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- Centroidal_Voronoi_tessellation abstract "In geometry, a centroidal Voronoi tessellation (CVT) is a special type of Voronoi tessellation or Voronoi diagrams. A Voronoi tessellation is called centroidal when the generating point of each Voronoi cell is also its mean (center of mass). It can be viewed as an optimal partition corresponding to an optimal distribution of generators. A number of algorithms can be used to generate centroidal Voronoi tessellations, including Lloyd's algorithm for K-means clustering.Gersho's conjecture, proven for one and two dimensions, says that \"asymptotically speaking, all cells of the optimal CVT, while forming a tessellation, are congruent to a basic cell which depends on the dimension.\" In two dimensions, the basic cell for the optimal CVT is a regular hexagon.Centroidal Voronoi tessellations are useful in data compression, optimal quadrature, optimal quantization, clustering, and optimal mesh generation. Many patterns seen in nature are closely approximated by a Centroidal Voronoi tessellation. Examples of this include the Giant's Causeway, the cells of the cornea, and the breeding pits of the male tilapia.A weighted centroidal Voronoi diagrams is a CVT in which each centroid is weighted according to a certain function. For example, a grayscale image can be used as a density function to weight the points of a CVT, as a way to create digital stippling.".
- Centroidal_Voronoi_tessellation thumbnail CentroidalVoronoiTessellation1.png?width=300.
- Centroidal_Voronoi_tessellation wikiPageID "14087640".
- Centroidal_Voronoi_tessellation wikiPageLength "3207".
- Centroidal_Voronoi_tessellation wikiPageOutDegree "20".
- Centroidal_Voronoi_tessellation wikiPageRevisionID "705523126".
- Centroidal_Voronoi_tessellation wikiPageWikiLink Category:Diagrams.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Category:Discrete_geometry.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Category:Geometric_algorithms.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Cluster_analysis.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Congruence_(geometry).
- Centroidal_Voronoi_tessellation wikiPageWikiLink Cornea.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Data_compression.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Geometry.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Giants_Causeway.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Grayscale.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Hexagon.
- Centroidal_Voronoi_tessellation wikiPageWikiLink K-means_clustering.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Lloyds_algorithm.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Numerical_integration.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Patterns_in_nature.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Quantization_(signal_processing).
- Centroidal_Voronoi_tessellation wikiPageWikiLink Stippling.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Tessellation.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Tilapia.
- Centroidal_Voronoi_tessellation wikiPageWikiLink Voronoi_diagram.
- Centroidal_Voronoi_tessellation wikiPageWikiLinkText "Centroidal Voronoi tessellation".
- Centroidal_Voronoi_tessellation wikiPageWikiLinkText "centroidal Voronoi tessellation".
- Centroidal_Voronoi_tessellation align "center".
- Centroidal_Voronoi_tessellation direction "horizontal".
- Centroidal_Voronoi_tessellation footerAlign "right".
- Centroidal_Voronoi_tessellation header "Three centroidal Voronoi tessellations of five points in a square".
- Centroidal_Voronoi_tessellation headerAlign "center".
- Centroidal_Voronoi_tessellation image "CentroidalVoronoiTessellation1.png".
- Centroidal_Voronoi_tessellation image "CentroidalVoronoiTessellation2.png".
- Centroidal_Voronoi_tessellation image "CentroidalVoronoiTessellation3.png".
- Centroidal_Voronoi_tessellation width "200".
- Centroidal_Voronoi_tessellation wikiPageUsesTemplate Template:Multiple_image.
- Centroidal_Voronoi_tessellation wikiPageUsesTemplate Template:Reflist.
- Centroidal_Voronoi_tessellation subject Category:Diagrams.
- Centroidal_Voronoi_tessellation subject Category:Discrete_geometry.
- Centroidal_Voronoi_tessellation subject Category:Geometric_algorithms.
- Centroidal_Voronoi_tessellation hypernym Type.
- Centroidal_Voronoi_tessellation type Algorithm.
- Centroidal_Voronoi_tessellation type Infographic.
- Centroidal_Voronoi_tessellation type Redirect.
- Centroidal_Voronoi_tessellation comment "In geometry, a centroidal Voronoi tessellation (CVT) is a special type of Voronoi tessellation or Voronoi diagrams. A Voronoi tessellation is called centroidal when the generating point of each Voronoi cell is also its mean (center of mass). It can be viewed as an optimal partition corresponding to an optimal distribution of generators.".
- Centroidal_Voronoi_tessellation label "Centroidal Voronoi tessellation".
- Centroidal_Voronoi_tessellation sameAs Q5062961.
- Centroidal_Voronoi_tessellation sameAs m.03ct35t.
- Centroidal_Voronoi_tessellation sameAs Q5062961.
- Centroidal_Voronoi_tessellation wasDerivedFrom Centroidal_Voronoi_tessellation?oldid=705523126.
- Centroidal_Voronoi_tessellation depiction CentroidalVoronoiTessellation1.png.
- Centroidal_Voronoi_tessellation isPrimaryTopicOf Centroidal_Voronoi_tessellation.