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Centroidal Voronoi tessellations: Applications and algorithms
 SIAM REV
, 1999
"... A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. We give some applications of such tessellations to problems in image compression, quadrature, finite difference methods, distribution of res ..."
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Cited by 389 (37 self)
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A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. We give some applications of such tessellations to problems in image compression, quadrature, finite difference methods, distribution
Superposition of Planar Voronoi Tesselations
 COMMUNICATIONS IN STATISTICS. STOCHASTIC MODELS
, 1999
"... We study the tessellation defined as the intersection of two independent planar PoissonVoronoi tessellations and derive the means of its main geometrical characteristics. For this intersection tessellation, we distinguish between six types of cells depending on whether they contain the nuclei of th ..."
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Cited by 3 (0 self)
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We study the tessellation defined as the intersection of two independent planar PoissonVoronoi tessellations and derive the means of its main geometrical characteristics. For this intersection tessellation, we distinguish between six types of cells depending on whether they contain the nuclei
VORONOI TESSELLATIONS FOR MATCHBOX MANIFOLDS
"... Abstract. Matchbox manifolds M are a special class of foliated spaces, which include as special examples the weak solenoids, suspensions of odometer and Toeplitz actions, and tiling spaces associated to aperiodic tilings with finite local complexity. They have many properties analogous to those of a ..."
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Cited by 5 (4 self)
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foliated subsets of general matchbox manifolds. This follows from the construction of uniform Voronoi tessellations on leaves, which is the main goal of this work. From this, we define a foliated Delaunay triangulation of M, adapted to the dynamics of F. The result is highly technical, but underlies
Constrained centroidal Voronoi tessellations for surfaces
 SIAM J. Sci. Comput
"... Abstract. Centroidal Voronoi tessellations are useful for subdividing a region in Euclidean space into Voronoi regions whose generators are also the centers of mass, with respect to a prescribed density function, of the regions. Their extensions to general spaces and sets are also available; for exa ..."
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Cited by 78 (24 self)
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Abstract. Centroidal Voronoi tessellations are useful for subdividing a region in Euclidean space into Voronoi regions whose generators are also the centers of mass, with respect to a prescribed density function, of the regions. Their extensions to general spaces and sets are also available
Anisotropic centroidal Voronoi tessellations and their applications
 SIAM J. Sci. Comput
, 2005
"... Abstract. In this paper, we introduce a novel definition of the anisotropic centroidal Voronoi tessellation (ACVT) corresponding to a given Riemann metric tensor. A directional distance function is used in the definition to simplify the computation. We provide algorithms to approximate the ACVT usin ..."
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Cited by 48 (6 self)
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Abstract. In this paper, we introduce a novel definition of the anisotropic centroidal Voronoi tessellation (ACVT) corresponding to a given Riemann metric tensor. A directional distance function is used in the definition to simplify the computation. We provide algorithms to approximate the ACVT
PoissonVoronoi Tesselation
, 2005
"... The ddimensional Poisson process of intensity λ is a random scattering of points (called particles) inR d that meets the following two requirements. Let S ⊆ R d denote a measurable set of finite volume μ and N(S) denote the number of particles falling in S. We have [1,2] • P {N(S) =n} = e −λμ (λμ) ..."
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The ddimensional Poisson process of intensity λ is a random scattering of points (called particles) inR d that meets the following two requirements. Let S ⊆ R d denote a measurable set of finite volume μ and N(S) denote the number of particles falling in S. We have [1,2] • P {N(S) =n} = e −λμ (λμ) n /n! for any S, for any n =0, 1, 2,..., and • if S1,...,Sk are disjoint measurable sets, then N(S1),...,N(Sk) are independent random variables. In particular, the location of S in R d is immaterial (stationarity) and E(N(S)) = λμ=Var(N(S)) (equality of mean and variance). An alternative characterization of the Poisson process involves the limit of the uniform distribution on expanding cubes C ⊆ R d.Letν denote the volume of C. Given m independent uniformly distributed particles in C and a measurable set S ⊆ C of volume μ, the probability that exactly n particles fall in S is m! n!(m − n)! µ ¶ μ n µ
Statistical properties of planar Voronoi tessellations
, 709
"... Abstract. I present a concise review of advances realized over the past three years on planar PoissonVoronoi tessellations. These encompass new analytic results, a new Monte Carlo method, and application to experimental data. PACS. PACS 02.50.r Probability theory, stochastic processes, and statist ..."
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Cited by 2 (0 self)
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Abstract. I present a concise review of advances realized over the past three years on planar PoissonVoronoi tessellations. These encompass new analytic results, a new Monte Carlo method, and application to experimental data. PACS. PACS 02.50.r Probability theory, stochastic processes
CLUSTER IDENTIFICATION VIA VORONOI TESSELLATION
, 1998
"... Abstract. We propose an automated method for detecting galaxy clusters in imaging surveys based on the Voronoi tessellation technique. It appears very promising, expecially for its capability of detecting clusters indipendently from their shape. After a brief explanation of our use of the algorithm, ..."
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Abstract. We propose an automated method for detecting galaxy clusters in imaging surveys based on the Voronoi tessellation technique. It appears very promising, expecially for its capability of detecting clusters indipendently from their shape. After a brief explanation of our use of the algorithm
On Centroidal Voronoi Tessellation  Energy Smoothness and Fast Computation
, 2008
"... Centroidal Voronoi tessellation (CVT) is a fundamental geometric structure that finds many applications in ..."
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Cited by 35 (16 self)
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Centroidal Voronoi tessellation (CVT) is a fundamental geometric structure that finds many applications in
Approximation by Piecewise Polynomials on Voronoi Tessellation
"... We propose a novel method to approximate a function on 2D domain by piecewise polynomials. The Voronoi tessellation is used as a partition of the domain, on which the best fitting polynomials in L2 metric are constructed. Our method optimizes the domain partition and the fitting polynomials simultan ..."
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We propose a novel method to approximate a function on 2D domain by piecewise polynomials. The Voronoi tessellation is used as a partition of the domain, on which the best fitting polynomials in L2 metric are constructed. Our method optimizes the domain partition and the fitting polynomials
Results 1  10
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7,646