# An Efficient Automatic Midsagittal Plane Extraction in Brain MRI
## 3 Results and Discussion
### Evaluation and Comparison on Synthetic Datasets  
The accuracy of the proposed algorithm for extracting MSP is also evaluated by creating a set of 50 symmetrical scans of the real brain MRI from the NFBS database [48]. Each head scan is manually adjusted and perfectly aligned followed by reflecting one half of the head volume about the known MSP to form the other half. The two mirror halves are stitched together to create a symmetrical head scan with known GT MSP. The reason for creating such volumes is that perfectly symmetric head volumes with GT can be manipulated and transformed arbitrarily. In this way, we can avoid typical subjective factors of human visual inspection. Moreover, in reality, no human head scan exhibits perfect digital symmetry [52]. Therefore, GT in real brain MRIs cannot be used directly for MSP algorithm evaluation [18]. \begin{table}
\begin{tabular}{c p{284.5 pt}} \hline \hline
**Datasets** & \multicolumn{1}{c}{**Detail of Images**} \\ \hline NFBS [48] & There are 125 T\({}_{1}\)-weighted MRI scans, 77 females and 48 males in the 21–45 age range (average: 31) with a variety of clinical and subclinical psychiatric symptoms. The size of the individual scan is 256 \(\times\) 256 \(\times\) 192 and each voxel size is 1 \(\times\) 1 \(\times\) 1 mm\({}^{3}\). The first two dimensions in each scan size indicate the individual image size (rows, columns) and the third dimension represents the number of images in the scan. \\ \hline IBSR [49] & Eighteen volumes of T\({}_{1}\)-weighted brain MRI from all age groups from juvenile to adult are available online with ground truth. The size of the individual scan is 256 \(\times\) 256 \(\times\) 128 and each voxel size is 1.5 \(\times\) 1.5 \(\times\) 1.5 mm\({}^{3}\). Most of the scans in this database have low-contrast images. \\ \hline MNI BITE [50] & Real T\({}_{1}\)-weighted brain MRI of 14 patients with brain tumors (gliomas). We have used scans from Group 2 (pre-operative MRIs) and Group 3 (post-resection MRIs). The size of each scan in Group 2 is 394 \(\times\) 466 \(\times\) 378. Group 3 contains scans of different sizes and dimensions. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Datasets used for evaluation. The presented algorithm results have been compared with a state-of-the-art MSP extraction method proposed by [PERSON] et al. [27]. The algorithm is based on maximization of bilateral symmetry using 3-D Sobel edge operator, thresholding, downsampling, and a multiscale scheme. To improve the quantitative analysis of MSP identification, the authors also introduced a new MSP estimation error metric called average \(z\)-distance. The detail of this metric is discussed in the succeeding paragraph. Figure 9: Visual comparison of the proposed algorithm in extracting the symmetric axis (MSP) from real brain MRIs, (**a**) the NFBS database [38], (**b**) images of the same subjects with Gaussian noise, (**c**) the IBSR database [39], (**d**) the MNI BITE database Group 2, and (**e**) the MNI BITE database Group 3 [40]. Metrics: Two metrics are measured to assess how accurately the algorithms detected the MSP. One is the angle difference (in degree) and is defined as the angle between normal vectors of GT MSP and estimated MSP. Mathematically, it can be computed using the inner product as:  
\[\alpha=\cos^{-1}\biggl{(}\frac{<u,v>}{\|u\|\|v\|}\biggr{)}\times\frac{180}{\pi} \tag{31}\]  
where \(\alpha\) is the angular difference, \(u\) is the normal vector of GT MSP, and \(v\) is the normal vector of calculated MSP. When the two planes are parallel, this error metric is not sufficient and may be misleading due to translation between the estimated MSP and GT MSP. This problem is circumvented by [PERSON] et al. (2017) who proposed a new, simple, and fast metric known as average \(z\)-distance or \(z\)-score (in voxels), to measure MSP estimation error as a function of the distance between the two planes.