## 2 Materials and Methods
### Immediate Calibration of the Scanner Coordinate System Using a Calibration Plate  
We developed a calibration plate (80 \(\times\) 80 mm in size) with four ceramic balls placed on an orthogonal cross using LEGO blocks (LEGO, LEGO, Billund, Denmark) in order to align the 3D optical scanner coordinate system with the CT coordinate system (Figure 1b). When the face of a patient was optically scanned, the coordinate system of the scanned model was commonly determined according to the arbitrarily positioned 3D optical scanner coordinate system. On the other hand, the CT scanner was typically positioned in the global coordinate system. Thus, we aligned the 3D optical scanner coordinate system with the global horizon by installing the calibration plate parallel with the global horizon. Then, the 3D optical scanner and CT coordinate systems coincided based on the global coordinate system. As a result, the calibration procedure was performed easily and immediately using the calibration plate.  
To align the 3D optical scanner coordinate system with the global horizon, we used the four ceramic balls on the scanned model of the calibration plate as landmarks for setting the coordinate axes (the bottom, up, left, and right points on the orthogonal cross) (Figure 1b). The coordinate system (\(\mathbf{P_{C}}\)) of the calibration plate model was determined based on the 3D positions of the four landmarks extracted manually. The x-axis was defined from the left point to the right point, and y-axis from the bottom to the top. The z-axis was determined by calculating the cross product of the unit vectors for the two axes (Figure 1b). The scanner coordinate system (\(\mathbf{P_{S}}\)) was aligned with the global horizon by orienting (\(\mathbf{P_{G}}\)) it to the determined coordinate system of the calibration plate model that was already oriented in the global horizon (Equation (1)) (Figure 1c,d). Then, the coordinate system of the 3D scanned patient model could also be aligned with the global horizon by applying the same  
Figure 1: The calibration plate was attached to the wall parallel with the global horizon using a digital spirit level (**a**). The coordinate system of the calibration plate model was determined by the positions of four ceramic balls (indicated by the dashed circles) on the orthogonal cross of the calibration plate (**b**). The scanned model was positioned arbitrarily in the scanner coordinate system before calibration (**c**). The scanner coordinate system was aligned with the coordinate system of the calibration plate that was already oriented in the global horizon after calibration (**d**).  
orientation, as both the calibration plate and the patient were scanned (\(\mathbf{m_{s0}}\)) by the same scanner under the same conditions (Equations (2) and (3)). As a result, we could acquire the 3D scanned patient head model in the NHP aligned with the global horizon (\(\mathbf{m_{s1}}\)) by applying the resulting orientation to the patient model.  
\[\mathbf{P_{C}}=\mathbf{P_{G}}\mathbf{P_{S}} \tag{1}\]  
\[\mathbf{m_{s1}}=\mathbf{P_{G}}\mathbf{m_{s0}} \tag{2}\]  
\[\mathbf{m_{s1}}=\mathbf{P_{C}}\mathbf{P_{S}}^{-1}\mathbf{m_{s0}} \tag{3}\]  
where \(\mathbf{P_{C}}\) is the calibration plate coordinate system, \(\mathbf{P_{S}}\), the scanner coordinate system, \(\mathbf{P_{G}}\), the rotation of the scanner, \(\mathbf{m_{s0}}\), the 3D scanned patient head model and \(\mathbf{m_{s1}}\), the 3D scanned patient head model oriented in NHP.