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Efficient algorithm for computing the EulerPoincaré characteristic of semialgebraic sets defined by few quadratic inequalities
 Computational Complexity
, 2006
"... Abstract. We present an algorithm which takes as input a closed semialgebraic set, S ⊂ R k, defined by P1 ≤ 0,...,Pℓ ≤ 0,Pi ∈ R[X1,...,Xk],deg(Pi) ≤ 2, and computes the EulerPoincaré characteristic of S. The complexity of the algorithm is k O(ℓ). Keywords. Semialgebraic sets, EulerPoincaré chara ..."
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Cited by 17 (10 self)
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Abstract. We present an algorithm which takes as input a closed semialgebraic set, S ⊂ R k, defined by P1 ≤ 0,...,Pℓ ≤ 0,Pi ∈ R[X1,...,Xk],deg(Pi) ≤ 2, and computes the EulerPoincaré characteristic of S. The complexity of the algorithm is k O(ℓ). Keywords. Semialgebraic sets, EulerPoincaré
On projections of semialgebraic sets defined by few quadratic inequalities
 in Discrete and Computational Geometry, available at [arXiv:math.AG/0602398]. SEMIALGEBRAIC GEOMETRY AND TOPOLOGY 73
"... Abstract. Let S ⊂ R k+m be a compact semialgebraic set defined by P1 ≥ 0,..., Pℓ ≥ 0, where Pi ∈ R[X1,..., Xk, Y1,..., Ym], and deg(Pi) ≤ 2, 1 ≤ i ≤ ℓ. Let π denote the standard projection from R k+m onto R m. We prove that for any q> 0, the sum of the first q Betti numbers of π(S) is bounded b ..."
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Cited by 9 (7 self)
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Abstract. Let S ⊂ R k+m be a compact semialgebraic set defined by P1 ≥ 0,..., Pℓ ≥ 0, where Pi ∈ R[X1,..., Xk, Y1,..., Ym], and deg(Pi) ≤ 2, 1 ≤ i ≤ ℓ. Let π denote the standard projection from R k+m onto R m. We prove that for any q> 0, the sum of the first q Betti numbers of π(S) is bounded
Algorithms in Semialgebraic Geometry
, 1996
"... In this thesis we present new algorithms to solve several very general problems of semialgebraic geometry. These are currently the best algorithms for solving these problems. In addition, we have proved new bounds on the topological complexity of real semialgebraic sets, in terms of the paramete ..."
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Cited by 9 (0 self)
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In this thesis we present new algorithms to solve several very general problems of semialgebraic geometry. These are currently the best algorithms for solving these problems. In addition, we have proved new bounds on the topological complexity of real semialgebraic sets, in terms
COMPUTATION OF THE DISTANCE TO SEMIALGEBRAIC SETS ∗
, 1998
"... Abstract. This paper is devoted to the computation of distance to set, called S, defined by polynomial equations. First we consider the case of quadratic systems. Then, application of results stated for quadratic systems to the quadratic equivalent of polynomial systems (see [5]), allows us to compu ..."
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Cited by 1 (0 self)
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to compute distance to semialgebraic sets. Problem of computing distance can be viewed as non convex minimization problem: d(u, S) =infx∈S‖x−u ‖ 2,whereuis in R n. To have, at least, lower approximation of distance, we consider the dual bound m(u) associated with the dual problem and give sufficient
Efficient Variants of the ICP Algorithm
 INTERNATIONAL CONFERENCE ON 3D DIGITAL IMAGING AND MODELING
, 2001
"... The ICP (Iterative Closest Point) algorithm is widely used for geometric alignment of threedimensional models when an initial estimate of the relative pose is known. Many variants of ICP have been proposed, affecting all phases of the algorithm from the selection and matching of points to the minim ..."
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Cited by 702 (5 self)
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sampling of the space of normals. We conclude by proposing a combination of ICP variants optimized for high speed. We demonstrate an implementation that is able to align two range images in a few tens of milliseconds, assuming a good initial guess. This capability has potential application to realtime 3D
Hierarchically Classifying Documents Using Very Few Words
, 1997
"... The proliferation of topic hierarchies for text documents has resulted in a need for tools that automatically classify new documents within such hierarchies. Existing classification schemes which ignore the hierarchical structure and treat the topics as separate classes are often inadequate in text ..."
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Cited by 521 (8 self)
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classification where the there is a large number of classes and a huge number of relevant features needed to distinguish between them. We propose an approach that utilizes the hierarchical topic structure to decompose the classification task into a set of simpler problems, one at each node in the classification
Betti numbers of semialgebraic sets defined by partly quadratic systems of polynomials
, 2007
"... ... degX (P) ≤ d, P ∈ P, #(P) = s, and S ⊂ Rℓ+k a semialgebraic set defined by a Boolean formula without negations, with atoms P = 0, P ≥ 0, P ≤ 0, P ∈ P ∪ Q. We prove that the sum of the Betti numbers of S is bounded by (ℓsmd) O(m+k). This is a common generalization of previous results in [7] an ..."
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Cited by 7 (3 self)
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] and [2] on bounding the Betti numbers of closed semialgebraic sets defined by polynomials of degree d and 2, respectively. We also describe algorithms for computing the EulerPoincaré characteristic, as well as all the Betti numbers of such sets, generalizing similar algorithms described in [7, 4
ALGORITHMIC AND TOPOLOGICAL ASPECTS OF SEMIALGEBRAIC SETS DEFINED BY QUADRATIC POLYNOMIALS
, 2007
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Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
Results 1  10
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