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387
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 582 (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.
Discrete DifferentialGeometry Operators for Triangulated 2Manifolds
, 2002
"... This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Vorono ..."
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Cited by 449 (14 self)
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This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Voronoi cells and the mixed FiniteElement/FiniteVolume method, and compare them to existing formulations. Building upon previous work in discrete geometry, these new operators are closely related to the continuous case, guaranteeing an appropriate extension from the continuous to the discrete setting: they respect most intrinsic properties of the continuous differential operators.
A local search approximation algorithm for kmeans clustering
, 2004
"... In kmeans clustering we are given a set of n data points in ddimensional space ℜd and an integer k, and the problem is to determine a set of k points in ℜd, called centers, to minimize the mean squared distance from each data point to its nearest center. No exact polynomialtime algorithms are kno ..."
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Cited by 113 (1 self)
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In kmeans clustering we are given a set of n data points in ddimensional space ℜd and an integer k, and the problem is to determine a set of k points in ℜd, called centers, to minimize the mean squared distance from each data point to its nearest center. No exact polynomialtime algorithms are known for this problem. Although asymptotically efficient approximation algorithms exist, these algorithms are not practical due to the very high constant factors involved. There are many heuristics that are used in practice, but we know of no bounds on their performance. We consider the question of whether there exists a simple and practical approximation algorithm for kmeans clustering. We present a local improvement heuristic based on swapping centers in and out. We prove that this yields a (9 + ε)approximation algorithm. We present an example showing that any approach based on performing a fixed number of swaps achieves an approximation factor of at least (9 − ε) in all sufficiently high dimensions. Thus, our approximation factor is almost tight for algorithms based on performing a fixed number of swaps. To establish the practical value of the heuristic, we present an empirical study that shows that, when combined with
On a Stochastic Sensor Selection Algorithm with Applications in Sensor Scheduling and Sensor Coverage
 AUTOMATICA
, 2006
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Fast hierarchical importance sampling with blue noise properties
 ACM TRANSACTIONS ON GRAPHICS
, 2004
"... This paper presents a novel method for efficiently generating a good sampling pattern given an importance density over a 2D domain. A Penrose tiling is hierarchically subdivided creating a sufficiently large number of sample points. These points are numbered using the Fibonacci number system, and th ..."
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Cited by 102 (8 self)
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This paper presents a novel method for efficiently generating a good sampling pattern given an importance density over a 2D domain. A Penrose tiling is hierarchically subdivided creating a sufficiently large number of sample points. These points are numbered using the Fibonacci number system, and these numbers are used to threshold the samples against the local value of the importance density. Precomputed correction vectors, obtained using relaxation, are used to improve the spectral characteristics of the sampling pattern. The technique is deterministic and very fast; the sampling time grows linearly with the required number of samples. We illustrate our technique with importancebased environment mapping, but the technique is versatile enough to be used in a large variety of computer graphics applications, such as light transport calculations, digital halftoning, geometry processing, and various rendering techniques.
Simulating Decorative Mosaic
 Proc. ACM SIGGRAPH ’01
, 2001
"... a b c d e f Figure 1: By overwriting voronoi regions, tile centroids are displaced away from an edge. Recentering tiles at their new centroids eventually moves them clear of the edge. This paper presents a method for simulating decorative tile mosaics. Such mosaics are challenging because the square ..."
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Cited by 102 (0 self)
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a b c d e f Figure 1: By overwriting voronoi regions, tile centroids are displaced away from an edge. Recentering tiles at their new centroids eventually moves them clear of the edge. This paper presents a method for simulating decorative tile mosaics. Such mosaics are challenging because the square tiles that comprise them must be packed tightly and yet must follow orientations chosen by the artist. Based on an existing image and userselected edge features, the method can both reproduce the image’s colours and emphasize the selected edges by placing tiles that follow the edges. The method uses centroidal voronoi diagrams which normally arrange points in regular hexagonal grids. By measuring distances with an manhattan metric whose main axis is adjusted locally to follow the chosen direction field, the centroidal diagram can be adapted to place tiles in curving square grids instead. Computing the centroidal voronoi diagram is made possible by leveraging the zbuffer algorithm available in many graphics cards. 1
Spatiallydistributed coverage optimization and control with limitedrange interactions
 ESAIM Control, Optimisation Calculus Variations
, 2005
"... Abstract. This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing/communication radius. Based on the geometry of Voronoi partitions and proximity grap ..."
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Cited by 96 (28 self)
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Abstract. This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing/communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with respect to appropriate proximity graphs. Numerical simulations illustrate the results.
Variance shadow maps
 In SI3D ’06: Proceedings of the 2006 symposium on Interactive 3D graphics and games, ACM
, 2006
"... Figure 1: Comparison of anisotropic filtering vs. no anisotropic filtering. Top: Regular shadow map with bilinear percentage closer filtering. Bottom: Variance shadow map with mipmapping and 16x anisotropic filtering. Shadow maps are a widely used shadowing technique in real time graphics. One major ..."
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Cited by 91 (1 self)
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Figure 1: Comparison of anisotropic filtering vs. no anisotropic filtering. Top: Regular shadow map with bilinear percentage closer filtering. Bottom: Variance shadow map with mipmapping and 16x anisotropic filtering. Shadow maps are a widely used shadowing technique in real time graphics. One major drawback of their use is that they cannot be filtered in the same way as color textures, typically leading to severe aliasing. This paper introduces variance shadow maps, a new real time shadowing algorithm. Instead of storing a single depth value, we store the mean and mean squared of a distribution of depths, from which we can efficiently compute the variance over any filter region. Using the variance, we derive an upper bound on the fraction of a shaded fragment that is occluded. We show that this bound often provides a good approximation to the true occlusion, and can be used as an approximate value for rendering. Our algorithm is simple to implement on current graphics processors and solves the problem of shadow map aliasing with minimal additional storage and computation.
Weighted Voronoi Stippling
 IN PROC. OF NPAR 2002
, 2002
"... The traditional artistic technique of stippling places small dots of ink onto paper such that their density give the impression of tone. The artist tightly controls the relative placement of the stipples on the paper to produce even tones and avoid artifacts, leading to long creation times for the d ..."
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Cited by 76 (1 self)
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The traditional artistic technique of stippling places small dots of ink onto paper such that their density give the impression of tone. The artist tightly controls the relative placement of the stipples on the paper to produce even tones and avoid artifacts, leading to long creation times for the drawings.