Methodological Review: Symmetry and asymmetry analysis and its implications to computer-aided diagnosis: A review of the literature <s> Research in symmetry axis/plane detection methods <s> A method for modeling symmetries of the neighborhoods in gray-value images is derived. It is based on the form of the iso-gray-value curves. For every neighborhood a complex number is obtained through a convolution of a complex-valued image with a complex-valued filter. The magnitude of the complex number is the degree of symmetry with respect to the a priori chosen harmonic function pair. The degree of symmetry has a clear definition which is based on the error in the Fourier domain. The argument of the complex number is the angle representing the relative dominance of one of the pair of harmonic functions compared to the other.<<ETX>> <s> BIB001 </s> Methodological Review: Symmetry and asymmetry analysis and its implications to computer-aided diagnosis: A review of the literature <s> Research in symmetry axis/plane detection methods <s> A simple algorithm is presented for finding all the axes of symmetry of symmetric and almost symmetric planar images having nonuniform gray-level (intensity images). The technique, which can also be used in conjunction with planar curves, is based on the identification of the centroids of the given image and other related sets of points, followed by a maximization of a specially defined coefficient of symmetry. Owing to the nature of the required procedures, which are strictly based on the computation of mean values, the method is not particularly affected by the presence of noise and is especially suited for application in conjunction with digitized figures. > <s> BIB002 </s> Methodological Review: Symmetry and asymmetry analysis and its implications to computer-aided diagnosis: A review of the literature <s> Research in symmetry axis/plane detection 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> BIB003 </s> Methodological Review: Symmetry and asymmetry analysis and its implications to computer-aided diagnosis: A review of the literature <s> Research in symmetry axis/plane detection methods <s> Active vision systems, and especially foveated vision systems, depend on efficient attentional mechanisms. We propose that machine visual attention should consist of both high-level, context-dependent components, and low-level, context free components. As a basis for the context-free component, we present an attention operator based on the intuitive notion of symmetry, which generalized many of the existing methods of detecting regions of interest. It is a low-level operator that can be applied successfully without a priori knowledge of the world. The resultingsymmetry edge map can be applied in various low, intermediate-and high- level tasks, such as extraction of interest points, grouping, and object recognition. In particular, we have implemented an algorithm that locates interest points in real time, and can be incorporated in active and purposive vision systems. The results agree with some psychophysical findings concerning symmetry as well as evidence concerning selection of fixation points. We demonstrate the performance of the transform on natural, cluttered images. <s> BIB004
Since symmetry is routinely employed by the neuroradiologists to assist their assessment of brain images, the misalignment of the patient's head in the scanner often leads to false clinical interpretation of the patients' scans. Despite the difficulty in realigning the head at hardware level, a compensational algorithmic (software) plan has fortunately shown promise to make the correction of this disorientation of the head. I will review the existing techniques in this section. In 2D applications, symmetry axis is defined as the axis best separating a planar brain image into two halves. Various approaches for detecting, analyzing, measuring and applying symmetry in image analysis have been suggested BIB004 BIB001 BIB002 . The usual way for determining symmetry axes assumes the object is somewhat elongated so the direction of the axis of least inertia  can be used to define the symmetry axes of a 2D planar shape. This is the axis about which the second moment of a thin sheet of material of the same shape is the smallest. For three dimensional brain images, the symmetry plane is also called mid-sagittal plane (MSP). A vast host of papers investigating ways to resolve the tilt of the head in volumetric brain images can be found in literature where an ideal MSP has been defined as a 3D anatomical structure about which the given volumetric neuro-image presents maximum mirror symmetry BIB003 . Thus if the MSP is precisely uncovered, the orientation of the head can be resolved and the tilt of the head can be detected and corrected. Based on this rationale, we divide the existing algorithms (to identify MSP) into the following dichotomies: (1) shape-based methods vs. content-based methods, and (2) 2D based methods vs. 3D based methods.