# 3D U-Net for Skull Stripping in Brain MRI
## 3 Experimental Results and Discussion
### Evaluation Metrics  
For quantitative evaluation of automatically extracted brain with the ground truth, three overlap metrics were computed, i.e., Dice coefficient, sensitivity, and specificity. The adopted metrics evaluate various performance characteristics between the extracted brain by the algorithms and the manual annotation (ground truth) brain segmentation. Sensitivity and specificity were used to measure the rate of classification (or misclassification) of the brain. The compromise between specificity and sensitivity metrics is a Dice coefficient; it assesses the tradeoff between the incorrect and the correct voxel segmentations.Dice coefficient measures the overlap between the ground truth and segmentation results obtained from the algorithm. It can be defined by using the notion of true positive (TP), false positive (FP), and false negative (FN) as:  
\[Dice=\frac{2 TP}{2 TP+FP+FN} \tag{3}\]  
where TP = Pixels correctly classified as a brain in ground truth and by algorithm; FP = Pixels not classified as a brain in ground truth but classified as brain by the algorithm; TN = Pixels not classified as a brain in ground truth and by algorithm; FN = Pixels classified as a brain in ground truth, but not classified as brain by the algorithm.  
Tables 2 and 3 show Dice score for all the 20 test scans for proposed (3D-UNet), BSE, ROBEX and [PERSON]'s method, respectively. The value of Dice coefficient varies from 0 (disjoint or complete disagree) to 1(for complete overlap or agreement).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Block** & **Kernel Size** & **Stride** & **MaxPool** & \begin{tabular}{c} **Activation** \\ **Function** \\ \end{tabular} & \
\begin{tabular}{c} **Batch** \\ **Norm.** \\ \end{tabular} & **Repeat** & **Input** & **Output** &
\begin{tabular}{c} **Number of** \\ **Parameters** \\ \end{tabular} \\ \hline
1 & 3\({}^{3}\) & 1 & No & ReLu & Yes & 2 & 64\({}^{3}\times 48\) & 63.504 \\
2 & 3\({}^{3}\) & 2 & 3\({}^{3}\) & - & No & 1 & 64\({}^{3}\times 48\) & 32\({}^{3}\times 48\) & - \\
3 & 3\({}^{3}\) & 1 & No & ReLu & Yes & 2 & 32\({}^{3}\times 48\) & 32\({}^{3}\times 96\) & 373,248 \\
4 & 3\({}^{3}\) & 2 & 3\({}^{3}\) & - & No & 1 & 32\({}^{3}\times 96\) & 16\({}^{3}\times 96\) & - \\
5 & 3\({}^{3}\) & 1 & No & ReLu & Yes & 2 & 16\({}^{3}\times 96\) & 16\({}^{3}\times 192\) & 1,492,992 \\
6 & 3\({}^{3}\) & 2 & 3\({}^{3}\) & - & No & 1 & 16\({}^{3}\times 192\) & 8\({}^{3}\times 192\) & \\
7 & 3\({}^{3}\) & 1 & No & ReLu & Yes & 2 & 8\({}^{3}\times 192\) & 8\({}^{3}\times 384\) & 5,971,968 \\
8 & 2\({}^{3}\) & 2 & No & ReLu & Yes & 1 & 8\({}^{3}\times 384\) & 16\({}^{3}\times(192+192)\) & 1,179,648 \\
9 & 3\({}^{3}\) & 1 & No & ReLu & Yes & 2 & 14\({}^{3}\times(192+192)\) & 16\({}^{3}\times 192\) & 2,985,984 \\
10 & 2\({}^{3}\) & 2 & No & ReLu & Yes & 1 & 16\({}^{3}\times 192\) & 32\({}^{3}\times(96+96)\) & 294,912 \\
11 & 3\({}^{3}\) & 1 & No & ReLu & Yes & 2 & 32\({}^{3}\times(96+96)\) & 32\({}^{3}\times 96\) & 746,496 \\
12 & 2\({}^{3}\) & 2 & No & ReLu & Yes & 1 & 32\({}^{3}\times 96\) & 64\({}^{3}\times 48\) & 73,728 \\
13 & 3\({}^{3}\) & 1 & No & ReLu & Yes & 2 & 64\({}^{3}\times 48\) & 64\({}^{3}\times 48\) & 186,624 \\
14 & 1\({}^{3}\) & 1 & No & SoftMax & No & 1 & 64\({}^{3}\times 48\) & 64\({}^{3}\times 2\) & 96 \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c c} \hline \hline  & & & & & & & & & \\ \end{tabular}
\end{table}
Table 1: 3D U-Net architecture.  
Sensitivity is also known as TP rate. It measures the proportion or percentage of the TPs that are correctly classified as the brain. Mathematically, it can be written as:  
\[Sensitivity=\frac{TP}{TP+FN} \tag{4}\]  
Specificity is also known as TN rate. It measures the proportion or percentage of the TNs that are correctly classified as non-brain. Mathematically, it can be written as:  
\[Sensitivity=\frac{TN}{TN+FP} \tag{5}\]