## 2 Materials and Methods
### Experimental Design and Procedures
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Landmarks** & **Legend** & **Description** \\ \hline Face scan Point & Legend & Description \\ Endocanthion Left & EN\_L & Endocanthion (EN) is the soft tissue point located at the inner commissure of each eye fissure. \\ Endocanthion Right & EN\_R & Endocanthion (EN) is the soft tissue point located at the inner commissure of each eye fissure. \\ Mid-Endocanthion & MEN & The middle point between the two ENs. \\ Mid-Tragyon & MTR & The middle point between the two TRs. \\ Nasion & N & Soft tissue nasion (N) is the midpoint on the soft tissue contour of the base of the nasal root at the level of the frontonasal suture. \\ Tragyon Left & TR\_L & Tragyon (Tr) is the point located at the upper margin of each tragus. \\ Tragyon Right & TR\_R & Tragyon (Tr) is the point located at the upper margin of each tragus. \\ Menton & M & Soft tissue menton (M) is the most inferior midpoint on the soft tissue contour of the chin located at the level of the 3D cephalometric hard tissue Menton landmark. \\ CBCT Point & Legend & Description \\ Sella & S & Sella is the center of the hypophyseal fossa \\ Sella & S & (Sella turcica). \\ Nasion & N & Nasion is the midpoint of the frontonasal suture. \\ Basin & Ba & Basin is the most anterior point of the great foramen \\  & & (foramen magnum). \\ Cribriform Left & Cr\_L & The deepest point in the cribform plate. \\ Cribriform Right & Cr\_R & The deepest point in the cribform plate. \\ Mid-Cribriform & MCR & The midpoint between the two cribform plates. \\ Incisive Foramen & IF & The anteroposterior and mediolateral center of the incisive foramen as it exits the maxilla viewed from the sagittal and axial views, respectively. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Face scan and CBCT landmark descriptions. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Dahlberg Error** & & & \\ \hline EN\_L & x & y & z \\ EN\_R & 0.101748 & 0.158439 & 0.170183 \\ EN\_R & 0.293203 & 0.104427 & 0.141493 \\ MEN & 0.17231 & 0.101827 & 0.303197 \\ MTR & 0.196255 & 0.124968 & 0.074406 \\ N & 0.066723 & 0.706758 & 0.295421 \\ TR\_L & 0.090969 & 0.107532 & 0.100185 \\ TR\_R & 0.089091 & 0.136929 & 0.098464 \\ M & 0.240336 & 0.296052 & 0.283187 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The Dahlberg error for the facial scan points. 1. Construction of the transverse plane through three points: Tragyon Right (TR_R), Tragyon Left (TR_L), and Mid-Endocanthion (MEN, midpoint between Right and Left Endocanthion). 2. Construction of the coronal plane between Tragyon Right (TR_R) and Tragyon Left (TR_L) and perpendicular to the axial plane. 3. Construction of the sagittal plane perpendicular to the other two planes and passing through MEN. In the second one, the reference system followed the following steps (FS2): 1. Construction of the transverse plane through three points: Tragyon Right (TR_R), Tragyon Left (TR_L), and Mid-Endocanthion (MEN, midpoint between Right and Left Endocanthion). 2. Construction of the sagittal plane perpendicular to the axial plane and passing through MEN and Mid-Tragyon point (MTR, midpoint between TR_R and TR_L). 3. Construction of the coronal plane perpendicular to the other two planes and passing through MEN. The two reference systems of the FSs were built on the same image using the same landmarks. Once the CBCT scan and the FS were aligned and superimposed, the three reference systems were built, one on the CBCT scan and two on the facial scan.