# An Efficient Automatic Midsagittal Plane Extraction in Brain MRI
## 1 Introduction
In this article, we have combined the advantages of both aforementioned techniques (to some extent) and developed a new principal component analysis (PCA) and symmetric feature-based approach to automatically compute and reorient the MSP in T\({}_{1}\)-weighted MRIs. In fact, the pathological disorder and variations, such as stroke, brain tumor, bleedings, and brain injury, only alter the local intensities and symmetries of brain MRIs. They do not affect the overall shape topological properties of the 3-D head. Furthermore, when the head volume demonstrates a low signal-to-noise ratio (SNR) and significant artifacts, the segmentation of external surfaces is easier as compared to that of internal structures. Therefore, by considering all these observations and assuming that the head is an ellipsoid-like 3-D solid object, a PCA-based algorithm is designed for MSP extraction. PCA is a fundamental and prevailing statistical technique also known as Hotelling transform substantially used in digital image processing for data dimension reduction [34], feature pattern recognition [35], quality control [36], data decorrelation [37], data compression [38], and segmentation [39]. It is also acknowledged as a low-level digital image processing tool for tasks such as the orientation assessment and alignment of particular shape objects [40; 41]. In this paper, PCA has been used for determining the rotation angle (yaw angle) of the bilateral symmetric axis of the brain. The parameters of MSP (yaw angle, roll angle, and offset) are estimated in two steps. In the first step, a coarse value of yaw angle has been estimated using PCA. The angle value is further refined using a cross-correlation method. After thresholding and elliptical area extraction, PCA is used to achieve a set of parallel lines (principal axes) from the selected 2-D slices of brain MRIs. In the second step, the roll angle and the plane offset (a perpendicular distance of MSP from the origin) have been computed by fitting a plane to these parallel lines using orthogonal regression [42]. Initial slices in brain MRIs, where no or very small brain is present (in size), show ambiguous symmetry features as compared to the slices near the center of the brain. Therefore, selected slices have been used for MSP extraction and automatically discarded the ambiguous slices based on semi-axes (major and minor of the ellipse). Similar to the work by [PERSON] [18] who used a weighted mean due to biasing in mean by the initial slices as compared to the superior slices, the removal of ambiguous slices of brain MRIs makes this technique to perform robustly and efficiently. Finally, an affine transformation has been applied to rotate the 3-D head volume to realign (recenter) within the required coordinate system (scanner coordinate system). The proposed technique is insensitive to pathological asymmetries, acquisition noises, and bias fields. The rest of the paper is categorized as follows: Section 2 describes the methodology of MSP extraction algorithm. Implementation of the algorithm, the description of datasets used for evaluation, and results are reported in Section 3. Section 4 discusses some limitations of the developed algorithm and concludes the proposed technique.