## 1. Introduction

Segmentation of brain in magnetic resonance images (MRIs) is one of the difficult and crucial steps of clinical diagnostic tools in medical images. The brain is the most complex organ in the human body that can be split into two approximately symmetrical hemispheres using a plane. This plane is known as the midsagittal plane (MSP) [

1]. In brain symmetric/asymmetric analysis, automatic MSP extraction that is independent for symmetrical and asymmetrical brain regions is an essential brain segmentation task [

2]. Enormous research reflects that the symmetrical structure of the brain deteriorates due to psychological and physical ailments in the brain [

3]. Clinical experts use the symmetry of the brain to identify qualitatively asymmetric patterns that signify an ample range of pathologies, such as brain tumors [

4,

5], brain infections [

6], metabolic disorders [

7], brain injury [

8], and perinatal brain lesions [

9]. Similarly, the computer-aided diagnostic and image analysis systems can use the symmetry and asymmetry information as a prior knowledge to embellish the system efficiency in the analysis of altered brain anatomy [

10].

Moreover, the detection of MSP is required in registration [

11] of medical images as the first step for spatial normalization [

12] and anatomical standardization [

13] of the brain images. However, legitimate evaluation of symmetric and asymmetric patterns in brain images is possible only when the symmetry axis or the symmetry plane (MSP) is accurately aligned and appropriately oriented within the coordinate system of the MRI scanner [

14]. This permits the system to adjust the possible misalignment of brain MRIs. A general phenomenon in brain MRI scanning is that many neuroimaging scanners produce tilted and distorted brain images. The tilt of the head is not always detectable, due to many reasons such as the health conditions, immobility of patients, imprecision of the data calibration systems, and the inexperience of the technicians. Consequently, the slices of the brain MRIs are no more alike within the same orientation, at either the axial or coronal level [

15]. Disoriented and misaligned brain MRIs can betray visual inspection and prevalently yield erroneous clinical perception [

16]. In summary, assessment of brain MRIs for any anomaly based on cross-referencing of brain hemispheres (left and right), either by a human expert or computer-based software could be affected by false geometrical representation. Consequently, it is essential to correct the tilt and realign the brain MRIs data before further analysis.

Manual misalignment correction is extremely time-consuming and laborious to perform on a huge scale. It also demands an urbane knowledge of brain anatomy. Therefore, it is neither sufficient nor efficient. Alignment or tilt correction of brain MRIs is tantamount to realigning the MSP with the center of the image matrix or image coordinate system [

14]. If the MSP is computed precisely, the orientation problem of the MRI volume can be resolved. Thus, the tilt of the head volume can be assessed and adjusted. An ideal MSP can be defined as a virtual geometric plane passing through the interhemispheric fissure (IF) [

17], about which the three-dimensional (3-D) anatomical structure of the brain (such as the ventricles, anterior/posterior commissures, corpus callosum, thalamus) exhibits maximum bilateral symmetry [

18].

Previously, several approaches that considered the problem of computing the MSP in brain MRIs and other brain image modalities (Computed Tomography (CT), Positron Emission Tomography (PET), Single Photon Emission Computed Tomography (SPECT)) have been published. These approaches can be divided into two distinct groups, varying in their exclusive interpretation of prescribed MSP: (1) shape-based algorithms that identify the location of cerebral IF using features of the head images to estimate MSP; and (2) content-based algorithms that considered MSP as the plane which maximizes the bilateral symmetry of the brain. A comprehensive survey of all the existing MSP extraction methods can be found in a recent review [

19].

Shape-based algorithms first segment the longitudinal fissure of the brain MRIs and employ it as a landmark for symmetry analysis and MSP extraction. For instance, Brummer [

20] utilized Hough transform for straight line identification on each coronal slice and computed the MSP using interpolation. Guillemaud et al. [

21] exploited linear snakes to find the control points on IF lines and estimate MSP plane through these lines using orthogonal regression. Volkau and Nowinski [

17,

22] and Kuijf et al. [

23] proposed simple and accurate methods based on Kullback and Leibler’s (KL) measure. These approaches are computationally efficient and independent of internal asymmetries. However, they became unstable in the presence of strong mass effect near IF or invisibility of IF, which is common in some imaging protocols (CT, PET or SPECT).

Content-based algorithms, also known as the similarity-based methods, maximize some similarity measure between the two halves (hemispheres) of the 3-D head volume. Ardekani et al. [

24] proposed an iterative local search-based algorithm that uses the cross-correlation between the voxels of either side of the estimated MSP. This method failed on images having asymmetries due to pathological effects. Liu et al. [

18] computed the MSP by extracting the two-dimensional (2-D) symmetry axes on each slice using cross-correlation from an edge image, followed by plane fitting. Another technique based on the similarity between two sides of the head volume using block matching was given by Prima et al. [

25]. These methods are computationally intensive due to their iterative nature and optimization scheme. Ruppert et al. [

26,

27] improved the efficiency of similarity and symmetric-based methods, and developed an algorithm using 3-D Sobel edge operator, downsampling, and a multiscale scheme. Although the algorithm used the sagittal orientation for MSP extraction, it can be applied to other orientations (axial, and coronal) as well. The authors tested the algorithm on limited imaging protocols and it is also sensitive to noise. The MSP extraction technique based on 3-D scale invariant feature transform (SIFT) was formulated by Wu et al. [

28]. The authors determined the MSP by parallel 3-D SIFT matching and voting, followed by least median of square (LMS) regression. The paper also compared the results of the algorithm with three other MSP extraction methods [

16,

27,

29]. The authors reported that the algorithm is sensitive to noise, blur, and asymmetry, greater than a certain threshold. Moreover, the parameter setting of the algorithm is somehow complex. A computationally simple and robust MSP extraction algorithm was presented by [

30] using curve fitting. The method depends on skull stripping in brain images and the authors reported that the algorithm may fail to identify the MSP correctly if the image slices have a rotation angle of greater than 15° or unsuccessful skull stripping.

Recently, Ferrari et al. [

31] devised a new MSP extraction algorithm using a sheetness measure obtained from 3-D phase congruency (PC) responses. The authors reported results on synthetic and real brain MRIs. A comparison study of three MSP extraction algorithms (symmetry-based [

27], phase congruency [

31], and Hessian-based [

32]) is presented in [

33]. In spite of the enormous variety of algorithms published on MSP extraction, there is no unanimity among the researchers about the best algorithm, due to the ambiguous longitudinal fissure lines, low-contrast brain images, mass effect, and absence of intensity standardization. Moreover, MSP extraction becomes more difficult and challenging when the brain MRIs having a pathological disorder [

18,

25].

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 Liu [

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.