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In mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete grid. For the case of a finite-dimensional graph (having a finite number of edges and vertices), the discrete Laplace operator is more commonly called the Laplacian matrix.

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rdf:type	yago:WikicatNumericalDifferentialEquations yago:Abstraction100002137 yago:Attribute100024264 yago:Communication100033020 yago:Difference104748836 yago:DifferentialEquation106670521 yago:Equation106669864 yago:MathematicalStatement106732169 yago:Message106598915 yago:Quality104723816 drug yago:Statement106722453 yago:WikicatFiniteDifferences
rdfs:label	Operador laplacià discret (ca) Laplace-Filter (de) Discrete Laplace operator (en) Laplacien discret (fr) Дискретный оператор Лапласа (ru)
rdfs:comment	En matemàtiques, l'operador laplacià discret és la versió discreta de l'operador laplacià continu, definit de manera que té sentit en un graf o una . En el cas d'un graf de dimensions finites (que conté un nombre finit de costats i vèrtexs) l'operador Laplacià discret és comunament anomenat . L'operador laplacià discret apareix en l'estudi de sistemes dinàmics discrets. Algunes aplicacions freqüents són el processament d'imatges, on és conegut com el filtre laplacià, i en aprenentatge automàtic de clustering. (ca) En mathématiques, le laplacien discret est une analogie du laplacien continu adaptée au cas de problèmes discret (graphes, par exemple). Il est notamment employé en analyse numérique, par exemple dans le cadre de la résolution de l'équation de la chaleur par la méthode des différences finies, ou en traitement d'images pour la détection de contours. (fr) Der Laplace-Filter bzw. diskrete Laplace-Operator ist ein Filter zur Kantendetektion,der den Laplace-Operator (Summe der beiden reinen zweiten Ableitungen) approximiert: Unter einer Kante versteht man nun eine Kurve , entlang derer der Gradient des Bildes immer in Normalenrichtung zeigt (das heißt eine Isolinie): Das Vektorfeld ist also im Bereich der Kante quellenfrei.Eine Kante kann sich also nur einstellen, falls folgende Gleichung erfüllt ist: (de) In mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete grid. For the case of a finite-dimensional graph (having a finite number of edges and vertices), the discrete Laplace operator is more commonly called the Laplacian matrix. (en) В математике дискретный оператор Лапласа — аналог непрерывного оператора Лапласа, определяемого как отношения на графе или дискретной сетке. В случае конечномерного графа (имеющего конечное число вершин и рёбер) дискретный оператор Лапласа имеет более общее название: матрица Лапласа. (ru)
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dcterms:subject	Finite differences Operator theory Numerical differential equations Graph theory Feature detection (computer vision) Geometry processing
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Wikipage revision ID	1120577338 (xsd:integer)
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