## 5 Discussion
Then, a new point cloud is generated in patient space by interpolation of the second strategy, in addition to the medical image and the point cloud in the patient space that has been mapped. In this process, the points in patient space that significantly affect residual rotation and translation error are eliminated and a new point cloud in patient space that best corresponds to the one in medical image space is created. Therefore, we believe that additional reductions in SRE and TRE are possible. As discussed by [PERSON] et al. (2020b), the registration accuracy can be improved in some cases by acquiring new point sets in patient space through least squares projection. We believe that the registration performance was improved in the present study for similar reasons. In addition, we expect that further improvements in registration accuracy can be achieved by combining the proper point set in patient space proposed in this study. The limitations of this study are as follows. First, since only a few lesion locations were used for TRE analysis, the accuracy of registration for the locations of various actual lesions could not be conclusively evaluated. In this study, TRE was evaluated using only six lesion locations in the hemisphere model and 15 target lesion locations in the plastic facial phantom. However, it was possible to confirm the superiority of the registration accuracy of the proposed algorithm despite the limited set of lesion locations, and we found that the error rate was reduced by 20% even when the locations of the target lesions were very deep as compared to the existing algorithm. In the future, CT images of actual human faces must be used to evaluate the error rate, given an accurate reflection of human anatomical structure. Second, as the skin tissue of the plastic facial phantom is hard, it was not possible to study the soft tissue of actual human skin and utilize the new technique in actual clinical practice. When obtaining a point cloud in patient space, there are inherent errors in the data due to the flexibility of actual human skin during probe tracing. Future research is required to verify the new registration algorithm, including further experiments on phantoms with skin-like soft tissue and, ultimately, actual clinical validation experiments. In conclusion, in this study, a new surface registration protocol was proposed to improve the accuracy of a surgical navigation system. To extract the optimal point cloud in patient space before registration, we propose a multi-step registration protocol consisting of augmentation of the point cloud and creation of an optimal point cloud in patient space that satisfies the minimum distance from the point cloud in medical image space. Compared with the conventional method of surface registration, the new protocol showed improvements in SRE and TRE of about 30% and 50%, respectively. In addition, a plastic facial phantom was designed, which was used to verify the accuracy and usefulness of the proposed registration method. The point cloud on the facial surface was obtained in the patient space using optical and electromagnetic systems. As a result of registration, TRE was reduced to about 28% and 21% in the optical and electromagnetic systems, respectively, thus showing improved accuracy. The proposed algorithm is expected to be applied to surgical navigation systems in the near future, which could increase the success rate of otolaryngological and neurological surgery. Conceptualization, A.C. and J.-H.M.; methodology, A.C.; validation, S.-S.L. and K.-Y.L. ; data curation, S.C. and H.J. ; writing--original draft preparation, A.C.; revision, T.-H.K. All authors have read and agreed to the published version of the manuscript. This research was supported by the Ministry of Trade, Industry & Energy (MOTIE), Korea Institute for Advancement of Technology (KIAT) through the Encouragement Program for the Industries of the Economic Cooperation Region (P0002272). Not applicable. The authors declare no conflict of interest.