Topological Skeletons
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Topological Skeletons
In shape analysis, skeleton (or topological skeleton) of a shape is a thin version of that shape that is equidistant to its boundaries. The skeleton usually emphasizes geometrical and topological properties of the shape, such as its connectivity, topology, length, direction, and width. Together with the distance of its points to the shape boundary, the skeleton can also serve as a representation of the shape (they contain all the information necessary to reconstruct the shape). Skeletons have several different mathematical definitions in the technical literature, and there are many different algorithms for computing them. Various different variants of skeleton can also be found, including straight skeletons, morphological skeletons, etc. In the technical literature, the concepts of skeleton and medial axis are used interchangeably by some authors,, Section 11.1.5, p. 650 while some other authors, Section 9.9, p. 382., Section 17.5.2, p. 234. regard them as ...
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Skel
Skel may refer to: * Steffen Skel (born 1972), German luger *Skel Roach (1871–1958), American baseball player and coach * "Skel", a 2023 song by Sigur Rós from ''Átta ''Átta'' () is the eighth studio album by Icelandic post-rock band Sigur Rós, released through Von Dur and BMG Rights Management on 16 June 2023. It is their first studio album in 10 years, following '' Kveikur'' (2013), and is their first si ...'' See also * Skell (other) {{Disambiguation, surname ...
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Pattern Recognition
Pattern recognition is the automated recognition of patterns and regularities in data. It has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning. Pattern recognition has its origins in statistics and engineering; some modern approaches to pattern recognition include the use of machine learning, due to the increased availability of big data and a new abundance of processing power. These activities can be viewed as two facets of the same field of application, and they have undergone substantial development over the past few decades. Pattern recognition systems are commonly trained from labeled "training" data. When no labeled data are available, other algorithms can be used to discover previously unknown patterns. KDD and data mining have a larger focus on unsupervised methods and stronger connection to business use. Pattern recognition focuses more on the s ...
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Quench
In materials science, quenching is the rapid cooling of a workpiece in water, oil, polymer, air, or other fluids to obtain certain material properties. A type of heat treating, quenching prevents undesired low-temperature processes, such as phase transformations, from occurring. It does this by reducing the window of time during which these undesired reactions are both thermodynamically favorable, and kinetically accessible; for instance, quenching can reduce the crystal grain size of both metallic and plastic materials, increasing their hardness. In metallurgy, quenching is most commonly used to harden steel by inducing a martensite transformation, where the steel must be rapidly cooled through its eutectoid point, the temperature at which austenite becomes unstable. In steel alloyed with metals such as nickel and manganese, the eutectoid temperature becomes much lower, but the kinetic barriers to phase transformation remain the same. This allows quenching to start at a lower ...
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Bedford, Massachusetts
Bedford is a town in Middlesex County, Massachusetts, United States. The population of Bedford was 14,383 at the time of the 2020 United States Census. History ''The following compilation comes from Ellen Abrams (1999) based on information from Abram English Brown's ''History of the Town of Bedford'' (1891), as well as other sources such as ''The Bedford Sampler Bicentennial Edition'' containing Daisy Pickman Oakley's articles, Bedford Vital Records, New England Historical and Genealogical Register, Town Directories, and other publications from the Bedford Historical Society.'' The land now within the boundaries of Bedford was first settled by Europeans around 1640. In 1729 it was incorporated from a portion of Concord (about 2/5 of Bedford) and a portion of Billerica (about 3/5 of Bedford). In 1630, John Winthrop and Thomas Dudley of the Massachusetts Bay Company arrived aboard the ''Arabella'' from Yarmouth, England. After a difficult ten-week voyage, they landed on th ...
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Hanscom Air Force Base
Hanscom Air Force Base (AFB) is a United States Air Force base located predominantly within Bedford, Massachusetts, with portions extending into the adjoining towns of Lincoln, Concord and Lexington. The facility is adjacent to Hanscom Field which provides general aviation and charter service. Hanscom AFB is the part of the Air Force Life Cycle Management Center, one of six centers under Air Force Materiel Command (AFMC). The Air Force Life Cycle Management Center is the single center responsible for total life cycle management of Air Force weapon systems and is headquartered at Wright-Patterson AFB, Ohio. The host unit at Hanscom is the 66th Air Base Group (66 ABG) assigned to AFMC. Overview A non-flying base, Hanscom Air Force Base is named after Laurence G. Hanscom (1906–1941), a pilot, aviation enthusiast, and State House reporter who was killed in a plane crash at Saugus, Massachusetts. Hanscom was a reporter for the Boston Globe, Worcester Telegram & Gazette and ...
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Harry Blum (scientist)
Harry Blum (January 30, 1924 – April 19, 1987) was a researcher at the National Institutes of Health, known for his work in 1967 introducing the medial axis and grassfire transform of a shape, and more generally for his work on Shape analysis (digital geometry), shape analysis, topological skeletonization, biological form, and visual perception. Life Blum was originally from New York City, where he was born on January 30, 1924. During World War II, he worked for the Navy in the New York Naval Shipyard. After the war, he became an engineer for the New York City Subway before going to Cornell University, where he graduated in 1950. From 1950 to 1958 he worked for the United States Air Force at the Rome Air Development Center, also earning a master's degree in electrical engineering at Syracuse University in 1958. From 1958 to 1960 he worked for NATO at the SHAPE Technical Centre in the Netherlands, and from 1960 to 1967 he worked for the Air Force Cambridge Research Laboratories, ...
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Discrete Space
In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a , meaning they are '' isolated'' from each other in a certain sense. The discrete topology is the finest topology that can be given on a set. Every subset is open in the discrete topology so that in particular, every singleton subset is an open set in the discrete topology. Definitions Given a set X: A metric space (E,d) is said to be '' uniformly discrete'' if there exists a ' r > 0 such that, for any x,y \in E, one has either x = y or d(x,y) > r. The topology underlying a metric space can be discrete, without the metric being uniformly discrete: for example the usual metric on the set \left\. Properties The underlying uniformity on a discrete metric space is the discrete uniformity, and the underlying topology on a discrete uniform space is the discrete topology. Thus, the different notions of discrete space are compatible with one ...
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Continuum (topology)
In the mathematical field of point-set topology, a continuum (plural: "continua") is a nonempty compact connected metric space, or, less frequently, a compact connected Hausdorff space. Continuum theory is the branch of topology devoted to the study of continua. Definitions * A continuum that contains more than one point is called nondegenerate. * A subset ''A'' of a continuum ''X'' such that ''A'' itself is a continuum is called a subcontinuum of ''X''. A space homeomorphic to a subcontinuum of the Euclidean plane R2 is called a planar continuum. * A continuum ''X'' is homogeneous if for every two points ''x'' and ''y'' in ''X'', there exists a homeomorphism ''h'': ''X'' → ''X'' such that ''h''(''x'') = ''y''. * A Peano continuum is a continuum that is locally connected at each point. * An indecomposable continuum is a continuum that cannot be represented as the union of two proper subcontinua. A continuum ''X'' is hereditarily indecomposable if every subcontinuum of ''X'' is ...
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Plant Morphology
Phytomorphology is the study of the morphology (biology), physical form and external structure of plants.Raven, P. H., R. F. Evert, & S. E. Eichhorn. ''Biology of Plants'', 7th ed., page 9. (New York: W. H. Freeman, 2005). . This is usually considered distinct from plant anatomy, which is the study of the internal Anatomy, structure of plants, especially at the microscopic level. Plant morphology is useful in the visual identification of plants. Recent studies in molecular biology started to investigate the molecular processes involved in determining the conservation and diversification of plant morphologies. In these studies transcriptome conservation patterns were found to mark crucial ontogenetic transitions during the plant life cycle which may result in evolutionary constraints limiting diversification. Scope Plant morphology "represents a study of the development, form, and structure of plants, and, by implication, an attempt to interpret these on the basis of similarit ...
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Protein Folding
Protein folding is the physical process by which a protein chain is translated to its native three-dimensional structure, typically a "folded" conformation by which the protein becomes biologically functional. Via an expeditious and reproducible process, a polypeptide folds into its characteristic three-dimensional structure from a random coil. Each protein exists first as an unfolded polypeptide or random coil after being translated from a sequence of mRNA to a linear chain of amino acids. At this stage the polypeptide lacks any stable (long-lasting) three-dimensional structure (the left hand side of the first figure). As the polypeptide chain is being synthesized by a ribosome, the linear chain begins to fold into its three-dimensional structure. Folding of many proteins begins even during translation of the polypeptide chain. Amino acids interact with each other to produce a well-defined three-dimensional structure, the folded protein (the right hand side of the figure), ...
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Image Compression
Image compression is a type of data compression applied to digital images, to reduce their cost for storage or transmission. Algorithms may take advantage of visual perception and the statistical properties of image data to provide superior results compared with generic data compression methods which are used for other digital data. Lossy and lossless image compression Image compression may be lossy or lossless. Lossless compression is preferred for archival purposes and often for medical imaging, technical drawings, clip art, or comics. Lossy compression methods, especially when used at low bit rates, introduce compression artifacts. Lossy methods are especially suitable for natural images such as photographs in applications where minor (sometimes imperceptible) loss of fidelity is acceptable to achieve a substantial reduction in bit rate. Lossy compression that produces negligible differences may be called visually lossless. Methods for lossy compression: * Transfor ...
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Visual Inspection
Visual inspection is a common method of quality control, data acquisition, and data analysis. Visual Inspection, used in maintenance of facilities, mean inspection of equipment and structures using either or all of raw human senses such as vision, hearing, touch and smell and/or any non-specialized inspection equipment. Inspections requiring Ultrasonic, X-Ray equipment, Infra-red, etc. are not typically regarded as Visual Inspection as these Inspection methodologies require specialized equipment, training and certification. Quality control A study of the visual inspection of small integrated circuits found that the modal duration of eye fixations of trained inspectors was about 200 ms. The most accurate inspectors made the fewest eye fixations and were the fastest. When the same chip was judged more than once by an individual inspector the consistency of judgment was very high whereas the consistency between inspectors was somewhat less. Variation by a factor of six in inspecti ...
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