and frequency-domain watermarking algorithms are elastic and typically low. The watermark capacity is however an important metric for assessing the non-interference watermarking schemes such as reversible watermarking and zero-watermarking, which are compared in Table 3. The design and processing of our proposed scheme help improve the watermark capacity, for example, the vertex-constrained blocking method makes a dense uniform watermark distribution and improves the number of embedded watermarks, and the construction of DTM creates a large amount of feature information that could provide a large space for constructing the zero-watermarks. In addition, the design of dual zero-watermarking increases the watermark capacity as compared to the single watermarking scheme. All these aspects that reflect the developed scheme could enhance the watermark capacity.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Data Set** & **2D Vector Data Set** & **Capacity** & **Basic Algorithm** & **Reference** \\ \hline G1 & Engineering Graphic & 1 & reversible & \\ G2 & Engineering Graphic & 1 & watermarking & \\ Average & Engineering Graphic & 1 & & \\ \hline Coastline map & Geospatial data & 1.98271 & & \\ Road map & Geospatial data & 1.97605 & reversible & \\ Windmill Islands map & Geospatial data & 1.95686 & watermarking & \\ Average & Geospatial data & 1.97187 & & \\ \hline G1 & Engineering Graphic & 3.9981 & & \\ G2 & Engineering Graphic & 3.9986 & reversible & \\ G3 & Engineering Graphic & 3.9956 & watermarking & \\ Average & Engineering Graphic & 3.9978 & & \\ \hline An engineering & & & & \\ graphic & Engineering graphic & 1 & zero-watermarking & [PERSON] and [PERSON] (2008) [55] \\ \hline ZC & Geospatial data & 3.55818 & & \\ SZ & Geospatial data & 3.44814 & zero-watermarking & The proposed \\ Average & Geospatial data & 3.50316 & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Watermark capacity of different methods (bit/vertex).