# Assessment of Cranial Deformation Indices by Automatic Smartphone-Based Photogrammetric Modelling
## 2 Materials and Methods
### PhotoMeDAS Modelling  
The coded cap was fixed to the dummy's head with glue in order to prevent the labels from being accidentally moved. Fifty-four 3D models were created after taking the corresponding fifty-four recordings on different days and at various intervals around the dummy's head with the PhotoMeDAS application using an Android smartphone with a  
Figure 1: Dummy with the coded cap on. The local reference system (XYZ axes) is displayed in yellow. good processor speed. To show the 3D models in the web browser and be able to interact with them, the 3D Heritage Online Presenter (3 DHOP) JavaScript library has been used [14]. The 3 DHOP package uses the multiresolution model format to send different resolutions to clients, i.e., web browsers, depending on their visualisation needs, reducing the data loading time; 3 DHOP also has a fast configuration and useful final user tools [15]. The 54 models can be seen superimposed at [[https://photomedas-dev.tk/pm/show_mounted_model_files_from_url/7e8a6954-c91c-4057-83a4-2](https://photomedas-dev.tk/pm/show_mounted_model_files_from_url/7e8a6954-c91c-4057-83a4-2) ba8843d2d88/]([https://photomedas-dev.tk/pm/show_mounted_model_files_from_url/7e8a6954-c91c-4057-83a4-2](https://photomedas-dev.tk/pm/show_mounted_model_files_from_url/7e8a6954-c91c-4057-83a4-2) ba8843d2d88/) (accessed on 9 November 2022). In the web browser, the user can zoom, rotate, show, and hide 3D models and use the section tool to see and measure the variations between the 3D models (Figure 2). In particular, as can be seen in the zoomed-in view in Figure 2d, where the surfaces of the 54 models are displayed, there is a maximum separation of 1.8 mm between models, which can be understood as the upper limit to the current measurement dispersion. For each 3D model, the coordinates of 536 points (corners of the coded stickers of the cap) were determined and used to compute the following anthropometric parameters and cranial deformation indices, which are common in paediatric diagnostics [16; 17] and whose numerical values are shown in the PhotoMeDAS report. Figures 3 and 4 depict the measured values from which the parameters and indices in Table 1 were computed. Figure 2: Visualisation of the PhotoMeDAS 3D models. (**a**) Fifty-four superimposed models, where it is possible to zoom, rotate, measure, create sections, show/hide content, and set the transparency of each model. (**b**) XY-plane section. (**c**) XZ-plane section. (**d**) Details of a section showing the maximum measured length among 3D models. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter or Index** & **Symbol** & **Formula or Explanation** \\ \hline Cranial perimeter & _CP_ & \\ Pseudo-cranial volume & _CV_ & Volume above the maximum CP \\ Maximum cranial width & \(d\) & \\ Maximum longitudinal distance & \(c\) & \\ \(a\) value & \(a\) & Distance between right-frontal bone and left-occipital bone \\ \(b\) value & \(b\) & Distance between left-frontal bone and right-occipital bone \\ _a_\(f\) value & _a_\(f\) & Frontal part of a \\ _b_\(f\) value & _b_\(f\) & Frontal part of b \\ _a_\(b\) value & _a_\(b\) & Back part of a \\ _b_\(b\) value & _b_\(b\) & Back part of b \\ Asymmetry index & _AI_ & \(AI=a-b\) & (1) \\ Asymmetry index, front & _AI_\(f\) & \(AI_{f}=a_{f}-b_{f}\) & (2) \\ Asymmetry index, back & _AI_\(b\) & \(AI_{b}=a_{b}-b_{b}\) & (3) \\ Oblique Cranial Length Ratio & _OCLR_ & \(OCLR=\frac{a}{b}\times 100\) & (4) \\ Perimeter30 & _Perimeter30_ & _Perimeter30_ = \(arc_{A}-arc_{B}\) & (5) \\ Cephalic index & _CI_ & \(CI=\frac{a}{b}\times 100\) & (6) \\ Towering index & _TI_ & \(TI=\frac{b}{b}\times 100\) & (7) \\ Metopic index & _MI_ & \(MI=\frac{a}{b}\times 100\) & (8) \\ Frontal angle & _FA_ & \\ Global & _Global_ & Mean right hemisphere minus left hemisphere \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Anthropometric parameters and cranial deformation indices. Figure 4: (**Left**): Measurements for computing the metopic index. (**Right**): Measurements for computing the frontal angle.