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434
The Quickhull algorithm for convex hulls
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1996
"... The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algo ..."
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Cited by 452 (0 self)
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The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floatingpoint arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick ” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.
Efficient and Effective Querying by Image Content
 Journal of Intelligent Information Systems
, 1994
"... In the QBIC (Query By Image Content) project we are studying methods to query large online image databases using the images' content as the basis of the queries. Examples of the content we use include color, texture, and shape of image objects and regions. Potential applications include medical ..."
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Cited by 429 (12 self)
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In the QBIC (Query By Image Content) project we are studying methods to query large online image databases using the images' content as the basis of the queries. Examples of the content we use include color, texture, and shape of image objects and regions. Potential applications include medical ("Give me other images that contain a tumor with a texture like this one"), photojournalism ("Give me images that have blue at the top and red at the bottom"), and many others in art, fashion, cataloging, retailing, and industry. We describe a set of novel features and similarity measures allowing query by color, texture, and shape of image object. We demonstrate the effectiveness of the QBIC system with normalized precision and recall experiments on test databases containing over 1000 images and 1000 objects populated from commercially available photo clip art images, and of images of airplane silhouettes. We also consider the efficient indexing of these features, specifically addre...
DavenportSchinzel Sequences and Their Geometric Applications
, 1998
"... An (n; s) DavenportSchinzel sequence, for positive integers n and s, is a sequence composed of n distinct symbols with the properties that no two adjacent elements are equal, and that it does not contain, as a (possibly noncontiguous) subsequence, any alternation a \Delta \Delta \Delta b \Delta \ ..."
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Cited by 416 (115 self)
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An (n; s) DavenportSchinzel sequence, for positive integers n and s, is a sequence composed of n distinct symbols with the properties that no two adjacent elements are equal, and that it does not contain, as a (possibly noncontiguous) subsequence, any alternation a \Delta \Delta \Delta b \Delta \Delta \Delta a \Delta \Delta \Delta b \Delta \Delta \Delta of length s + 2 between two distinct symbols a and b. The close relationship between DavenportSchinzel sequences and the combinatorial structure of lower envelopes of collections of functions make the sequences very attractive because a variety of geometric problems can be formulated in terms of lower envelopes. A nearlinear bound on the maximum length of DavenportSchinzel sequences enable us to derive sharp bounds on the combinatorial structure underlying various geometric problems, which in turn yields efficient algorithms for these problems.
Efficient similarity search in sequence databases
, 1994
"... We propose an indexing method for time sequences for processing similarity queries. We use the Discrete Fourier Transform (DFT) to map time sequences to the frequency domain, the crucial observation being that, for most sequences of practical interest, only the first few frequencies are strong. Anot ..."
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Cited by 413 (20 self)
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We propose an indexing method for time sequences for processing similarity queries. We use the Discrete Fourier Transform (DFT) to map time sequences to the frequency domain, the crucial observation being that, for most sequences of practical interest, only the first few frequencies are strong. Another important observation is Parseval's theorem, which specifies that the Fourier transform preserves the Euclidean distance in the time or frequency domain. Having thus mapped sequences to a lowerdimensionality space by using only the first few Fourier coe cients, we use Rtrees to index the sequences and e ciently answer similarity queries. We provide experimental results which show that our method is superior to search based on sequential scanning. Our experiments show that a few coefficients (13) are adequate to provide good performance. The performance gain of our method increases with the number and length of sequences.
Coverage Control for Mobile Sensing Networks
, 2002
"... This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functio ..."
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Cited by 348 (49 self)
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This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closedloop behavior is adaptive, distributed, asynchronous, and verifiably correct.
Coverage Problems in Wireless Adhoc Sensor Networks
 in IEEE INFOCOM
, 2001
"... Wireless adhoc sensor networks have recently emerged as a premier research topic. They have great longterm economic potential, ability to transform our lives, and pose many new systembuilding challenges. Sensor networks also pose a number of new conceptual and optimization problems. Some, such as ..."
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Cited by 325 (9 self)
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Wireless adhoc sensor networks have recently emerged as a premier research topic. They have great longterm economic potential, ability to transform our lives, and pose many new systembuilding challenges. Sensor networks also pose a number of new conceptual and optimization problems. Some, such as location, deployment, and tracking, are fundamental issues, in that many applications rely on them for needed information. In this paper, we address one of the fundamental problems, namely coverage. Coverage in general, answers the questions about quality of service (surveillance) that can be provided by a particular sensor network. We first define the coverage problem from several points of view including deterministic, statistical, worst and best case, and present examples in each domain. By combining computational geometry and graph theoretic techniques, specifically the Voronoi diagram and graph search algorithms, we establish the main highlight of the paper  optimal polynomial time worst and average case algorithm for coverage calculation. We also present comprehensive experimental results and discuss future research directions related to coverage in sensor networks. I.
Searching in Metric Spaces
, 1999
"... The problem of searching the elements of a set which are close to a given query element under some similarity criterion has a vast number of applications in many branches of computer science, from pattern recognition to textual and multimedia information retrieval. We are interested in the rather ge ..."
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Cited by 319 (33 self)
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The problem of searching the elements of a set which are close to a given query element under some similarity criterion has a vast number of applications in many branches of computer science, from pattern recognition to textual and multimedia information retrieval. We are interested in the rather general case where the similarity criterion defines a metric space, instead of the more restricted case of a vector space. A large number of solutions have been proposed in different areas, in many cases without crossknowledge. Because of this, the same ideas have been reinvented several times, and very different presentations have been given for the same approaches. We
Voronoi Diagrams and Delaunay Triangulations
 Computing in Euclidean Geometry
, 1992
"... The Voronoi diagram is a fundamental structure in computationalgeometry and arises naturally in many different fields. This chapter surveys properties of the Voronoi diagram and its geometric dual, the Delaunay triangulation. The emphasis is on practical algorithms for the construction of Voronoi ..."
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Cited by 196 (3 self)
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The Voronoi diagram is a fundamental structure in computationalgeometry and arises naturally in many different fields. This chapter surveys properties of the Voronoi diagram and its geometric dual, the Delaunay triangulation. The emphasis is on practical algorithms for the construction of Voronoi diagrams. 1 Introduction Let S be a set of n points in ddimensional euclidean space E d . The points of S are called sites. The Voronoi diagram of S splits E d into regions with one region for each site, so that the points in the region for site s2S are closer to s than to any other site in S. The Delaunay triangulation of S is the unique triangulation of S so that there are no elements of S inside the circumsphere of any triangle. Here `triangulation' is extended from the planar usage to arbitrary dimension: a triangulation decomposes the convex hull of S into simplices using elements of S as vertices. The existence and uniqueness of the Delaunay triangulation are perhaps not obvio...
The TVtree  an index structure for highdimensional data
 VLDB Journal
, 1994
"... We propose a file structure to index highdimensionality data, typically, points in some feature space. The idea is to use only a few of the features, utilizing additional features whenever the additional discriminatory power is absolutely necessary. We present in detail the design of our tree struc ..."
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Cited by 193 (7 self)
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We propose a file structure to index highdimensionality data, typically, points in some feature space. The idea is to use only a few of the features, utilizing additional features whenever the additional discriminatory power is absolutely necessary. We present in detail the design of our tree structure and the associated algorithms that handle such `varying length' feature vectors. Finally we report simulation results, comparing the proposed structure with the R tree, which is one of the most successful methods for lowdimensionality spaces. The results illustrate the superiority of our method, with up to 80% savings in disk accesses. Type of Contribution: New Index Structure, for highdimensionality feature spaces. Algorithms and performance measurements. Keywords: Spatial Index, Similarity Retrieval, Query by Content 1 Introduction Many applications require enhanced indexing, capable of performing similarity searching on several, nontraditional (`exotic') data types. The targ...
Fast Computation of Generalized Voronoi Diagrams Using Graphics Hardware
, 1999
"... We present a new approach for computing generalized 2D and 3D Voronoi diagrams using interpolationbased polygon rasterization hardware. We compute a discrete Voronoi diagram by rendering a three dimensional distance mesh for each Voronoi site. The polygonal mesh is a boundederror approximation of ..."
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Cited by 193 (26 self)
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We present a new approach for computing generalized 2D and 3D Voronoi diagrams using interpolationbased polygon rasterization hardware. We compute a discrete Voronoi diagram by rendering a three dimensional distance mesh for each Voronoi site. The polygonal mesh is a boundederror approximation of a (possibly) nonlinear function of the distance between a site and a 2D planar grid of sample points. For each sample point, we compute the closest site and the distance to that site using polygon scanconversion and the Zbuffer depth comparison. We construct distance meshes for points, line segments, polygons, polyhedra, curves, and curved surfaces in 2D and 3D. We generalize to weighted and farthestsite Voronoi diagrams, and present efficient techniques for computing the Voronoi boundaries, Voronoi neighbors, and the Delaunay triangulation of points. We also show how to adaptively refine the solution through a simple windowing operation. The algorithm has been implemented on SGI workstations and PCs using OpenGL, and applied to complex datasets. We demonstrate the application of our algorithm to fast motion planning in static and dynamic environments, selection in complex userinterfaces, and creation of dynamic mosaic effects.