# Automatic Segmentation of Mandible from Conventional Methods to Deep Learning--A Review
## 3 Results
### Methodology
#### 3.4.1. SSM-Based, ASM-Based and AAM-Based Methods  
Statistical shape model-based (SSM-based) segmentation algorithms take advantage of the prior shape information to extract the structures of the objects. A dataset of object shapes is needed for training in this technique. Procrustes alignment is applied to align the landmark point set of the objects, which is placed at key features and/or along the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Metric** & **Abbreviation** & **Definition** \\ \hline \multicolumn{3}{c}{Overlap-based metrics, reported in percents (\%)} \\ \hline Dice similarity index & Dice & \(Dice=\frac{2|Y_{r}\cap Y_{r}|}{|Y_{r}|+|Y_{p}|}=\frac{2 TP}{2 TP+FP+FN}\) \\ Sensitivity & Sen & \(Sen=\frac{|Y_{r}\cap Y_{r}|}{|Y_{r}|}=\frac{TP}{TP+FN}\) \\ Recall & Rec & \(Recall=Sen\) \\ Positive Predictive Value & PVV & \(PVV=\frac{|Y_{r}\cap Y_{r}|}{|Y_{r}|}=\frac{TP}{TP+FP}\) \\ Jaccard similarity coefficient & Jac & \(Jac=\frac{|Y_{r}\cap Y_{r}|}{|Y_{r}\cap Y_{r}|}=\frac{TP}{TP+FP+FN}\) \\ Intersection over union & IoU & IoU = Jac \\ Specificity & Spe & \(Specificity=\frac{|(1-Y_{r})\cap(1-Y_{r})|}{|Y_{r}|}=\frac{TN}{TN+FP}\) \\ False positive volume fraction & FPVF & \(FPVF=\frac{|Y_{r}-Y_{r}|}{|Y_{r}|}=\frac{FP}{TP+FN}\) \\ False negative volume fraction & FNVF & \(FNVF=\frac{|Y_{r}-Y_{r}|}{|Y_{r}|}=\frac{FN}{TP+FN}\) \\ \hline \multicolumn{3}{c}{Distance-based metrics, reported in millimeters (mm)} \\ \hline Average symmetric surface distance & ASD & \(\text{ASD}(A,B)=\frac{d(A,B)+d(B,A)}{2}\), \\  & & where \(d(A,B)=\frac{1}{N}\sum_{a\in A}\min_{b\in B}\|a-b\|\), \\ Hausdorff distance & HD & \(\text{D}_{\text{HD}}(A,B)=\max(h(A,B),h(B,A))\), \\  & & where \(h(A,B)=\max_{a\in A}\min_{b\in B}\|a-b\|\) \\
95 th-percentile Hausdorff distance & 95 HD & \(95\text{HD}=\max(h^{95\%}(A,B),h^{95\%}(B,A))\), \\  & & where \(h^{95\%}(A,B)=\max_{a\in A}\min_{b\in B^{95\%}}\|a-b\|\) \\ Mean square error & MSE & \(MSE=\frac{1}{n}\sum_{t=1}^{n}\|A_{i}-B_{i}\|^{2}\), \\  & & where \(A_{i}\) is the boundary of the \(i\)-th OAR and \(B_{i}\) is the boundary of the \(i\)-th prediction. \\ Root mean square error & RMSE & \(RMSE=\sqrt{MSE}\) \\ \hline \multicolumn{3}{c}{Volume-based metrics, reported in percents (\%)} \\ \hline Volume overlap error & VOE & \(1-\frac{|Y_{r}\cap Y_{r}|}{|Y_{r}|}\) \\ Volume error & VE & \(VE=\frac{Y_{r}-Y_{r}}{Y_{r}}\) or \(\frac{Y_{r}-Y_{r}}{Y_{r}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance metrics applied to performance measurement of automatic segmentation of the mandible and the corresponding references and mathematical definitions. Note: \(Y_{r}\) indicates the pixels in the reference standard (ground truth), and \(Y_{p}\) is the pixels in the automatic segmentation. \(|.|\) represents the number of voxels. \(\|.\|\) represents the \(L_{2}\) norm. \(a\) and \(b\) are corresponding points on the boundary of \(A\) and \(B\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Methodology Categories** & **Publications** & **Number of Publications** \\ \hline SSM-based & [18; 37; 38; 39] & 4 \\ ASM-based & [40; 41; 42] & 3 \\ AAM-based & [43; 44] & 2 \\ Atlas-based & [45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78; 79; 80; 81; 82; 83; 84; 85; 86; 87; 88; 88; 89; 90; 82; 84; 87; 88; 89; 91; 83; 85; 89; 92; 86; 87; 88; 89; 93; 94; 95; 96; 97; 98; 99; 100; 99; 101; 102; 103; 104; 105; 106] \\ Level & [9,63] & 2 \\ Classical machine learning-based & [19; 36; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 76; 75; 77; 78; 79; 82; 93; 94; 96; 97; 98; 99; 100; 101; 102; 104; 106] \\ Deep learning-based & [5; 24; 32; 77; 78; 79; 100; 101; 102; 103; 104; 106] & 33 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Methodology applied to automatic mandible segmentation in the head and neck region, and the corresponding references. contour of the object shapes [107]. Principal component analysis (PCA) is employed to build a template shape of the objects [108].