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Boundary points and resolution
, 2009
"... Abstract. We use the notion of boundary points to study resolution proofs. Given a CNF formula F, a lit(x)boundary point is a complete assignment falsifying only clauses of F having the same literal lit(x) of variable x. A lit(x)boundary point mandates a resolution on variable x. Adding the resolv ..."
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Cited by 9 (6 self)
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Abstract. We use the notion of boundary points to study resolution proofs. Given a CNF formula F, a lit(x)boundary point is a complete assignment falsifying only clauses of F having the same literal lit(x) of variable x. A lit(x)boundary point mandates a resolution on variable x. Adding
Boundary Point Method
"... Abstract. The determination of the sensitivity of the acoustical characteristics of vibrating systems with respect to the variation of the design parameters can provide a method to lownoise design of mechanical structure objectively and quantitatively. Using the Distributed source energy boundary p ..."
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point method, the expressions of the change of the acoustical energy density with respect to design variable is presented in this paper. The Distributed source energy boundary point method is a speedy and precise method which can avoid the complex computing of the singularity integral in EBEM
Generalizing Boundary Points
 Proceedings of the Seventeenth National Conference on Articial Intelligence (pp. 570576). Menlo Park
, 2000
"... The complexity of numerical domain partitioning depends on the number of potential cut points. In multiway partitioning this dependency is often quadratic, even exponential. Therefore, reducing the number of candidate cut points is important. For a large family of attribute evaluation functions only ..."
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Cited by 5 (4 self)
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only boundary points need to be considered as candidates. We prove that an even more general property holds for many commonlyused functions. Their optima are located on the borders of example segments in which the relative class frequency distribution is static. These borders are a subset of boundary
Chapter 7 Boundary Points and Resolution
"... We use the notion of boundary points to study resolution proofs. Given a CNF formula F, an l(x)boundary point is a complete assignment falsifying only clauses of F having the same literal l(x) of variable x. An l(x)boundary point p mandates a resolution on variable x. Adding the resolvent of this ..."
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We use the notion of boundary points to study resolution proofs. Given a CNF formula F, an l(x)boundary point is a complete assignment falsifying only clauses of F having the same literal l(x) of variable x. An l(x)boundary point p mandates a resolution on variable x. Adding the resolvent
Surface reconstruction from unorganized points
 COMPUTER GRAPHICS (SIGGRAPH ’92 PROCEEDINGS)
, 1992
"... We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be know ..."
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Cited by 811 (8 self)
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We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed
Spacetime Interest Points
 IN ICCV
, 2003
"... Local image features or interest points provide compact and abstract representations of patterns in an image. In this paper, we propose to extend the notion of spatial interest points into the spatiotemporal domain and show how the resulting features often reflect interesting events that can be use ..."
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Cited by 791 (22 self)
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Local image features or interest points provide compact and abstract representations of patterns in an image. In this paper, we propose to extend the notion of spatial interest points into the spatiotemporal domain and show how the resulting features often reflect interesting events that can
Detection and Tracking of Point Features
 International Journal of Computer Vision
, 1991
"... The factorization method described in this series of reports requires an algorithm to track the motion of features in an image stream. Given the small interframe displacement made possible by the factorization approach, the best tracking method turns out to be the one proposed by Lucas and Kanade i ..."
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Cited by 622 (2 self)
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The factorization method described in this series of reports requires an algorithm to track the motion of features in an image stream. Given the small interframe displacement made possible by the factorization approach, the best tracking method turns out to be the one proposed by Lucas and Kanade in 1981. The method defines the measure of match between fixedsize feature windows in the past and current frame as the sum of squared intensity differences over the windows. The displacement is then defined as the one that minimizes this sum. For small motions, a linearization of the image intensities leads to a NewtonRaphson style minimization. In this report, after rederiving the method in a physically intuitive way, we answer the crucial question of how to choose the feature windows that are best suited for tracking. Our selection criterion is based directly on the definition of the tracking algorithm, and expresses how well a feature can be tracked. As a result, the criterion is optima...
BORDER: Efficient Computation of Boundary Points
, 2005
"... In this work, we investigate the problem of finding boundary points in multidimensional datasets. Boundary points are data points that are located at the margin of densely distributed data (e.g. a cluster). In this paper, we propose a simple yet novel approach BORDER (a BOundaRy points DEtectoR) to ..."
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Cited by 3 (0 self)
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In this work, we investigate the problem of finding boundary points in multidimensional datasets. Boundary points are data points that are located at the margin of densely distributed data (e.g. a cluster). In this paper, we propose a simple yet novel approach BORDER (a BOundaRy points DEtecto
OPTICS: Ordering Points To Identify the Clustering Structure
, 1999
"... Cluster analysis is a primary method for database mining. It is either used as a standalone tool to get insight into the distribution of a data set, e.g. to focus further analysis and data processing, or as a preprocessing step for other algorithms operating on the detected clusters. Almost all of ..."
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Cited by 511 (49 self)
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.g. representative points, arbitrary shaped clusters), but also the intrinsic clustering structure. For medium sized data sets, the clusterordering can be represented graphically and for very large data sets, we introduce an appropriate visualization technique. Both are suitable for interactive exploration
Removal of Quantifiers by Elimination of Boundary Points
, 1204
"... Abstract—We consider the problem of elimination of existential quantifiers from a Boolean CNF formula. Our approach is based on the following observation. One can get rid of dependency on a set of variables of a quantified CNF formula F by adding resolvent clauses of F eliminating boundary points. T ..."
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Abstract—We consider the problem of elimination of existential quantifiers from a Boolean CNF formula. Our approach is based on the following observation. One can get rid of dependency on a set of variables of a quantified CNF formula F by adding resolvent clauses of F eliminating boundary points
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