- Unimodal Thresholding
Image Lena stasjon.jpg thumb 250px Original image Image Lena stasjon edges.png thumb 250px Edge map inverted Image Lena stasjon Otsu.png thumb 250px Thresholded edge map using Otsu s algorithm Image Lena stasjon Rosin.png thumb 250px Thresholded edge map using Rosin s algorithm Most algorithms for Thresholding image processing automatic image threshold selection assume that the intensity histogram is multi modal typically bimodal. However, some types of images are essentially unimodal since a much larger proportion of just one class of pixels e.g. the background is present in the image, and dominates the histogram. In such circumstances many of the standard threshold selection algorithms will fail. However, a few algorithms have been designed to specifically cope with such images. Methods Some examples of unimodal image threshold selection algorithms are T point algorithm the tail of the histogram is fitted by two line segments, and the threshold is selected at their intersection ref cite journal last Coudray first Nicholas coauthors Buessler, Urban title Robust threshold estimation for images with unimodal histograms journal Pattern Recognition Letters year 2010 volume 31 issue 9 pages 1010 1019 ref maximum deviation algorithm a straight line is drawn from the histogram peak to the end of the tail, and the threshold is selected at the point of the histogram furthest from the straight line ref cite journal last Rosin first Paul L. title Unimodal thresholding journal Pattern Recognition year 2001 volume 34 issue 11 pages 2083 2096 ref Rayleigh distribution model algorithm the mode peak is assumed to correspond to noise. The user specifies an allowable proportion of noise from which the threshold is determined using the model ref cite journal last Voorhees first Harry coauthors Poggio title Detecting textons and texture boundaries in natural images journal IEEE International Conference on Computer Vision year 1987 pages 250 258 ref Citations reflist Category Image pro ... more details
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- Function
wiktionary function Function may refer to Diatonic function , a term in music theory Function E 40 song , a 2012 song by American rapper E 40 featuring YG rapper YG , iAmSu & Problem Function biology , explaining why a feature survived selection Function computer science , or subroutine, a portion of code within a larger program, performs a specific task Function engineering , related to the selected property of a system Function language , in linguistics, a way of achieving an aim using language Function mathematics , an abstract entity that associates an input to a corresponding output according to some rule Function model , a structured representation of the functions, activities or processes Function object , or functor or functionoid, a concept of object oriented programming Function Drinks , a beverage company based in Redondo Beach, California. An organised event such as a party or meeting See also Functionalism disambiguation Function hall Functional disambiguation Functionality in polymer chemistry see Structural unit Functor disambiguation bg bs Funkcija vor ca Funci desambiguaci cs Funkce da Funktion de Funktion et Funktsioon es Funci n eo Funkcio eu Funtzio argipena fr Fonction ko id Fungsi it Funzione lt Funkcija lmo Funziun nl Functie ja no Funksjon nn Funksjon pl Funkcja ujednoznacznienie pt Fun o desambigua o ro Func ie dezambiguizare ru simple Function sk Funkcia sl Funkcija razlo itev sr sh Funkcija razvrstavanje sv Funktion olika betydelser th uk zh ... more details
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- S-function
In mathematics, S function may refer to sigmoid function Schur polynomials In physics, it may refer to Action physics action functional mathdab Short pages monitor This long comment was added to the page to prevent it from being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Long comment. Please do not remove the monitor template without removing the comment as well. ... more details
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- T-function
Image VEST Core4 LowLevel.png thumbnail 320px right VEST 4 T function followed by a transposition layer In cryptography , a T function is a bijection bijective mapping that updates every bit of the state computer science state in a way that can be described as math x i x i f x 0, cdots, x i 1 math , or in simple words an update function in which each bit of the state is updated by a linear combination of the same bit and a function of a subset of its less significant bits. If every single less significant bit is included in the update of every bit in the state, such a T function is called triangular . Thanks to their bijectivity no collisions, therefore no entropy loss regardless of the used Boolean function s and regardless of the selection of inputs as long as they all come from one side of the output bit , T functions are now widely used in cryptography to construct block cipher s, stream cipher s, PRNG s and cryptographic hash function hash functions . T functions were first proposed in 2002 by Alexander Klimov A. Klimov and Adi Shamir A. Shamir in their paper A New Class of Invertible Mappings . Ciphers such as TSC 1 , TSC 3 , TSC 4 , ABC stream cipher ABC , Mir 1 and VEST are built with different types of T functions. Because arithmetic operation s such as addition , subtraction and multiplication are also T functions triangular T functions , software efficient word based T functions can be constructed by combining bitwise logic with arithmetic operations. Another important property of T functions based on arithmetic operations is predictability of their period mathematics period , which is highly attractive to cryptographers. Although triangular T functions are naturally vulnerable to guess and determine attacks, well chosen bitwise transposition mathematics transposition ... bit. Subsequent transposition of the output bits and iteration of the T function also do not affect ... and losing the T function bias of depending only on the less significant bits of the state. References ... more details
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- Quasiconvex function
Image Quasiconvex function.png right thumb A quasiconvex function that is not convex. Image Nonquasiconvex function.png right thumb A function that is not quasiconvex the set of points in the domain of the function for which the function values are below the dashed red line is the union of the two red ... density function of the normal distribution is quasiconcave but not concave. In mathematics , a quasiconvex function is a real number real valued function mathematics function defined on an interval ... the highest point is one of the endpoints. The negative of a quasiconvex function is said to be quasiconcave . All convex function s are also quasiconvex, but not all quasiconvex functions are convex, so quasiconvexity is a generalization of convexity. Quasiconvexity extends the notion of unimodal ity for functions with a single real argument. Definition and properties A function math f ... does not give a higher a value of the function than do both of the other points, then f is quasiconvex ... convex function math f x math is to require that each sub levelset math S alpha f x f x leq alpha ... of the function than one of the other points does. A quasiconcave function is a function whose negative is quasiconvex, and a strictly quasiconcave function is a function whose negative is strictly quasiconvex. Equivalently a function math f math is quasiconcave if math f lambda x 1 lambda y geq ... y big math Image Monotonicity example2.png right thumb A quasilinear function is both quasiconvex and quasiconcave. Image Quasi concave function graph.png right thumb The graph of a function that is both concave and quasi convex on the nonnegative real numbers. A strictly quasiconvex function has strictly convex lower contour set s, while a strictly quasiconcave function has strictly convex upper contour set s. A function that is both quasiconvex and quasiconcave is quasilinear . Applications Quasiconvex ... function Lagrangian Lagrange duality dual problems . ref cite book last Di Guglielmo ... more details
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- Omega function
In mathematics, omega function or function may refer to Pearson Cunningham function Lambert W function Wright Omega function Mathematical disambiguation ... more details
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- G-function
Barnes G function , related to the Gamma function Meijer G function , a generalization of the hypergeometric function Siegel G function , a class of functions in transcendence theory mathdab ... more details
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- Sigma function
In mathematics, by sigma function one can mean one of the following The Divisor function sum of divisors function sub a sub n , an arithmetic function Weierstrass sigma function , related to elliptic functions Kronecker s sigma function Rado s sigma function, see busy beaver See also sigmoid function . mathdab de Teilersumme fr Fonction sigma ... more details
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- Function test
Function test or functional test can refer to Thyroid function tests Liver function tests Lung function test Functional testing disambig ... more details
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- Comparison function
wiktionary Comparison function may refer to Nachbin s theorem a theorem in the area of complex analysis Class kappa function a special function used control theory Class kappa ell function a special function used control theory . Disambig ... more details
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- Green function
Green function might refer to Green s function of a differential operator. Deligne Lusztig theory Green function in the representation theory of finite groups of Lie type. Green s function many body theory Green s function in many body theory . disambig ... more details
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- Riemann function
Riemann function may refer to one of the several function mathematics functions named after the mathematician Bernhard Riemann , including Riemann zeta function Thomae s function Riemann theta function . dab fr Fonction de Riemann ... more details
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- Mass function
Mass function may refer to Initial mass function , a function that describes the mass distribution of a population of stars in terms of their initial mass Probability mass function , a function that gives the probability that a discrete random variable is exactly equal to some value disambig ... more details
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- ? function
In mathematics, the function named for the Greek letter or Xi may refer to Riemann function , a variant of the Riemann zeta function with a simpler functional equation Harish Chandra s function , a special spherical function on a semisimple Lie group Mathematical disambiguation ... more details
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- Zeta function
In mathematics , a zeta function is usually a function mathematics function analogous to the original example the Riemann zeta function math zeta s sum n 1 infty frac 1 n s . math Zeta functions include Airy zeta function , related to the zeros of the Airy function Arithmetic zeta function Artin Mazur zeta function Artin Mazur zeta function of a dynamical system Barnes zeta function Beurling zeta function of Beurling generalized primes Dedekind zeta function Dedekind zeta function of a number field Real analytic Eisenstein series Epstein zeta function Epstein zeta function of a quadratic form. Goss zeta function of a function field Hasse Weil zeta function Hasse Weil zeta function of a variety Hurwitz zeta function Hurwitz zeta function A generalization of the Riemann zeta function Ihara zeta function Ihara zeta function of a graph Igusa zeta function Igusa zeta function Jacobi zeta function This is related to elliptic functions and is not analogous to the Riemann zeta function. L function , a twisted zeta function. Lefschetz zeta function Lefschetz zeta function of a morphism Lerch zeta function Lerch zeta function A generalization of the Riemann zeta function Local zeta function of a characteristic p variety Matsumoto zeta function Minakshisundaram Pleijel zeta function of a Laplacian Motivic zeta function of a motive Mordell Tornheim zeta function of several variables Multiple zeta function p adic zeta function of a p adic number Prime zeta function Like the Riemann zeta function, but only summed over primes. Riemann zeta function The archetypal example. Selberg zeta function Selberg zeta function of a Riemann surface Shimizu L function Shintani zeta function Weierstrass zeta function This is related to elliptic functions and is not analogous to the Riemann zeta function. Witten zeta function of a Lie group Zeta function operator Zeta function of an operator See also Artin conjecture L functions Artin conjecture Birch and Swinnerton Dyer conjecture Riemann hypothesis ... more details
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- Pi function
In mathematics , two different function mathematics functions are known as the pi or Pi function math pi x , math pi function &ndash the prime counting function math Pi x , math Pi function &ndash the Gamma function when offset to coincide with the factorial disambig th ... more details
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- Potential function
The term potential function may refer to A mathematical function mathematics function whose values are a physical potential . The class of functions known as harmonic function s, which are the topic of study in potential theory . The potential function of a potential game . A function used in the potential method of amortized analysis to describe an investment of resources by past operations that can be used by future operations. mathdab ... more details
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- Psi function
Psi function can refer to the Dedekind psi function math psi n math the Chebyshev function math psi x math the polygamma function math psi m z math or its special cases the digamma function math psi z math the trigamma function math psi 1 z math mathdab de Psi Funktion ... more details
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- Dedekind function
In number theory , Dedekind function can refer to any of three functions, all introduced by Richard Dedekind Dedekind eta function Dedekind psi function Dedekind zeta function disambig de Dedekindsche Funktion ... more details
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- Function value
Function value may refer to In mathematics, the value of a function mathematics function when applied to an argument In computer science, a closure computer science closure disambiguation ... more details
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- Influence function
In mathematics , influence function is used to mean either a synonym for a Green s function Influence function statistics , the effect on an estimator of changing one point of the sample. disambig ... more details
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- C-function
In mathematics, c function may refer to Smooth function Harish Chandra s c function in the theory of Lie groups List of C functions for the programming language C mathdab ... more details
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- Partition function
dabconcept Partition function may refer to Partition function number theory Partition function mathematics , which generalizes its use in statistical mechanics and quantum field theory Partition function statistical mechanics Partition function quantum field theory disambig es Funci n de partici n su Fungsi partisi ... more details
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- Tau function
Tau function may refer to Tau function Ramanujan tau function , giving the Fourier coefficients of the Ramanujan modular form. Divisor function , an arithmetic function giving the number of divisors of an integer. tau function representation theory Tau function in the representation theory of affine Lie algebra s and integrable system soliton equations . disambig Long comment to prevent listing on Special Shortpages.......................................................................... more details
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- Function field
Function field may refer to Function field of an algebraic variety Function field scheme theory Algebraic function field Function field sieve Function field analogy mathdab Short pages monitor This long comment was added to the page to prevent it being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Longcomment. Please do not remove the monitor template without removing the comment as well. de Funktionenk rper ... more details
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