# An Efficient Automatic Midsagittal Plane Extraction in Brain MRI
## 1 Introduction
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, [PERSON] [20] utilized Hough transform for straight line identification on each coronal slice and computed the MSP using interpolation. [PERSON] et al. [21] exploited linear snakes to find the control points on IF lines and estimate MSP plane through these lines using orthogonal regression. [PERSON] and [PERSON] [17; 22] and [PERSON] 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. [PERSON] 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. [PERSON] 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 [PERSON] et al. [25]. These methods are computationally intensive due to their iterative nature and optimization scheme. [PERSON] 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 [PERSON] 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\({}^{\circ}\) or unsuccessful skull stripping. Recently, [PERSON] 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].