## 2 Materials and Methods
### Experimental Design and Procedures  
Records of all of the patients of the School of Orthodontics at the University of Naples Federico II and the Section of Orthodontics at Aarhus University were screened to find patients with full-field-of-view CBCT and an FS performed at a maximum of 10 days apart in order to find a total number of 60 subjects, 30 growing subjects (8-17 years old) and 30 non-growing subjects (older than 21 years old). The FSs were carried out in both centers (Naples and Aarhus) in a standard similar setting, which included similar lighting conditions (no light) and a fixed scanner position, with the same type of scanner (3 dMD, Atlanta, GA, USA; Figure 1). The 3 dMD system uses structured light and stereophotogrammetry. The system is composed of three pairs of stereo cameras, two texture cameras, and four geometric cameras with the lenses slightly convergent toward the participant's position. The capture time is 1.5 ms at the highest resolution. The usual acquisition protocol requires firstly the calibration of the system. The patient is positioned approximately 110 cm away from the scanner. Patients are seated and instructed to look straight ahead with their head held in a natural head position (NHP), with their teeth together and eyes opened. The system has algorithms that merge the pictures into one 3D model in.obj extension or \".stl\" extension, which can be imported into software such as Mimics (Mimics v.19 Materialise Interactive Medical Image Control System, Leuven, Belgium) to place landmarks or perform other evaluations, such as angle and distance measurements. The CBCT examinations were conducted using the NewTom 5G machine (NewTom 5G, QR, Verona, Italy) with an 18 \(\times\) 16 cm field of view. The image acquisition parameters included settings of 110 kV and 3-7 mA, an 18 s scanning time, a 3.6 s exposure time, and with patients in a supine position. All CBCT scans were reconstructed with an isotropic voxel dimension of 0.3 mm. The raw data obtained from CBCT scanning were exported in DICOM format and imported into a specific software program (MIMICS 19.0, Materialise, Leuven, Belgium). The threshold level was determined for each CBCT data set individually based on a profile line and the corresponding vertical intersecting lines. With the profile line, it was possible to visualize the profile of the gray values or Hounsfield Units (HUs) along a pre-defined line. Based on the minimal and maximal threshold values, a layer of the relevant structures was defined (i.e., skeletal, soft tissues, and airways) and color-coded. This layer was called a \"mask\". From the masks, the corresponding 3D surfaces could be generated. In Mimics, a new template for a 3D construction of reference planes was created. Using this template, three landmarks (Nasion N, Basion Ba, and Incisive Foramen IF) were identified for constructing the sagittal, coronal, and axial plane in adults and three landmarks (Nasion  
Figure 1: The 3 dMD system. N, Mid-Cribform MCR, and Incisive Foramen IF) were identified for children [27]. All landmarks were identified on the sagittal view of the midsagittal plane to better simulate what was normally performed on lateral cephalograms, and their position was checked on all of the orthogonal planes (Table 1). The first constructed plane was the sagittal plane passing through the three points [27]; next, the transversal plane passing through Na and Ba perpendicular to the sagittal plane was constructed, and finally, the coronal plane passing through Na and perpendicular to the other two planes was constructed. The FSs were superimposed with a best-fit alignment on the CBCT data using the nasal bridge and forehead areas, which are the areas least affected by gravity and facial expression [28]. After this alignment phase, the CBCT scan was hidden, and 8 landmarks were identified on the FS (Table 2). These landmarks were used for the construction of two different reference systems. In the first one, the reference system followed these steps (FS1):