Methodological Review: Symmetry and asymmetry analysis and its implications to computer-aided diagnosis: A review of the literature <s> 2D based methods vs. 3D based methods <s> Simple methods are described using correlation analysis to rotate functional brain images to a standard vertical orientation, identify the antero-posterior centerline, and align multiple images from the same brain level. These methods are completely objective and can easily be automated <s> BIB001 </s> Methodological Review: Symmetry and asymmetry analysis and its implications to computer-aided diagnosis: A review of the literature <s> 2D based methods vs. 3D based methods <s> A technique is presented for automatic detection of the longitudinal fissure in tomographic scans of the brain. The technique utilizes the planar nature of the fissure and is a three-dimensional variant of the Hough transform principle. Algorithmic and computational aspects of the technique are discussed. Results and performance on coronal and transaxial magnetic resonance data show that the algorithm is robust with respect to variations in image contrast in the data and to slight anatomic anomalies. A crucial resolution requirement in the data for accurate parameter estimations is a sufficient number of slices covering the whole brain. The Sobel magnitude edge operator, used for preprocessing, proved adequate for magnetic resonance scans with positive and negative brain/cerebrospinal fluid contrast. <s> BIB002 </s> Methodological Review: Symmetry and asymmetry analysis and its implications to computer-aided diagnosis: A review of the literature <s> 2D based methods vs. 3D based methods <s> This paper focuses on the evaluation of an ideal midsagittal plane (iMSP) extraction algorithm. The algorithm was developed for capturing the iMSP from 3D normal and pathological neural images. The main challenges are the drastic structural asymmetry that often exists in pathological brains, and the sparse, nonisotropic data sampling that is common in clinical practice. A simple edge-based, cross-correlation approach is presented that decomposes the iMSP extraction problem into discovery of symmetry axes from 2D slices, followed by robust estimation of 3D plane parameters. The algorithm’s tolerance to brain asymmetries, input image offsets and image noise is quantitatively measured. It is found that the algorithm can extract the iMSP from input 3D images with (1) large asymmetrical lesions; (2) arbitrary initial yaw and roll angle errors; and (3) low signal-to-noise level. Also, no significant difference is found between the iMSP computed by the algorithm and the midsagittal plane estimated by two trained neuroradiologists. <s> BIB003 </s> Methodological Review: Symmetry and asymmetry analysis and its implications to computer-aided diagnosis: A review of the literature <s> 2D based methods vs. 3D based methods <s> We present a new method to automatically compute, reorient, and recenter the mid-sagittal plane in anatomical and functional three-dimensional (3-D) brain images. This iterative approach is composed of two steps. At first, given an initial guess of the mid-sagittal plane (generally, the central plane of the image grid), the computation of local similarity measures between the two sides of the head allows to identify homologous anatomical structures or functional areas, by way of a block matching procedure. The output is a set of point-to-point correspondences: the centers of homologous blocks. Subsequently, we define the mid-sagittal plane as the one best superposing the points on one side and their counterparts on the other side by reflective symmetry. Practically, the computation of the parameters characterizing the plane is performed by a least trimmed squares estimation. Then, the estimated plane is aligned with the center of the image grid, and the whole process is iterated until convergence. The robust estimation technique we use allows normal or abnormal asymmetrical structures or areas to be treated as outliers, and the plane to be mainly computed from the underlying gross symmetry of the brain. The algorithm is fast and accurate, even for strongly tilted heads, and even in presence of high acquisition noise and bias field, as shown on a large set of synthetic data. The algorithm has also been visually evaluated on a large set of real magnetic resonance (MR) images. We present a few results on isotropic as well as anisotropic anatomical (MR and computed tomography) and functional (single photon emission computed tomography and positron emission tomography) real images, for normal and pathological subjects. <s> BIB004
2D based methods extract 2D lines first from each individual slice and then compute the 3D plane from those lines by using standard interpolation technique. For example, some used Hough transformation to compute the longitudinal fissure at each coronal slice BIB002 ; Liu et al. estimated the 2D mid-sagittal axis for each coronal or axial slice, and then computed a 3D plane from set of these lines BIB003 ; Junck et al. used a cross correlation analysis for the detection of the line of symmetry in a transverse positron emission tomography (PET) or SPECT slice BIB001 . . This figure illustrates the dissymmetry field computation (left, norm of the field) and the application of the ||F||div(F) operator (right) on the realigned image of a real subject (middle). Note that the dissymmetry field is a 3D image. This illustration is adapted from  . Because these methods process head volume slice-by-slice, the global symmetry of the whole brain is not captured. In case when the head is strongly tilted, the structures displayed in the same axial slice do not reside in the same axial level. The midlines computed independently from each axial slice, are likely to be a misrepresentation of the real symmetry axes, therefore the 3D interpolation of those lines leads to meaningless results. 3D based approaches consider the head volume as a whole mass, hence the plane that maximizes the bilateral symmetry is captured. Minoshima extended Junck's method to 3D, and improved its tolerance to pathological asymmetries by applying the stochastic sign change (SSC) criterion as an index of image alignment  . But the results only demonstrated its success in PET image and the performance on MRI and other image modalities remains unknown. Ardekani conducted iterative search on the unit sphere, in order to find the plane with respect to which the image exhibits maximum cross correlation  . In general, the algorithms that are based on local search, enjoy the computational advantage, but are likely to fail in pathological brain images where gross asymmetries happen. Thirion et al. used the ''Demons" algorithm to find the anatomical counterpart via a non-rigid registration method  . However, non-rigid registration will provide aberrant matching when a lesion is present only on one hemisphere. The meaningless correspondences can degrade the LS criterion and its minimization. Prima et al. modified this method and computed local similarity measures between two sides of the brain, using block matching procedure BIB004 . This method generated a robust estimation of MSP other than plain registration based methods. Contrary to the 2D based methods, when the whole 3D volume is taken into account, the overall gross anatomy of the volumetric brain is used. 3D based methods are less sensitive to the initial condition of the head's orientation and variability of the inter-hemispheric fissure. For most existing 3D methods, however, one common drawback is the computational cost due to the optimization scheme when searching over the 3D space for the maximum matching hemispheres. The existing work on the MSP detection is summarized as in Table 1. In terms of computational efficiency, one should be aware of if the algorithm is realistic to be implemented in the clinical settings. Generally speaking, content-based algorithms are more time consuming than shape-based methods. Said that, most algorithms do not seem pose a significant threat to be implemented in realistic settings. In addition, a number of techniques can be used to facilitate the computation, for instance, down-sample the volumetric data or employ the multi-scale scheme.