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Publication
700views
16 years 10 months ago
Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems - [ Mumford-Shah ]
"The purpose of this paper is to introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision. In com...
David Mumford and Jayant Shah
STOC
2003
ACM
117views Algorithms» more  STOC 2003»
16 years 2 months ago
Distinct distances in three and higher dimensions
Improving an old result of Clarkson et al., we show that the number of distinct distances determined by a set P of n points in three-dimensional space is (n77/141) = (n0.546 ), fo...
Boris Aronov, János Pach, Micha Sharir, G&a...
116
Voted
FOCS
2009
IEEE
15 years 9 months ago
Instance-Optimal Geometric Algorithms
We prove the existence of an algorithm A for computing 2-d or 3-d convex hulls that is optimal for every point set in the following sense: for every set S of n points and for ever...
Peyman Afshani, Jérémy Barbay, Timot...
124
Voted
SMA
2009
ACM
208views Solid Modeling» more  SMA 2009»
15 years 9 months ago
Accelerating geometric queries using the GPU
We present practical algorithms for accelerating geometric queries on models made of NURBS surfaces using programmable Graphics Processing Units (GPUs). We provide a generalized f...
Adarsh Krishnamurthy, Sara McMains, Kirk Haller
SIBGRAPI
2008
IEEE
15 years 8 months ago
Tradeoffs in Approximate Range Searching Made Simpler
Range searching is a fundamental problem in computational geometry. The problem involves preprocessing a set of n points in Rd into a data structure, so that it is possible to det...
Sunil Arya, Guilherme Dias da Fonseca, David M. Mo...