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Size Function
Size functions are shape descriptors, in a geometrical/topological sense. They are functions from the half-plane x Formal definition In , the size function associated with the[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Connected Component (topology)
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. Connectedness is one of the principal topological properties that are used to distinguish topological spaces. A subset of a topological space X is a if it is a connected space when viewed as a subspace of X. Some related but stronger conditions are path connected, simply connected, and n-connected. Another related notion is ''locally connected'', which neither implies nor follows from connectedness. Formal definition A topological space X is said to be if it is the union of two disjoint non-empty open sets. Otherwise, X is said to be connected. A subset of a topological space is said to be connected if it is connected under its subspace topology. Some authors exclude the empty set (with its unique topology) as a connected space, but this article does not follow that practice. For a topological s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete And Computational Geometry
'' Discrete & Computational Geometry'' is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986 by Jacob E. Goodman and Richard M. Pollack, the journal publishes articles on discrete geometry and computational geometry. Abstracting and indexing The journal is indexed in: * ''Mathematical Reviews'' * ''Zentralblatt MATH'' * ''Science Citation Index'' * ''Current Contents''/Engineering, Computing and Technology Notable articles The articles by Gil Kalai with a proof of a subexponential upper bound on the diameter of a polyhedron and by Samuel Ferguson on the Kepler conjecture, both published in Discrete & Computational geometry, earned their author the Fulkerson Prize The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at e .... References External link ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Size Theory
In mathematics, size theory studies the properties of topological spaces endowed with \mathbb^k-valued functions, with respect to the change of these functions. More formally, the subject of size theory is the study of the natural pseudodistance between size pairs. A survey of size theory can be found in .Silvia Biasotti, Leila De Floriani, Bianca Falcidieno, Patrizio Frosini, Daniela Giorgi, Claudia Landi, Laura Papaleo, Michela Spagnuolo, Describing shapes by geometrical-topological properties of real functions, ACM Computing Surveys, vol. 40 (2008), n. 4, 12:1–12:87. History and applications The beginning of size theory is rooted in the concept of size function, introduced by Frosini.Patrizio Frosini, ''A distance for similarity classes of submanifolds of a Euclidean space'', Bulletin of the Australian Mathematical Society, 42(3):407–416, 1990. Size functions have been initially used as a mathematical tool for shape comparison in computer vision and pattern reco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matching Distance
In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ..., the matching distanceMichele d'Amico, Patrizio Frosini, Claudia Landi, ''Using matching distance in Size Theory: a survey'', International Journal of Imaging Systems and Technology, 16(5):154–161, 2006.Michele d'Amico, Patrizio Frosini, Claudia Landi, ''Natural pseudo-distance and optimal matching between reduced size functions'', Acta Applicandae Mathematicae, 109(2):527-554, 2010. is a metric (mathematics), metric on the space of size functions. The core of the definition of matching distance is the observation that the information contained in a size function can be combinatorially stored in a formal series of lines and points of the plane, called respectively ''size function, cornerlines'' and ''size function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angela Y
Angela may refer to: Places * Angela, Montana * Angela Lake, in Volusia County, Florida * Lake Angela, in Lyon Township, Oakland County, Michigan * Lake Angela, the reservoir impounded by the source dam of the South Yuba River Fiction * Angela (character), in the ''Spawn'' and Marvel universes * Angela (Inheritance), a character in the Inheritance Cycle novels * Angela Martin, a character in ''The Office'' * Angela, a character in the '' Gargoyles'' TV series * Angela, a character in the '' Stranger Things'' Netflix TV Series, portplayed by Elodie Grace Orkin Music * angela (band), from Japan * ''Angela'' (album) by José Feliciano, 1976 * "Angela" (The Lumineers song), 2016 * "Angela" (Jarvis Cocker song), 2009 * "Angela" (Bee Gees song), 1987 * "Angela", a song by John Lennon and Yoko Ono from their album ''Some Time in New York City'' * "Angela", a song by Mötley Crüe from ''Decade of Decadence'' * "Angela", a song by Saïan Supa Crew from the album '' KLR'' * "An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Pseudodistance
In size theory, the natural pseudodistance between two size pairs (M,\varphi:M\to \mathbb)\ , (N,\psi:N\to \mathbb)\ is the value \inf_h \, \varphi-\psi\circ h\, _\infty\ , where h\ varies in the set of all homeomorphisms from the manifold M\ to the manifold N\ and \, \cdot\, _\infty\ is the supremum norm. If M\ and N\ are not homeomorphic, then the natural pseudodistance is defined to be \infty\ . It is usually assumed that M\ , N\ are C^1\ closed manifolds and the measuring functions \varphi,\psi\ are C^1\ . Put another way, the natural pseudodistance measures the infimum of the change of the measuring function induced by the homeomorphisms from M\ to N\ . The concept of natural pseudodistance can be easily extended to size pairs where the measuring function \varphi\ takes values in \mathbb^m\ .Patrizio Frosini, Michele Mulazzani, ''Size homotopy groups for computation of natural size distances'', Bulletin of the Belgian Mathematical Society, 6:455-464, 1999. Whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonincreasing Function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is called ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-decreasing Function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is called ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y\ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hausdorff Space
In topology and related branches of mathematics, a Hausdorff space ( , ), separated space or T2 space is a topological space where, for any two distinct points, there exist neighbourhoods of each which are disjoint from each other. Of the many separation axioms that can be imposed on a topological space, the "Hausdorff condition" (T2) is the most frequently used and discussed. It implies the uniqueness of limits of sequences, nets, and filters. Hausdorff spaces are named after Felix Hausdorff, one of the founders of topology. Hausdorff's original definition of a topological space (in 1914) included the Hausdorff condition as an axiom. Definitions Points x and y in a topological space X can be '' separated by neighbourhoods'' if there exists a neighbourhood U of x and a neighbourhood V of y such that U and V are disjoint (U\cap V=\varnothing). X is a Hausdorff space if any two distinct points in X are separated by neighbourhoods. This condition is the third separation axiom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Locally Connected
In topology and other branches of mathematics, a topological space ''X'' is locally connected if every point admits a neighbourhood basis consisting entirely of open, connected sets. Background Throughout the history of topology, connectedness and compactness have been two of the most widely studied topological properties. Indeed, the study of these properties even among subsets of Euclidean space, and the recognition of their independence from the particular form of the Euclidean metric, played a large role in clarifying the notion of a topological property and thus a topological space. However, whereas the structure of ''compact'' subsets of Euclidean space was understood quite early on via the Heine–Borel theorem, ''connected'' subsets of \R^n (for ''n'' > 1) proved to be much more complicated. Indeed, while any compact Hausdorff space is locally compact, a connected space—and even a connected subset of the Euclidean plane—need not be locally connected (see below). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Vision
Computer vision is an interdisciplinary scientific field that deals with how computers can gain high-level understanding from digital images or videos. From the perspective of engineering, it seeks to understand and automate tasks that the human visual system can do. Computer vision tasks include methods for acquiring, processing, analyzing and understanding digital images, and extraction of high-dimensional data from the real world in order to produce numerical or symbolic information, e.g. in the forms of decisions. Understanding in this context means the transformation of visual images (the input of the retina) into descriptions of the world that make sense to thought processes and can elicit appropriate action. This image understanding can be seen as the disentangling of symbolic information from image data using models constructed with the aid of geometry, physics, statistics, and learning theory. The scientific discipline of computer vision is concerned with the theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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