Methodological Review: Symmetry and asymmetry analysis and its implications to computer-aided diagnosis: A review of the literature <s> Shape-based methods vs. content-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> BIB001 </s> Methodological Review: Symmetry and asymmetry analysis and its implications to computer-aided diagnosis: A review of the literature <s> Shape-based methods vs. content-based methods <s> An algorithm for identifying symmetry of a 3-D object given by its octree is presented, and the symmetry degree (a measure of object symmetry) is proposed. The algorithm is based on traversals of the octree obtained by the principal axis transform of an input octree. An object can be in an arbitrary position and with arbitrary orientation within the octree space, and a wide range of symmetries represented by groups of proper and improper rotations can be identified. It is shown that the octree data structure supports these operations well, especially for objects whose symmetry types are simpler or equal in complexity with a fourfold rotational symmetry. The operation of the algorithm is illustrated using some synthetic test objects. The results, which are composed of identified symmetry types and the corresponding symmetry degrees, were satisfactory. > <s> BIB002 </s> Methodological Review: Symmetry and asymmetry analysis and its implications to computer-aided diagnosis: A review of the literature <s> Shape-based methods vs. content-based methods <s> There are various applications, both in medical and non-medical image analysis, which require the automatic detection of the line (2D images) or plane (3D) of reflective symmetry of objects. There exist relatively simple methods of finding reflective symmetry when object images are complete (i.e., completely symmetric and perfectly segmented from image “background”). A much harder problem is finding the line or plane of symmetry when the object of interest contains asymmetries, and may not have well defined edges. <s> BIB003 </s> Methodological Review: Symmetry and asymmetry analysis and its implications to computer-aided diagnosis: A review of the literature <s> Shape-based methods vs. content-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> BIB004 </s> Methodological Review: Symmetry and asymmetry analysis and its implications to computer-aided diagnosis: A review of the literature <s> Shape-based methods vs. content-based methods <s> Abstract A rapid algorithm for robust, accurate, and automatic extraction of the midsagittal plane (MSP) of the human cerebrum from normal and pathological neuroimages is proposed. The MSP is defined as a plane formed from the interhemispheric fissure line segments having the dominant orientation. The algorithm extracts the MSP in four steps: (1) determine suitable axial slices for processing, (2) localize the fissure line segments on them, (3) select inliers from the extracted fissure line segments through histogram-based outlier removal, and (4) calculate the equation of the MSP from the selected inliers. The fissure line segments are localized by minimizing the local symmetry index characterizing anatomical properties of images in the vicinity of the interhemispheric fissure. A two-stage angular and distance outlier removal is introduced to handle abnormalities. The algorithm has been validated quantitatively with 125 structural MRI and CT cases from 10 centers on three continents by studying its accuracy; tolerance to rotation, noise, asymmetry, and bias field; sensitivity to parameters; and performance. A statistical relationship between algorithm accuracy and the data's adherence to planarity is also determined. The algorithm extracts the MSP below 6 s on Pentium 4 (2.4 GHz) with the average angular and distance errors of (0.40°; 0.63 mm) for normal and (0.59°; 0.73 mm) for pathological cases. The robustness to noise, asymmetry, rotation, and bias field is achieved by extracting the MSP based on the dominant orientation and local symmetry index. A low computational cost results from applying simple operations capturing intrinsic anatomic features, constraining the searching space to the local vicinity of the interhemispheric fissure, and formulating a noniterative algorithm with a coarse and fine fixed-step searching. In comparison to the existing methods, our algorithm is much faster, performs accurately and robustly for a wide range of diversified data, and is fully automatic and thoroughly validated, which make it suitable for clinical applications. <s> BIB005 </s> Methodological Review: Symmetry and asymmetry analysis and its implications to computer-aided diagnosis: A review of the literature <s> Shape-based methods vs. content-based methods <s> We propose a novel method to automatically compute the symmetry plane and correct the 3D orientation of patient brain images. Many images of the brain are clinically unreadable because of the misalignment of the patient’s head in the scanner. We proposed an algorithm that represents the brain volume as a re-parameterized surface point cloud where each location has been parameterized by its elevation (latitude), azimuth (longitude) and radius. The removal of the interior contents of the brain makes this approach perform robustly in the presence of the brain pathologies e.g. tumor, stroke and bleed. Thus, we decompose the symmetry plane computation problem into a surface matching routine. The search for the best matching surface is implemented in a multi-resolution paradigm so as to decrease computational time considerably. Spatial affine transform then is performed to rotate the 3D brain images and align them within the coordinate system of the scanner. The corrected brain volume is re-sliced such that each planar image represents the brain at the same axial level. <s> BIB006
Shape-based methods focus on using the geometric landmarks or topological features of the head as a cue to discover the orientation of the symmetry plane, while content-based methods utilize internal signal intensities of brain matters to perform the venue. One shaped-based example is to use the inter-hemispheric fissure as a simple landmark to extract the mid-sagittal plane. For example, Brummer proposed a method of using the Hough transform to identify cerebral interhemisphereic fissure BIB001 . Marais extracted the fissure using snakes. Methods using inter-hemispheric fissure enjoy the computational efficiency and robustness against strong internal asymmetries  . These methods, however, are sensitive to the presence of a large mass near the fissure, or invisibility of the fissure in some of the image modalities. Liu et al. BIB006 proposed a method using external surface point cloud as the main features for the hemisphere-wise matching, and the validation of this work is still in the process. Another branch of shape-based methods is to use inertia matrices to describe the dispersion of a given 3D dataset. This approach, also called the principal component analysis (PCA), deems head as a 3D rigid body with three distinctive principal axes that are orthogonal to each other and about which the moments of inertia are minimized. Those axes are used to characterize rigid bodies by representing the spatial distribution of their mass. Minovic et al. hypothesized that ''Any plane of symmetry in a body is orthogonal to a principal axis" BIB002 . Some other authors implemented this idea and presented a method for detecting dominant plane of bilateral symmetry in an image of arbitrary dimension  . These algorithms, however, are only tested on the synthesized images or a small number of images of the head. The major obstacle preventing this algorithm from wide adoption in realistic neuro-applications is its deficiencies in handling incomplete dataset. For instance, when the data is truncated or the field of view includes non-head structures (e.g., neck and shoulder), the assumption that the head is ellipsoid-like 3D object is not met and the technique may produce flawed results. Content-based methods, treating the head as two halves of gray-level volumes that the intensities of one half can be matched to those of the other half through registration. By geometrically aligning one hemisphere to its reflection the symmetry plane is derived. Typically, an optimization scheme is proposed to seek the maximum value of the similarity measure between hemispheres. Methods vary in this regards; the searching process can, either be global BIB004 or local   BIB005 ; the chosen features can be the intensities of the voxels  , edge images BIB004 , or characteristics of the sampled distributions BIB003  .