## 4 Discussion
We used 3D landmark points on an orthogonal cross across the calibration plate measured in the scanned model to align the scanner coordination system to the global horizon. Although the calibration and scanning procedures using the calibration plate were easy and convenient, the calibration accuracy may depend on the landmark positions manually measured on the plate. Manual measurement of landmark positions will cause inter- and intra-observer variations, which can decrease calibration accuracy and, eventually, the accuracy of the NHP reproduction. Thus, we used the average of several measurements of the landmark positions. To minimize inaccuracy, the automatic extraction of landmarks using image processing should eventually replace manual measurement. We registered the patient's CT head model with their optically scanned head model in the NHP aligned with the global horizon using the surface registration method of a modified coherent point drift (CPD) algorithm [16; 17]. The coarse registration between the CT model and the scanned NHP model was first performed using a principal component analysis (PCA) [16]. Then, fine registration was performed using the CPD algorithm to obtain a more precise match. The CPD considered the alignment of the two models as a probability density estimation, where one model represented the Gaussian mixture model (GMM) centroids, and the other represented the target of movements [17]. As the CPD uses a probability density estimation, such as a Gaussian mixture model (GMM), this probabilistic method performs better than the general iterative closest point (ICP) algorithm, which is commonly used for surface registration, especially in the presence of noise and outliers [17]. In this study, we automatically reproduced the 3D NHP CT model by applying the resulting transformation from the registrations to the patient's CT head model without manually selecting landmarks on the CT model for registration. Although the 3D CT head model was rotated to the NHP model semi-automatically by applying a pose from orthography and scaling with iterations (POSIT) algorithm [9], the method required time and labor to accurately extract the positions of the landmarks in the 3D CT head model and 2D image. Moreover, in the present study, there will be no intra- or inter-observer variation in accuracy of the NHP reproduction because NHP reproduction is performed automatically using the modified CPD registration. However, the positive and negative definite deviations for the patient's face were higher than those for the mannequin phantom when using the modified CPD registration. The registration error increased as human skin was more deformable. Nonetheless, the registration errors for most of the patient's face surface were lower than one millimeter. The accuracy of the developed method for recording and reproducing the NHP model was \(-0.05\)\(\pm\)\(0.13^{\circ}\), \(0.08\)\(\pm\)\(0.22^{\circ}\), and \(-0.05\)\(\pm\)\(0.18^{\circ}\) in the roll, pitch, and yaw directions, respectively. This accuracy was similar to those previously shown using the POSIT method: \(-0.04\)\(\pm\)\(0.15^{\circ}\), \(-0.17\)\(\pm\)\(0.50^{\circ}\) and \(-0.02\)\(\pm\)\(0.37^{\circ}\) in the roll, pitch, and yaw directions, respectively [9]. The angular deviations using the stereophotogrammetry method were \(0.2\)\(\pm\)\(0.0778^{\circ}\), \(0.2\)\(\pm\)\(0.1042^{\circ}\), and \(0.2\)\(\pm\)\(0.0780^{\circ}\) in the roll, pitch, and yaw directions, respectively [13]. Therefore, the accuracy and range of the present method is similar to those of previous studies using other scanning methods or photographs. Since the difference was less than \(2^{\circ}\), our results were clinically acceptable and even the worst case was satisfactory [5]. However, the 3D images cannot be obtained by the structured light scanner system, and the accuracy of this system can be lowered when the scanning field is too bright, as it is sensitive to illumination of the scanning field.