## 3 Results  
This study included 40 CBCT scans of patients from whom we analyzed 160 interforaminal mandibular paramedian and 40 mandibular symphyseal cross sections for the 2D morphogeometric analysis. For the 3D morphogeometric analysis, 80 hemimandibles were used. \begin{table}
\begin{tabular}{c c c c} \hline
**ID** & **Abbreviations** & **Name** & **Description** \\ \hline L1 & S & Symphysis & Alveolar ridge at the symphysis level. \\ L2 & M & Menton & Lowest point at the level of the symphysis. \\ L3 & MF & Mental foramen & Anterior margin of the mental foramen. \\ L4 & L & Lingual & Medial point between mental spines at the lingual side. \\ \hline \end{tabular}
\end{table} 
Table 1: Reference landmarks. Figure 2: Three-dimensional landmarks and curves digitized on the interforaminal hemimandibular region. (**a**) Buccal view; (**b**) lingual view. The intra-observer reliability and reproducibility were obtained via the ICC. For 2D and 3D coordinate digitization, a high concordance was shown between the two operators (2D: 0.998 and 3D: 0.999). For the first part of the 2D morphogeometric analysis, the PCA of the cross sections of the mandibular interfacimal region, excluding the symphysis region, identified four principal components (PCs), wherein four PCs explained approximately 84% of the cumulative variance. The shape variations are presented in Figure 3. PC1 explained 54.78% of the total variance, followed by PC2 (17.65%), PC3 (11.77%), and, finally, PC4 (5.71%). In general, all PCs revealed different resorption patterns of the cortical bone that defines the interfacimal mandibular region, in comparison with Procrustes fit. PC1 or elongated drop shape is described as homogeneous bone resorption along the buccal and lingual bone plates of the alveolar process and the basal zone. This resorption pattern was thinner than the Procrustes fit. PC2 or wineskin shape is described as more marked bone resorption of the buccal plate from the suprabasal area, with a reabsorption pattern that resembles a slight protrusion of the buccal basal area. PC3 or pear shape is described as a marked sharpening of the crestal area and widening of the basal zone. PC4 or eggplant shape is described as buccal ridge atrophy and a resorption pattern that resembles a lingual protrusion; in the suprabasal area, a lingual atrophy and buccal protrusion were observed, keeping basal area constant. The second part of the 2D morphogeometric analysis was performed in the cross sections of the symphysis region. In this analysis, four PCs were identified, representing approximately 83% of the cumulative variance. PC1 explained 62.13% of the total variance, followed by PC2 (11.64%), PC3 (9.71%), and PC4 (4.96%). The patterns among the shapes are shown in Figure 4.  
Figure 4: Principal components of the cross-sections of the symphysis region. Light blue line: Procrustes fit, Blue line: PCs. Red area: atrophy; Green area: protrusion. Figure 3: Principal components of the cross-sections of the mandibular interfacimal region. Light blue line: Procrustes fit, blue line: PCs. Red area: atrophy; Green area: protrusion. A parallel line to point 11 was drawn to divide the cross section into a suprabasal and basal zone. PC1 or elongated drop shape is described as a suprabasal atrophy and a wider base. PC2 or ovoid shape is described as an ovoid shape with a slight protrusion in the buccal plate in the suprabasal area. The basal area presented atrophy of the buccal zone and a wider lingual area. PC3 or triangular shape is described as a sharpening of the crestal area of the alveolar process and a wider basal zone with a tendency for lingual protrusion. PC4 or tuber shape is described as a wider crestal area than the Procrustes fit with a lingual protrusion of the suprabasal area, keeping the basal area constant. For 3D morphogeometric analysis, the PCA of the mandibular interfoariminal region identified four PCs, shown in Figure 5, wherein they represent about 83% of the cumulative variance.