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116
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
 Biometrika
, 1995
"... Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determi ..."
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Cited by 846 (19 self)
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Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determination, where the dimensionality of the parameter vector is typically not xed. This article proposes a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of di ering dimensionality, which is exible and entirely constructive. It should therefore have wide applicability in model determination problems. The methodology is illustrated with applications to multiple changepoint analysis in one and two dimensions, and toaBayesian comparison of binomial experiments.
Voronoi diagrams  a survey of a fundamental geometric data structure
 ACM COMPUTING SURVEYS
, 1991
"... This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development. ..."
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Cited by 572 (5 self)
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This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development. The paper puts particular emphasis on the unified exposition of its mathematical and algorithmic properties. Finally, the paper provides the first comprehensive bibliography on Voronoi diagrams and related structures.
Voronoi diagrams and Delaunay triangulations,” in Handbook of discrete and computational
"... The Voronoi diagram of a set of sites partitions space into regions one per site the region for a site s consists of all points closer to s than to any other site The dual of the Voronoi diagram the Delaunay triangulation is the unique triangulation so that the circumsphere of every triangle co ..."
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Cited by 197 (3 self)
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The Voronoi diagram of a set of sites partitions space into regions one per site the region for a site s consists of all points closer to s than to any other site The dual of the Voronoi diagram the Delaunay triangulation is the unique triangulation so that the circumsphere of every triangle contains no sites in its interior Voronoi diagrams
Fast Polygonal Approximation of Terrains and Height Fields
, 1995
"... Several algorithms for approximating terrains and other height fields using polygonal meshes are described, compared, and optimized. These algorithms take a height field as input, typically a rectangular grid of elevation data H(x; y), and approximate it with a mesh of triangles, also known as a tri ..."
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Cited by 144 (5 self)
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Several algorithms for approximating terrains and other height fields using polygonal meshes are described, compared, and optimized. These algorithms take a height field as input, typically a rectangular grid of elevation data H(x; y), and approximate it with a mesh of triangles, also known as a triangulated irregular network, or TIN. The algorithms attempt to minimize both the error and the number of triangles in the approximation. Applications include fast rendering of terrain data for flight simulation and fitting of surfaces to range data in computer vision. The methods can also be used to simplify multichannel height fields such as textured terrains or planar color images. The most successful method we examine is the greedy insertion algorithm. It begins with a simple triangulation of the domain and, on each pass, finds the input point with highest error in the current approximation and inserts it as a vertex in the triangulation. The mesh is updated either with Delaunay triangul...
The Relative Neighbourhood Graph of a Finite Planar Set
 Pattern Recognition
, 1980
"... The relative neighbourhood graph (RNG) of a set of n points on the plane is defined. The ability of the RNG to extract a perceptually meaningful structure from the set of points is briefly discussed and compared to that of two other graph structures: the minimal spanning tree (MST) and the Delaunay ..."
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Cited by 67 (1 self)
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The relative neighbourhood graph (RNG) of a set of n points on the plane is defined. The ability of the RNG to extract a perceptually meaningful structure from the set of points is briefly discussed and compared to that of two other graph structures: the minimal spanning tree (MST) and the Delaunay (Voronoi) triangulation (DT). It is shown that the RNG is a superset of the MST and a subset of the DT. Two algorithms for obtaining the RNG of n points on the plane are presented. One algorithm runs in O(n 2 ) time and the other runs in O(n 3 ) time but works also for the ddimensional case. Finally, several open problems concerning the RNG in several areas such as geometric complexity, computational perception, and geometric probability, are outlined. 1 Introduction In many problems in pattern recognition, such as clustering [18] and computational approaches to perception [13], one is given a set of points on the plane and it is desired to find some structure among the points in the ...
The Farthest Point Strategy for Progressive Image Sampling
 IEEE TRANS. ON IMAGE PROCESSING
, 1997
"... A new method of farthest point strategy (FPS) for progressive image acquisition—an acquisition process that enables an approximation of the whole image at each sampling stage—is presented. Its main advantage is in retaining its uniformity with the increased density, providing efficient means for s ..."
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Cited by 59 (1 self)
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A new method of farthest point strategy (FPS) for progressive image acquisition—an acquisition process that enables an approximation of the whole image at each sampling stage—is presented. Its main advantage is in retaining its uniformity with the increased density, providing efficient means for sparse image sampling and display. In contrast to previously presented stochastic approaches, the FPS guarantees the uniformity in a deterministic minmax sense. Within this uniformity criterion, the sampling points are irregularly spaced, exhibiting antialiasing properties comparable to those characteristic of the best available method (Poisson disk). A straightforward modification of the FPS yields an imagedependent adaptive sampling scheme. An efficient O(N log N) algorithm for both versions is introduced, and several applications of the FPS are discussed.
Aspects of Unstructured Grids and FiniteVolume Solvers for the Euler and NavierStokes Equations, von Karman Institute for Fluid Dynamics
 Lecture Series 199405, RhodeSaintGenèse
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A Comparison of Sequential Delaunay Triangulation Algorithms
, 1996
"... This paper presents an experimental comparison of a number of different algorithms for computing the Deluanay triangulation. The algorithms examined are: Dwyer’s divide and conquer algorithm, Fortune’s sweepline algorithm, several versions of the incremental algorithm (including one by Ohya, Iri, an ..."
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Cited by 56 (0 self)
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This paper presents an experimental comparison of a number of different algorithms for computing the Deluanay triangulation. The algorithms examined are: Dwyer’s divide and conquer algorithm, Fortune’s sweepline algorithm, several versions of the incremental algorithm (including one by Ohya, Iri, and Murota, a new bucketingbased algorithm described in this paper, and Devillers’s version of a Delaunaytree based algorithm that appears in LEDA), an algorithm that incrementally adds a correct Delaunay triangle adjacent to a current triangle in a manner similar to gift wrapping algorithms for convex hulls, and Barber’s convex hull based algorithm. Most of the algorithms examined are designed for good performance on uniformly distributed sites. However, we also test implementations of these algorithms on a number of nonuniform distibutions. The experiments go beyond measuring total running time, which tends to be machinedependent. We also analyze the major highlevel primitives that algorithms use and do an experimental analysis of how often implementations of these algorithms perform each operation.
Curves and Surfaces for CAGD
, 1993
"... This article provides a historical account of the major developments in the area of curves and surfaces as they entered the area of CAGD – Computer Aided Geometric Design – until the middle 1980s. We adopt the definition that CAGD deals with the construction and representation of freeform curves, s ..."
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Cited by 53 (0 self)
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This article provides a historical account of the major developments in the area of curves and surfaces as they entered the area of CAGD – Computer Aided Geometric Design – until the middle 1980s. We adopt the definition that CAGD deals with the construction and representation of freeform curves, surfaces, or volumes. 1.
Fast Randomized Point Location without Preprocessing in Two and Threedimensional Delaunay Triangulations
 IN PROC. 12TH ANNU. ACM SYMPOS. COMPUT. GEOM
, 1996
"... This paper studies the point location problem in Delaunay triangulations without preprocessing and additional storage. The proposed procedure finds the query point simply by "walking through" the triangulation, after selecting a "good starting point" by random sampling. The analy ..."
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Cited by 47 (2 self)
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This paper studies the point location problem in Delaunay triangulations without preprocessing and additional storage. The proposed procedure finds the query point simply by "walking through" the triangulation, after selecting a "good starting point" by random sampling. The analysis generalizes and extends a recent result for d = 2 dimensions by proving this procedure to take expected time close to O(n 1=(d+1) ) for point location in Delaunay triangulations of n random points in d = 3 dimensions. Empirical results in both two and three dimensions show that this procedure is efficient in practice.