Nonlinear dimensionality reductionNonlinear dimensionality reduction, also known as manifold learning, refers to various related techniques that aim to project high-dimensional data onto lower-dimensional latent manifolds, with the goal of either visualizing the data in the low-dimensional space, or learning the mapping (either from the high-dimensional space to the low-dimensional embedding or vice versa) itself. The techniques described below can be understood as generalizations of linear decomposition methods used for dimensionality reduction, such as singular value decomposition and principal component analysis.
Active contour modelActive contour model, also called snakes, is a framework in computer vision introduced by Michael Kass, Andrew Witkin, and Demetri Terzopoulos for delineating an object outline from a possibly 2D . The snakes model is popular in computer vision, and snakes are widely used in applications like object tracking, shape recognition, , edge detection and stereo matching. A snake is an energy minimizing, deformable spline influenced by constraint and image forces that pull it towards object contours and internal forces that resist deformation.
Mean curvature flowIn the field of differential geometry in mathematics, mean curvature flow is an example of a geometric flow of hypersurfaces in a Riemannian manifold (for example, smooth surfaces in 3-dimensional Euclidean space). Intuitively, a family of surfaces evolves under mean curvature flow if the normal component of the velocity of which a point on the surface moves is given by the mean curvature of the surface. For example, a round sphere evolves under mean curvature flow by shrinking inward uniformly (since the mean curvature vector of a sphere points inward).
Edge-preserving smoothingEdge-preserving smoothing or edge-preserving filtering is an technique that smooths away noise or textures while retaining sharp edges. Examples are the median, bilateral, guided, anisotropic diffusion, and Kuwahara filters. In many applications, e.g., medical or satellite imaging, the edges are key features and thus must be preserved sharp and undistorted in smoothing/denoising. Edge-preserving filters are designed to automatically limit the smoothing at “edges” in images measured, e.g., by high gradient magnitudes.
Brodmann area 40Brodmann area 40 (BA40) is part of the parietal cortex in the human brain. The inferior part of BA40 is in the area of the supramarginal gyrus, which lies at the posterior end of the lateral fissure, in the inferior lateral part of the parietal lobe. It is bounded approximately by the intraparietal sulcus, the inferior postcentral sulcus, the posterior subcentral sulcus and the lateral sulcus. It is bounded caudally by the angular area 39 (H), rostrally and dorsally by the caudal postcentral area 2, and ventrally by the subcentral area 43 and the superior temporal area 22 (Brodmann-1909).
Deformation (mathematics)In mathematics, deformation theory is the study of infinitesimal conditions associated with varying a solution P of a problem to slightly different solutions Pε, where ε is a small number, or a vector of small quantities. The infinitesimal conditions are the result of applying the approach of differential calculus to solving a problem with constraints. The name is an analogy to non-rigid structures that deform slightly to accommodate external forces.
Prime manifoldIn topology, a branch of mathematics, a prime manifold is an n-manifold that cannot be expressed as a non-trivial connected sum of two n-manifolds. Non-trivial means that neither of the two is an n-sphere. A similar notion is that of an irreducible n-manifold, which is one in which any embedded (n − 1)-sphere bounds an embedded n-ball. Implicit in this definition is the use of a suitable , such as the category of differentiable manifolds or the category of piecewise-linear manifolds.
Web Map ServiceA Web Map Service (WMS) is a standard protocol developed by the Open Geospatial Consortium in 1999 for serving georeferenced map images over the Internet. These images are typically produced by a map server from data provided by a GIS database. The Open Geospatial Consortium (OGC) became involved in developing standards for web mapping after a paper was published in 1997 by Allan Doyle, outlining a "WWW Mapping Framework".
A-weightingA-weighting is the most commonly used of a family of curves defined in the International standard IEC 61672:2003 and various national standards relating to the measurement of sound pressure level. A-weighting is applied to instrument-measured sound levels in an effort to account for the relative loudness perceived by the human ear, as the ear is less sensitive to low audio frequencies. It is employed by arithmetically adding a table of values, listed by octave or third-octave bands, to the measured sound pressure levels in dB.
Visual variableA visual variable, in cartographic design, graphic design, and data visualization, is an aspect of a graphical object that can visually differentiate it from other objects, and can be controlled during the design process. The concept was first systematized by Jacques Bertin, a French cartographer and graphic designer, and published in his 1967 book, Sémiologie Graphique. Bertin identified a basic set of these variables and provided guidance for their usage; the concept and the set of variables has since been expanded, especially in cartography, where it has become a core principle of education and practice.
