## 5 Discussion  
Various attempts have been made to improve the surface matching performance of surgical navigation systems. Recently, in an attempt to reduce the TRE, point clouds in patient space have been extracted using a non-contact method via scanners and other devices [2; 7; 9; 12]. [PERSON] et al. (2008) extracted patient space coordinates using a commercial laser range scanner. The facial surface and the cortical surface of the brain were measured using different cradles, and the size of the scanner device was large and cumbersome, which limited task performance. Recently, [PERSON] et al. (2014, 2017) attempted to easily extract point clouds in patient space using a mobile scanner (GoISCAN scanner, Sense 3D scanner). The authors were able to extract a point cloud by scanning up to the back of the actual head, resulting in improved matching accuracy. However, since scanners with guaranteed precision are generally expensive and are not integrated with commercial navigation systems [3], their use necessitates an additional coordinate transformation, and \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Optical System**} & \multicolumn{2}{c}{**Electromagnetic System**} \\ \cline{2-5}  & **Conventional** & **Proposed** & **Conventional** & **Proposed** \\ \hline Front & 3.10 (0.8) & 1.79 (0.6) & 4.23 (0.8) & 3.37 (1.0) \\ Middle & 3.55 (0.7) & 2.65 (0.3) & 4.44 (0.9) & 3.58 (1.1) \\ Rear & 4.16 (0.6) & 3.32 (0.5) & 4.90 (1.0) & 3.78 (1.0) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of TRE between the conventional and proposed registration strategies and between target locations in the optical and electromagnetic systems. Figure 9: Visualized comparison of SRE between the conventional and proposed registration strategies (representative trials) (**A**,**B**). there is an increased possibility that cumulative errors will occur in this process. Therefore, the objective of this study is to propose a new protocol that can reduce the registration error by utilizing the face surface tracing method that is currently in widespread clinical use. In the registration result of the hemisphere model, the SRE tended to decrease as the number of points increased, and the accuracy of the proposed registration protocol was excellent for all cases (Figures 4 and 5). Previous studies have attempted to increase the accuracy of registration by increasing the number of points acquired in the patient space, and the highest accuracy was achieved at 300,000 points [18]. Similar studies also showed that when the number of points increases (up to 40,000), the registration error (about 2 mm) decreases rapidly [7]. This is because the larger the number of points, the higher the positional accuracy of the corresponding points in different spaces. The more points that are located within the same area, the smaller the distance between the points in the corresponding space, thus reducing SRE [10]. However, since the acquisition of many points requires a lot of time and processing steps [7], an appropriate number of points must be determined. The first strategy proposed in this work is based on the results of the existing studies mentioned above. It aims to improve accuracy by performing the matching process in a stepwise manner and establishing appropriate thresholds of differences from previous-stage errors. The optimal point cloud extraction strategy in patient space that is proposed in this study showed improved performance compared to the conventional registration method in all cases (hemisphere and plastic facial phantom) (Figures 4, 5, 8 and 9 and Table 1). The proposed registration protocol reduces SRE by generating patient space points that correspond as closely as possible to the medical image data cluster through the first point augmentation strategy. In this process, the target position error is decreased by reducing the residual rotation and translation error.