# An Efficient Automatic Midsagittal Plane Extraction in Brain MRI
## 3 Results and Discussion
### Evaluation and Comparison on Synthetic Datasets
This distance can be measured ([PERSON] et al., 2017; [PERSON] et al., 2017) by computing \(z\) coordinate from the plane equations, for the GT plane and the estimated plane, using each \"\(x\)\" and \"\(y\)\". It can be written as:  
\[z\;distance=\frac{\sum\limits_{(x,y)}\left(|z_{coord.}(GT)-z_{coord.}(Est.)| \right)}{dim(x)\times dim(y)} \tag{32}\]  
where \(dim\) is the image dimension along \(x\) and \(y\) axes, and \(GT\), and \(Est.\) stands for ground truth and estimated MSPs, respectively. Both the algorithms (the proposed algorithm and [PERSON] et al. algorithm) are evaluated for all the slices in the perfectly symmetrical head volume by determining their average \(z\)-distance with respect to each corresponding GT MSP. The mean \(z\)-scores obtained for both algorithms on 50 perfectly symmetric datasets are shown in Table 2.  
The plot of average \(z\)-distance for the individual scan is illustrated in Figure 10. [PERSON] et al. approach was unable to truly estimate the MSP in some scans and showed substantially large values for average \(z\)-distances, as indicated by the black square in Figure 10. These scans were not considered when measuring the mean \(z\)-score and the mean of angle differences, since they would synthetically intensify the \(z\)-score and standard deviation results of [PERSON] et al. algorithm. The values of \(z\)-score are almost similar as they reported in their paper, except for some scans having a rotation angle (either yaw or roll) of greater than \(5^{\circ}\), as displayed in Figure 11. The situations at which their algorithm relied, i.e., smoothing, Sobel operator followed by thresholding of 5% brightest voxels, and symmetric score, are not satisfied in the presence of noise, image artifacts, and intensity inhomogeneity. This causes the offsets of plane underestimated. From Table 2, it is evident that [PERSON] et al. algorithm accurately estimated the orientation of the MSP but failed to correctly calculate the offset of MSP. On the other hand, the proposed algorithm results are more consistent and accurate in orientations as well as in offsets. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & **[PERSON] et al. Algorithm** & & & **Proposed Algorithm** & \\ \cline{2-7}  & \(z\) **Score** & **Angle** & **Time (s)** & **\(z\)-Score** & **Angle** & **Time (s)** \\  & **(Voxels)** & **Difference (\({}^{\circ}\))** & **Time (s)** & **(Voxels)** & **Difference (\({}^{\circ}\))** & **Time (s)** \\ \hline Mean & 1.246 & 0.10 & 35.02 & 0.336 & 0.06 & 1.04 \\ Std. & 2.041 & 0.22 & 1.12 & 0.324 & 0.21 & 0.02 \\ Median & 0.50 & 0.00 & 34.86 & 0.250 & 0.00 & 1.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Quantitative results comparison for perfectly symmetric datasets. Figure 11: Visual comparison of the proposed algorithm with [PERSON] et al. algorithm for extracting the symmetric axis (MSP) from perfectly symmetric datasets: (**a**) input slice, (**b**) ground-truth slice, (**c**) [PERSON] et al. [27] algorithm results, and (**d**) proposed algorithm results. Figure 10: Average \(z\)-distances of perfectly symmetric datasets (\(z\)-distances indicated by the square are not included for mean \(z\)-score calculation). To precisely inspect the accuracy of the proposed algorithm, many illustrative slices orthogonal to the estimated MSP are displayed in Figure 11. The lines in different colors (magenta, blue and green) are the intersecting lines between the extracted MSP and the respective orthogonal slice. The first column represents the input images and the second column shows the input images with the GT MSP intersection line (magenta color line). Similarly, third and fourth columns contain the images of [PERSON] et al. and proposed algorithm results, respectively. Visual comparison in Figure 11 also reveals that the proposed algorithm outperformed [PERSON] et al. algorithm in terms of accuracy, both in orientation and offsets. [PERSON] et al.