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- W2014465300 abstract "Given a setS ofsources (points or segments) in ℜ211C;d, we consider the surface in ℜ211C; d+1 that is the graph of the functiond(x)=min pεS ρ(x, p) for some metricρ. This surface is closely related to the Voronoi diagram, Vor(S), ofS under the metricρ. The upper envelope of a set of theseVoronoi surfaces, each defined for a different set of sources, can be used to solve the problem of finding the minimum Hausdorff distance between two sets of points or line segments under translation. We derive bounds on the number of vertices on the upper envelope of a collection of Voronoi surfaces, and provide efficient algorithms to calculate these vertices. We then discuss applications of the methods to the problems of finding the minimum Hausdorff distance under translation, between sets of points and segments." @default.
- W2014465300 created "2016-06-24" @default.
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- W2014465300 date "1993-03-01" @default.
- W2014465300 modified "2023-10-06" @default.
- W2014465300 title "The upper envelope of voronoi surfaces and its applications" @default.
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- W2014465300 doi "https://doi.org/10.1007/bf02189323" @default.
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