# A Two-Step Surface Reconstruction Method Using Signed Marching Cubes
## 3 Results
To ensure the generated mesh satisfies the need of practical applications, a best reconstruction size should be specified to extract the target isosurface. At present, there are few studies about the best reconstruction size. However, based on the analysis of the minimum bounding box, the best reconstruction size can be approximately evaluated by the above three types of accuracy. Table 3 demonstrates the approximate number of evaluated points using the marching cubes method and the two-step reconstruction method. \(N\) is the number of interpolation points, \(S_{c}\) is the size of voxel, \(N_{MC}\) is the number of evaluation points using marching cubes method, \(N_{SMC,p^{\prime}}\) is the number of evaluation points using signed marching cubes method with a lower expansion order \(p^{\prime}\), \(N_{SMC,p}\) is the number of evaluation points using signed marching cubes method with a higher expansion order \(p\), and \(\gamma=N_{SMC,p}/N_{SMC,p^{\prime}}\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Models** & \(N\) & \(S_{C}\) & \(N_{MC}\) & \(N_{SMC,p^{\prime}}\) & \(N_{SMC,p}\) & \(\gamma\) \\ \hline \multirow{3}{*}{Figure 6a} & \multirow{3}{*}{10,704} & 5 & \(2.75\times 10^{7}\) & \(2.75\times 10^{7}\) & \(2.65\times 10^{5}\) & 0.96\% \\  & & 10 & \(3.45\times 10^{6}\) & \(3.45\times 10^{6}\) & \(6.61\times 10^{4}\) & 1.92\% \\  & & 20 & \(4.37\times 10^{5}\) & \(4.37\times 10^{5}\) & \(1.59\times 10^{4}\) & 3.64\% \\ \hline \multirow{3}{*}{Figure 6b} & \multirow{3}{*}{6999} & 2 & \(1.57\times 10^{5}\) & \(1.57\times 10^{5}\) & \(1.59\times 10^{4}\) & 10.07\% \\  & & 5 & \(1.09\times 10^{4}\) & \(1.09\times 10^{4}\) & \(2.45\times 10^{3}\) & 22.53\% \\  & & 8 & \(2.65\times 10^{3}\) & \(2.65\times 10^{3}\) & \(9.14\times 10^{2}\) & 34.54\% \\ \hline \multirow{3}{*}{Figure 6c} & \multirow{3}{*}{3735} & 10 & \(1.20\times 10^{6}\) & \(1.20\times 10^{6}\) & \(7.05\times 10^{4}\) & 5.88\% \\  & & 15 & \(3.62\times 10^{5}\) & \(3.62\times 10^{5}\) & \(3.12\times 10^{4}\) & 8.61\% \\  & & 30 & \(4.65\times 10^{4}\) & \(4.65\times 10^{4}\) & \(7.51\times 10^{3}\) & 16.16\% \\ \hline \multirow{3}{*}{Figure 6d} & \multirow{3}{*}{1767} & 5 & \(2.15\times 10^{6}\) & \(2.15\times 10^{6}\) & \(1.01\times 10^{5}\) & 4.69\% \\  & & 10 & \(2.72\times 10^{5}\) & \(2.72\times 10^{5}\) & \(2.52\times 10^{4}\) & 9.26\% \\  & & 20 & \(3.44\times 10^{4}\) & \(3.44\times 10^{4}\) & \(6.13\times 10^{3}\) & 17.81\% \\ \hline \multirow{3}{*}{Figure 6e} & \multirow{3}{*}{3747} & 5 & \(4.13\times 10^{5}\) & \(4.13\times 10^{5}\) & \(3.01\times 10^{4}\) & 7.28\% \\  & & 10 & \(5.32\times 10^{4}\) & \(5.32\times 10^{4}\) & \(6.67\times 10^{3}\) & 12.54\% \\  & & 15 & \(1.64\times 10^{4}\) & \(1.64\times 10^{4}\) & \(2.65\times 10^{3}\) & 16.18\% \\ \hline \multirow{3}{*}{Figure 6f} & \multirow{3}{*}{3735} & 5 & \(8.93\times 10^{5}\) & \(8.93\times 10^{5}\) & \(2.27\times 10^{4}\) & 2.55\% \\  & & 10 & \(1.16\times 10^{5}\) & \(1.16\times 10^{5}\) & \(4.96\times 10^{3}\) & 4.29\% \\ \cline{1-1}  & & 12 & \(6.70\times 10^{4}\) & \(6.70\times 10^{4}\) & \(3.37\times 10^{3}\) & 5.03\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Number of evaluation points about the reconstructed models in Figure 6.  
The experiment results show that the number of evaluation points with a higher expansion order is far less than the number of evaluation points with a lower expansion order. Therefore, although the total evaluation number of evaluation points increases, the efficiency of the two-step reconstruction method is superior to the traditional marching cubes method. Furthermore, with the decrease of voxel size, the improved efficiency was more obvious.