## 2 Materials and Methods
### Phantom Experiment  
We used a mannequin phantom to evaluate the accuracy of the developed method. The whole procedure for recording and reproducing the NHP was as followed (Figure 2). The phantom was firmly mounted on a dedicated acrylic stand (Figure 3a). Then, four ceramic ball markers (1 mm diameter) were placed on the four corners of the top side of the acrylic stand base (Figure 3a). The marker positions were used to determine the true coordinate system of the phantom. The stand mounted by the phantom was bolted to a rotation stage with three degrees of freedom for controlling the rotation of the phantom (Figure 3a). Before CT scanning, we separated the rotation stage from the acrylic stand of the phantom. The phantom was arbitrarily positioned in the CT coordinate system during CT scanning.  
The NHP recording procedure used for the phantom was the same as that used for the patients. First, we optically scanned the calibration plate installed parallel to the global horizon to the wall using a 3D scanner (Figure 1a). Then, the rotation stage, with three degrees of freedom, was again bolted to the acrylic stand of the phantom. We placed the rotation stage parallel to the wall and aligned the stage parallel with the global horizon using a digital spirit level. This made the coordinate system of the phantom parallel to the global horizon, and the phantom's posture was determined as the NHP of the phantom. The phantom in the NHP was optically scanned using the 3D scanner with the same conditions described previously (Figure 3b). Then, the coordinate system of the scanned phantom model was aligned with the global horizon using the orientation from the calibration plate. Finally,the NHP rotation of the phantom's CT model was calculated by performing CPD registration between the phantom's CT head model and the optically scanned model.  
Figure 3: A mannequin phantom was mounted on an acrylic stand combined with a rotation stage, and the phantom’s true coordinate system (indicated by the dashed arrow) was determined using ceramic spherical markers (indicated by the circle) placed on the acrylic stand (**a**). The phantom in the NHP was optically scanned using a 3D scanner (**b**). The 3D scanned phantom model shown before calibration (**c**), and the model aligned with the global horizon after calibration (**d**).  
Figure 2: The whole procedure for recording and reproducing the NHP.  
Optical scanning of the phantom was performed 15 times; CT scanning was performed only once and was used to calculate the phantom's NHP in all measurements without loss of generality. The true NHP of the phantom on CT imaging was determined based on the positions of the four ceramic markers placed on the acrylic stand base. The accuracy was calculated as the angle difference (\({}^{\circ}\)) between the true and calculated, as assessed by the developed method, orientations in the roll, pitch, and yaw directions.  
For the evaluation of accuracy, a one-sample t-test was performed to determine whether the orientations obtained by the developed method were statistically different from the true orientations at a significance level of 0.05 (\(p\)-value). The data were statistically analyzed using SPSS (version 24, IBM, Armonk, NY, USA).