## Materials and Methods
### 3D Virtual Reconstruction: Model Building  
The 3D bone model reconstruction was carried out using the Mimics Innovation Suite by Materialise (Materialise HQ, Technologielaan 15, 3001 Leuven, Belgium). Patients' CT scans are mandatory to perform a 3D reconstruction: indeed, results accuracy mostly relies on how the CT is carried out. Artefacts can compromise the quality of the 3D reconstruction. It is advisable to check that all CT slices are in order and sequential, and show a correct orientation (right-anterior-back) so that the 3D image can be designed correctly with respect to the reference system. The software Mimics converts the clinical images according to specific instructions regarding the orientation of the individual slices, and displays the CT from different levels (as shown in Figure S4 in Supplementary Material). To obtain a usable 3D model, it is necessary to segment images according to the most common methods of image discretization. Digital filters are applied to enhance the quality of the images by performing high degree noise reduction, with the final goal of making the model the most identical possible to the anatomy of the patients. Binomial blur filters are traditionally used to remove noise from images, by attenuating high spatial frequencies. A curvature flow filter performs an edge-preserving smoothing on the images. The discrete Gaussian filter computes the convolution of the image with a Gaussian kernel. It is used to smooth and reduce the image detail, preserving the edges for the low variance. Gradient magnitude is mainly used to help in the determination of object contours and separation of homogenous regions. The mena filter is commonly used for simple image noise reduction. The median filter is useful to reduce speckle noise and salt and pepper noise [45]. It is necessary to define a mask, which is created by a digitization process that allows to convert tissue analogic signals so that they can be processed with numerical calculation devices, by considering \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Cases**} & **Radiological Equipment** & \multirow{2}{*}{**Manufacturer**} & **FOW Diameter** & **Pixel Size** & **Slice** & **Exposure** \\  & & & **(mm)** & **(mm)** & **Thickness** & **Parameters** \\ \hline \multirow{2}{*}{Case 1} & \multirow{2}{*}{CBCT} & Imaging Science Int. & \multirow{2}{*}{96} & \multirow{2}{*}{0.2} & \multirow{2}{*}{120 kV, 5 mA} \\  & & 1 CAT & & & & \\ \multirow{2}{*}{Case 2} & \multirow{2}{*}{CBCT} & Imaging Science Int. & \multirow{2}{*}{85} & \multirow{2}{*}{0.4} & \multirow{2}{*}{0.4} & \multirow{2}{*}{120 kV, 5 mA} \\  & & ICAT & & & & \\ \multirow{2}{*}{Case 3} & \multirow{2}{*}{CBCT} & de Gotzen Actoon & \multirow{2}{*}{104} & \multirow{2}{*}{0.2} & \multirow{2}{*}{0.2} & \multirow{2}{*}{85 kV, 8 mA} \\  & & Group & & & & \\ \multirow{2}{*}{Case 4} & \multirow{2}{*}{CBCT} & Sirona & \multirow{2}{*}{82} & \multirow{2}{*}{0.16} & \multirow{2}{*}{0.16} & \multirow{2}{*}{85 kV, 7 mA} \\  & & & & & & \\ \multirow{2}{*}{Case 5} & \multirow{2}{*}{CT} & Toshiba & \multirow{2}{*}{256} & \multirow{2}{*}{0.5} & \multirow{2}{*}{2} & \multirow{2}{*}{120 kV, 50 mA} \\  & & & & & & \\ \multirow{2}{*}{Case 6} & \multirow{2}{*}{CT} & GE & \multirow{2}{*}{148} & \multirow{2}{*}{0.3} & \multirow{2}{*}{0.625} & \multirow{2}{*}{100 kV, 100 mA} \\ \hline \end{tabular}
\end{table} 
Table 1: Type of radiological equipment, manufacturer, and exposure parameters used for image acquisition of the six analyzed cases. the variation of the gray scale. A range of values is defined to represent a particular tissue: In our case, the adult compact bone range is around 500 to 2000 Hounsfield unit (HU) [46], while SmartBone(r) is in the range 100 to 400 HU. The gray value, defined in HU, precisely defines the tissue in each point. The HU is a value attributed to a voxel, which coincides to the average attenuation of the corresponding tissue volume. The choice of this range allows optimal tissue discrimination within the CT [47; 48].