## 1 Introduction  
It is important to acquire the correct head position accurately to improve orthognathic surgery outcomes [1]. To obtain the correct head position, the natural head position (NHP), in which the head is positioned upright with the eyes focused on a distant point at eye level, has been introduced [2, 3]. Previously, intracranial cephalometric landmarks were used as a logical reference for evaluating the orthodontic facial morphology in two-dimensional (2D) cephalometric analyses [4, 5, 6]. Recently, a three-dimensional (3D) NHP reproduction method has been introduced [7]. An important factor for diagnosing and treating orthognathic patients with severe facial asymmetry is the rotation of the patient's 3D skull model to the NHP [1]. However, the 3D skull model cannot be rotated to the NHPusing intracranial landmarks and planes for craniomaxillofacial patients with severe asymmetry [8]. Clinical CT images of patients do not represent the NHP because the patient head is oriented randomly in the CT coordinate system during CT scanning [9]. Therefore, a general CT image does not reflect the patient's NHP in clinical practice [9]. To overcome this limitation of CT imaging for the diagnosis and treatment of orthognathic patients, several studies have been conducted to record 3D NHPs [1; 9; 10; 11; 12; 13; 14].  
In one method, the authors recorded the 3D NHP using an orientation or gyroscope sensor mounted on a personalized bite jig [1; 10; 11]; however, the weight of the sensor caused distortions in the shape of the lips [9; 12]. Since the position of the upper lip significantly affects predictions regarding soft tissue changes during 3D surgical simulations, the shape of the lips should not be deformed in computer-assisted orthognathic surgery [8; 9; 10; 11]. In another method, the CT model was rotated to the 3D NHP using the position of the radiopaque stickers attached to the horizontal and vertical laser lines on the face to avoid changing the shape of the lips [12]. In another method, the 3D NHP of the CT model was reproduced by a pose from orthography and scaling with iterations (POSIT) algorithm using a common 2D digital camera and ceramic markers [9]. The limitation of these studies was the need to attach fiducial markers to the patient's face for NHP recording. As the positions of these fiducial markers were manually extracted in the 3D CT model, the accuracy of the NHP reproduction might have been influenced by the extracted positions of the fiducial markers. Moreover, the POSIT algorithm might fail in planar configuration of marker points on the patient face [15]. In recent methods, the 3D NHP of CT models was recorded without affecting the patient's face and was reproduced using 3D scanned images obtained using a stereophotographic system [13; 14]. The methods based on the stereophotographic system required thecalibration or alignment of the scanner coordinate system with a physical reference using a reference board or a laser level device. However, the calibration procedure for the system was complex and time-consuming, and the system to scan the patient was difficult to install and bulky.  
In the previous studies, the patient's head was optically scanned in the NHP with markers or sensors attached to the patient, or the calibration or alignment of the scanner coordinate system was complex and time-consuming. Therefore, the aim of this paper is to develop a new method to easily record and automatically reproduce the 3D NHP of CT models without soft tissue changes of the patient using a portable 3D scanner based on immediate calibration.