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Nearly Optimal ExpectedCase Planar Point Location
, 2000
"... We consider the planar point location problem from the perspective of expected search time. We are given a planar polygonal subdivision S and for each polygon of the subdivision the probability that a query point lies within this polygon. The goal is to compute a search structure to determine which ..."
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of the distribution is the dominant term in the lower bound on the expectedcase search time, and further there exist search trees achieving expected search times of at most H +2. Prior to this work, there has been no known structure for planar point location with an expected search time better than 2H
Nearly Optimal ExpectedCase Planar Point Location
"... We consider the planar point location problem from the perspective of expected search time. We are given a planar polygonal subdivision S and for each polygon of the subdivision the probability that a query point lies within this polygon. The goal is to compute a search structure to determine which ..."
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Cited by 19 (5 self)
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of the distribution is the dominant term in the lower bound on the expectedcase search time, and further there exist search trees achieving expected search times of at most H + 2. Prior to this work, there has been no known structure for planar point location with an expected search time better than 2H
Efficient ExpectedCase Algorithms for Planar Point Location
, 2000
"... . Planar point location is among the most fundamental search problems in computational geometry. Although this problem has been heavily studied from the perspective of worstcase query time, there has been surprisingly little theoretical work on expectedcase query time. We are given an nvertex ..."
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Cited by 15 (4 self)
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. Planar point location is among the most fundamental search problems in computational geometry. Although this problem has been heavily studied from the perspective of worstcase query time, there has been surprisingly little theoretical work on expectedcase query time. We are given an n
Abstract Lower Bounds for ExpectedCase Planar Point Location
"... Given a planar polygonal subdivision S, the point location problem is to preprocess S into a data structure so that the cell of the subdivision that contains a given query point can be reported efficiently. Suppose that we are given for each cell z ∈ S the probability pz that a query point lies in z ..."
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in z. The entropy H of the resulting discrete probability distribution is a lower bound on the expectedcase query time. Further it is known that it is possible to construct a data structure that answers pointlocation queries in H + 2 √ 2H + o ( √ H) expected number of comparisons. A fundamental
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
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Cited by 1513 (20 self)
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Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear measurements do we need to recover objects from this class to within accuracy ɛ? This paper shows that if the objects of interest are sparse or compressible in the sense that the reordered entries of a signal f ∈ F decay like a powerlaw (or if the coefficient sequence of f in a fixed basis decays like a powerlaw), then it is possible to reconstruct f to within very high accuracy from a small number of random measurements. typical result is as follows: we rearrange the entries of f (or its coefficients in a fixed basis) in decreasing order of magnitude f  (1) ≥ f  (2) ≥... ≥ f  (N), and define the weakℓp ball as the class F of those elements whose entries obey the power decay law f  (n) ≤ C · n −1/p. We take measurements 〈f, Xk〉, k = 1,..., K, where the Xk are Ndimensional Gaussian
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...
ExpectedCase Complexity of Approximate Nearest Neighbor Searching
 IN PROC. 11TH ACMSIAM SYMPOS. DISCRETE ALGORITHMS
, 2000
"... Most research in algorithms for geometric query problems has focused on their worstcase performance. But when information on the query distribution is available, the alternative paradigm of designing and analyzing algorithms from the perspective of expectedcase performance appears more attractive. ..."
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Cited by 14 (2 self)
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Most research in algorithms for geometric query problems has focused on their worstcase performance. But when information on the query distribution is available, the alternative paradigm of designing and analyzing algorithms from the perspective of expectedcase performance appears more attractive
The Cricket LocationSupport System
, 2000
"... This paper presents the design, implementation, and evaluation of Cricket, a locationsupport system for inbuilding, mobile, locationdependent applications. It allows applications running on mobile and static nodes to learn their physical location by using listeners that hear and analyze informatio ..."
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Cited by 1036 (11 self)
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This paper presents the design, implementation, and evaluation of Cricket, a locationsupport system for inbuilding, mobile, locationdependent applications. It allows applications running on mobile and static nodes to learn their physical location by using listeners that hear and analyze
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