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This article provides a brief introduction to the definition, properties, and use of Voronoi diagrams, including the special cases of the Poisson–Voronoi and centroidal Voronoi diagrams. It highlights applications to problems in spatial statistics, probability, and large‐scale simultaneous hypothesis testing. Generalizations of the Voronoi diagram and computational considerations are also discussed. These diagrams have been widely used in the fields of statistics, mathematics, computational geometry, and various applied sciences, making them an important topic of study. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization Data: Types and Structure > Image and Spatial Data Data: Types and Structure > Graph and Network Data Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification
The simple planar Voronoi diagram and its dual graph, the Delaunay triangulation. (a) Unrestricted simple planar Voronoi diagram using 10 generator points. (b) Delaunay triangulation (blue lines) and its dual, the Voronoi diagram (black lines).
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Three types of weighted Voronoi diagrams. (a) Multiplicative, (b) Additive, and (c) Compound.
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A sample centroidal Voronoi diagram (a) and the movement from original generators used in Figure (blue) to black centroidal generators (b) following Lloyd's algorithm. (a) A centroidal Voronoi diagram. (b) Movement of generators to form a CVD.
[ Normal View | Magnified View ]

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Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification
Data: Types and Structure > Graph and Network Data
Data: Types and Structure > Image and Spatial Data
Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization

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