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In statistics, a central tendency is a central or typical value for a probability distribution. It may also be called a center or location of the distribution. Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late 1920s.
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Objects that tensors may map between include vectors and scalars, and even other tensors. There are many types of tensors, including scalars and vectors, dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system.
In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. It is the outer product of direct space and reciprocal space. The concept of phase space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré, and Josiah Willard Gibbs.
High-dimensional data, meaning data that requires more than two or three dimensions to represent, can be difficult to interpret. One approach to simplification is to assume that the data of interest lies within lower-dimensional space. If the data of interest is of low enough dimension, the data can be visualised in the low-dimensional space.
Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset. MDS is used to translate "information about the pairwise 'distances' among a set of objects or individuals" into a configuration of points mapped into an abstract Cartesian space.
Missile defense is a system, weapon, or technology involved in the detection, tracking, interception, and destruction of attacking missiles. Conceived as a defense against nuclear-armed intercontinental ballistic missiles (ICBMs), its application has broadened to include shorter-ranged non-nuclear tactical and theater missiles.
Scale-space theory is a framework for multi-scale signal representation developed by the computer vision, image processing and signal processing communities with complementary motivations from physics and biological vision. It is a formal theory for handling image structures at different scales, by representing an image as a one-parameter family of smoothed images, the scale-space representation, parametrized by the size of the smoothing kernel used for suppressing fine-scale structures. The parameter in this family is referred to as the scale parameter, with the interpretation that image structures of spatial size smaller than about have largely been smoothed away in the scale-space level at scale .
Ron Kimmel is a professor of Computer Science at the Technion Israel Institute of Technology. He holds a D.Sc. degree in electrical engineering (1995) from the Technion, and he was a post-doc at UC Berkeley and Berkeley Labs, and a visiting professor at Stanford University. He has worked in various areas of image and shape analysis in computer vision, image processing, and computer graphics. Kimmel's interest in recent years has been non-rigid shape processing and analysis, medical imaging, computational biometry, deep learning, numerical optimization of problems with a geometric flavor, and applications of metric and differential geometry. Kimmel is an author of two books, an editor of one, and an author of numerous articles. He is the founder of the Geometric Image Processing Lab, and a founder and advisor of several successful image processing and analysis companies.
Roger Newland Shepard is an American cognitive scientist and author of the "universal law of generalization" (1987). He is considered a father of research on spatial relations. He studied mental rotation, and was an inventor of non-metric multidimensional scaling, a method for representing certain kinds of statistical data in a graphical form that can be apprehended by humans. The optical illusion called Shepard tables and the auditory illusion called Shepard tones are named for him.
Function Representation is used in solid modeling, volume modeling and computer graphics. FRep was introduced in "Function representation in geometric modeling: concepts, implementation and applications" as a uniform representation of multidimensional geometric objects (shapes). An object as a point set in multidimensional space is defined by a single continuous real-valued function of point coordinates which is evaluated at the given point by a procedure traversing a tree structure with primitives in the leaves and operations in the nodes of the tree. The points with belong to the object, and the points with are outside of the object. The point set with is called an isosurface.
GMDS may refer to:
The generalized Hough transform (GHT), introduced by Dana H. Ballard in 1981, is the modification of the Hough transform using the principle of template matching. The Hough transform was initially developed to detect analytically defined shapes. In these cases, we have knowledge of the shape and aim to find out its location and orientation in the image. This modification enables the Hough transform to be used to detect an arbitrary object described with its model.
USS Bronstein (DE-189) was a Cannon-class destroyer escort in service with the United States Navy from 1943 to 1945. In 1952, she was sold to Uruguay, where she served as ROU Artigas (DE-2) until being decommissioned and scrapped in 1988.
In mathematics, geometric measure theory (GMT) is the study of geometric properties of sets through measure theory. It allows mathematicians to extend tools from differential geometry to a much larger class of surfaces that are not necessarily smooth.
Sammon mapping or Sammon projection is an algorithm that maps a high-dimensional space to a space of lower dimensionality by trying to preserve the structure of inter-point distances in high-dimensional space in the lower-dimension projection. It is particularly suited for use in exploratory data analysis. The method was proposed by John W. Sammon in 1969. It is considered a non-linear approach as the mapping cannot be represented as a linear combination of the original variables as possible in techniques such as principal component analysis, which also makes it more difficult to use for classification applications.
The following outline is provided as an overview of and topical guide to object recognition:
In algebra, the hyperdeterminant is a generalization of the determinant. Whereas a determinant is a scalar valued function defined on an n × n square matrix, a hyperdeterminant is defined on a multidimensional array of numbers or tensor. Like a determinant, the hyperdeterminant is a homogeneous polynomial with integer coefficients in the components of the tensor. Many other properties of determinants generalize in some way to hyperdeterminants, but unlike a determinant, the hyperdeterminant does not have a simple geometric interpretation in terms of volumes.
Chingis A. Izmailov was a Russian psychophysiologist and psychophysicist, the principal author of the spherical model of color space.
A heat kernel signature (HKS) is a feature descriptor for use in deformable shape analysis and belongs to the group of spectral shape analysis methods. For each point in the shape, HKS defines its feature vector representing the point's local and global geometric properties. Applications include segmentation, classification, structure discovery, shape matching and shape retrieval.
In continuum mechanics, the generalized Lagrangian mean (GLM) is a formalism – developed by D.G. Andrews and M.E. McIntyre – to unambiguously split a motion into a mean part and an oscillatory part. The method gives a mixed Eulerian–Lagrangian description for the flow field, but appointed to fixed Eulerian coordinates.
References
- Bronstein AM, Bronstein MM, Kimmel R (January 2006). "Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching". Proc. Natl. Acad. Sci. U.S.A. 103 (5): 1168–72. doi: 10.1073/pnas.0508601103 . PMC 1360551 . PMID 16432211.
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