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An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions
 ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1994
"... Consider a set S of n data points in real ddimensional space, R d , where distances are measured using any Minkowski metric. In nearest neighbor searching we preprocess S into a data structure, so that given any query point q 2 R d , the closest point of S to q can be reported quickly. Given any po ..."
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Cited by 786 (31 self)
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Consider a set S of n data points in real ddimensional space, R d , where distances are measured using any Minkowski metric. In nearest neighbor searching we preprocess S into a data structure, so that given any query point q 2 R d , the closest point of S to q can be reported quickly. Given any positive real ffl, a data point p is a (1 + ffl)approximate nearest neighbor of q if its distance from q is within a factor of (1 + ffl) of the distance to the true nearest neighbor. We show that it is possible to preprocess a set of n points in R d in O(dn log n) time and O(dn) space, so that given a query point q 2 R d , and ffl ? 0, a (1 + ffl)approximate nearest neighbor of q can be computed in O(c d;ffl log n) time, where c d;ffl d d1 + 6d=ffle d is a factor depending only on dimension and ffl. In general, we show that given an integer k 1, (1 + ffl)approximations to the k nearest neighbors of q can be computed in additional O(kd log n) time.
Similarity Indexing with the SStree
 In Proceedings of the 12th International Conference on Data Engineering
, 1996
"... jain0ece.ucsd.edu ..."
ANN: A Library for Approximate Nearest Neighbor Searching
, 1997
"... 3.37> ffl There are no exponential factors in space, implying that the data structure is practical even for very large data sets in high dimensional spaces, irrespective of ffl. ANN is written as a testbed for a class of nearest neighbor searching algorithms, particularly those based on orthogonal ..."
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Cited by 194 (9 self)
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3.37> ffl There are no exponential factors in space, implying that the data structure is practical even for very large data sets in high dimensional spaces, irrespective of ffl. ANN is written as a testbed for a class of nearest neighbor searching algorithms, particularly those based on orthogonal decompositions of space. These include kd trees [3, 4], balanced boxdecomposition trees [2] and other related spatial data structures (see Samet [5]). The library supports a number of different methods for building search structures. It also supports two methods for searching these structures: standard treeordered search [1] and priority search [2]. In priority search, the cells of the data structure are visited in increasing order of distance from the query point. In addition to the library there are two programs provided for testing and evaluating the performance of various search methods. The first, called ann<F2
Face Recognition: A Convolutional Neural Network Approach
 IEEE Transactions on Neural Networks
, 1997
"... Faces represent complex, multidimensional, meaningful visual stimuli and developing a computational model for face recognition is difficult [43]. We present a hybrid neural network solution which compares favorably with other methods. The system combines local image sampling, a selforganizing map n ..."
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Cited by 155 (0 self)
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Faces represent complex, multidimensional, meaningful visual stimuli and developing a computational model for face recognition is difficult [43]. We present a hybrid neural network solution which compares favorably with other methods. The system combines local image sampling, a selforganizing map neural network, and a convolutional neural network. The selforganizing map provides a quantization of the image samples into a topological space where inputs that are nearby in the original space are also nearby in the output space, thereby providing dimensionality reduction and invariance to minor changes in the image sample, and the convolutional neural network provides for partial invariance to translation, rotation, scale, and deformation. The convolutional network extracts successively larger features in a hierarchical set of layers. We present results using the KarhunenLoeve transform in place of the selforganizing map, and a multilayer perceptron in place of the convolutional netwo...
Approximate Nearest Neighbor Queries in Fixed Dimensions
, 1993
"... Given a set of n points in ddimensional Euclidean space, S ae E d , and a query point q 2 E d , we wish to determine the nearest neighbor of q, that is, the point of S whose Euclidean distance to q is minimum. The goal is to preprocess the point set S, such that queries can be answered as effic ..."
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Cited by 105 (10 self)
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Given a set of n points in ddimensional Euclidean space, S ae E d , and a query point q 2 E d , we wish to determine the nearest neighbor of q, that is, the point of S whose Euclidean distance to q is minimum. The goal is to preprocess the point set S, such that queries can be answered as efficiently as possible. We assume that the dimension d is a constant independent of n. Although reasonably good solutions to this problem exist when d is small, as d increases the performance of these algorithms degrades rapidly. We present a randomized algorithm for approximate nearest neighbor searching. Given any set of n points S ae E d , and a constant ffl ? 0, we produce a data structure, such that given any query point, a point of S will be reported whose distance from the query point is at most a factor of (1 + ffl) from that of the true nearest neighbor. Our algorithm runs in O(log 3 n) expected time and requires O(n log n) space. The data structure can be built in O(n 2 ) expe...
Approximate Range Searching
 in Proc. 11th Annu. ACM Sympos. Comput. Geom
, 1995
"... The range searching problem is a fundamental problem in computational geometry, with numerous important applications. Most research has focused on solving this problem exactly, but lower bounds show that if linear space is assumed, the problem cannot be solved in polylogarithmic time, except for the ..."
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Cited by 86 (20 self)
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The range searching problem is a fundamental problem in computational geometry, with numerous important applications. Most research has focused on solving this problem exactly, but lower bounds show that if linear space is assumed, the problem cannot be solved in polylogarithmic time, except for the case of orthogonal ranges. In this paper we show that if one is willing to allow approximate ranges, then it is possible to do much better. In particular, given a bounded range Q of diameter w and ffl ? 0, an approximate range query treats the range as a fuzzy object, meaning that points lying within distance fflw of the boundary of Q either may or may not be counted. We show that in any fixed dimension d, a set of n points in R d can be preprocessed in O(n log n) time and O(n) space, such that approximate queries can be answered in O(logn + (1=ffl) d ) time. The only assumption we make about ranges is that the intersection of a range and a ddimensional cube can be answered in const...
ClosestPoint Problems in Computational Geometry
, 1997
"... This is the preliminary version of a chapter that will appear in the Handbook on Computational Geometry, edited by J.R. Sack and J. Urrutia. A comprehensive overview is given of algorithms and data structures for proximity problems on point sets in IR D . In particular, the closest pair problem, th ..."
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Cited by 65 (14 self)
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This is the preliminary version of a chapter that will appear in the Handbook on Computational Geometry, edited by J.R. Sack and J. Urrutia. A comprehensive overview is given of algorithms and data structures for proximity problems on point sets in IR D . In particular, the closest pair problem, the exact and approximate postoffice problem, and the problem of constructing spanners are discussed in detail. Contents 1 Introduction 1 2 The static closest pair problem 4 2.1 Preliminary remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Algorithms that are optimal in the algebraic computation tree model . 5 2.2.1 An algorithm based on the Voronoi diagram . . . . . . . . . . . 5 2.2.2 A divideandconquer algorithm . . . . . . . . . . . . . . . . . . 5 2.2.3 A plane sweep algorithm . . . . . . . . . . . . . . . . . . . . . . 6 2.3 A deterministic algorithm that uses indirect addressing . . . . . . . . . 7 2.3.1 The degraded grid . . . . . . . . . . . . . . . . . . ...
R.: Optimised KDtrees for fast image descriptor matching
 In CVPR, IEEE Computer Society
, 2008
"... In this paper, we look at improving the KDtree for a specific usage: indexing a large number of SIFT and other types of image descriptors. We have extended priority search, to priority search among multiple trees. By creating multiple KDtrees from the same data set and simultaneously searching amo ..."
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Cited by 40 (0 self)
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In this paper, we look at improving the KDtree for a specific usage: indexing a large number of SIFT and other types of image descriptors. We have extended priority search, to priority search among multiple trees. By creating multiple KDtrees from the same data set and simultaneously searching among these trees, we have improved the KDtree’s search performance significantly. We have also exploited the structure in SIFT descriptors (or structure in any data set) to reduce the time spent in backtracking. By using Principal Component Analysis to align the principal axes of the data with the coordinate axes, we have further increased the KDtree’s search performance. 1.
PrimitiveBased Movement Classification for Humanoid Imitation
 in ‘Proceedings, First IEEERAS International Conference on Humanoid Robotics (Humanoids2000)’, MIT
"... Abstract. Motor control is a complex problem and imitation is a powerful mechanism for acquiring new motor skills. In this paper, we describe perceptuomotor primitives, a biologicallyinspired notion for a basis set of perceptual and motor routines. Primitives serve as a vocabulary for classifying ..."
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Cited by 38 (11 self)
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Abstract. Motor control is a complex problem and imitation is a powerful mechanism for acquiring new motor skills. In this paper, we describe perceptuomotor primitives, a biologicallyinspired notion for a basis set of perceptual and motor routines. Primitives serve as a vocabulary for classifying and imitating observed human movements, and are derived from the imitator’s motor repertoire. We describe a model of imitation based on such primitives and demonstrate the feasibility of the model in a constrained implementation. We present approximate motion reconstruction generated from visually captured data of typically imitated tasks taken from aerobics, dancing, and athletics. 1