## 6 Discussion
From left to right: the original surface of the kidney and the contradictory contours, the surface reconstructed by BPA, the surface reconstructed by Power Crust, the surface reconstructed by Poisson, and the surface reconstructed by VSR. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multicolumn{2}{c}{**Surface**} & \multirow{2}{*}{**Mean**} & \multirow{2}{*}{**std**} & \multirow{2}{*}{**rms**} & \multicolumn{2}{c}{**Hausdorff**} & \multirow{2}{*}{**Medial**} & \multirow{2}{*}{**Difference**} & \multirow{2}{*}{**Difference**} \\  & **Reconstruction** & & & & & & & & **(\%)** & **(\%)** \\ \hline \multirow{4}{*}{Non-contradictory contours} & BPA & 5.4036 & 4.3796 & 6.9542 & 18.9081 & 4.2757 & \(-\)48.10 & \(-\)86.11 \\  & Power Crust & 2.8995 & 2.9608 & 4.1430 & 14.0522 & 1.8748 & \(-\)12.56 & \(-\)26.25 \\ \cline{1-1}  & Poisson & 5.9510 & 5.2079 & 7.9063 & 23.448 & 4.3753 & 110.84 & \(-\)61.14 \\ \cline{1-1}  & VSR & 2.5736 & 2.9142 & 3.8868 & 14.539 & 1.3793 & \(-\)7.49 & \(-\)11 \\ \hline \multirow{4}{*}{Contradictory contours} & BPA & 6.1428 & 6.0208 & 8.5992 & 29.3689 & 3.9117 & \(-\)54.21 & \(-\)89.94 \\ \cline{1-1}  & Power Crust & 3.7181 & 3.3860 & 5.0277 & 15.5735 & 2.7963 & \(-\)17.79 & \(-\)35.19 \\ \cline{1-1}  & Poisson & 7.8823 & 6.5397 & 10.239 & 26.9386 & 5.9497 & 40.99 & \(-\)62.38 \\ \cline{1-1}  & VSR & 2.6500 & 2.8585 & 3.8968 & 14.6123 & 1.6135 & \(-\)8.74 & \(-\)13 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Difference between the reconstructed surfaces from contradictory contours and the original surface (HUMAN KIDNEY). As seen in row (d) of Figure 14, most methods had some problems dealing with the contradictory contours. The surface reconstructed by the BPA method lay on the outer red contour, which led to a bump on the reconstructed surface, while the original surface of the kidney should lie on the inner blue contour. There was a concave near the contradictory contours on the surface reconstructed by the Power Crust method, which indicated that it could not produce a correct surface from contradictory contours. The surface reconstructed by the VSR method lay between the outer read contour and the inner blue contour, which was a better result than the BPA and Power Crust methods. The surface reconstructed by the Poisson method lay on the inner blue contour correctly, indicating that it was the best method for dealing with contradictory contours. Because contradictory contours usually come from inconsistencies in the input data, they can be compensated for by an additional preprocessing step that solves such inconsistencies before the surface reconstruction. They can also be slightly compensated for when using approximation instead of interpolation. The results of Figure 14 may suggest a new way of combining the VSR and Poisson methods to solve the problem. We will investigate this in future work. Moreover, the VSR method was computationally expensive and needed considerable memory. Computation times were slow for a large number of constraints. This problem could be solved by reducing the constraints, using GPU-based parallel computing strategies, and using a fast computing algorithm such as the fast multipole method, which was suggested by [PERSON] _et al._[50].