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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 790 (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.
Quantization
 IEEE TRANS. INFORM. THEORY
, 1998
"... The history of the theory and practice of quantization dates to 1948, although similar ideas had appeared in the literature as long ago as 1898. The fundamental role of quantization in modulation and analogtodigital conversion was first recognized during the early development of pulsecode modula ..."
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Cited by 665 (11 self)
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The history of the theory and practice of quantization dates to 1948, although similar ideas had appeared in the literature as long ago as 1898. The fundamental role of quantization in modulation and analogtodigital conversion was first recognized during the early development of pulsecode modulation systems, especially in the 1948 paper of Oliver, Pierce, and Shannon. Also in 1948, Bennett published the first highresolution analysis of quantization and an exact analysis of quantization noise for Gaussian processes, and Shannon published the beginnings of rate distortion theory, which would provide a theory for quantization as analogtodigital conversion and as data compression. Beginning with these three papers of fifty years ago, we trace the history of quantization from its origins through this decade, and we survey the fundamentals of the theory and many of the popular and promising techniques for quantization.
Similarity Indexing: Algorithms and Performance
 In Proceedings SPIE Storage and Retrieval for Image and Video Databases
, 1996
"... Efficient indexing support is essential to allow contentbased image and video databases using similaritybased retrieval to scale to large databases (tens of thousands up to millions of images). In this paper, we take an in depth look at this problem. One of the major difficulties in solving this pr ..."
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Cited by 113 (1 self)
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Efficient indexing support is essential to allow contentbased image and video databases using similaritybased retrieval to scale to large databases (tens of thousands up to millions of images). In this paper, we take an in depth look at this problem. One of the major difficulties in solving this problem is the high dimension (6100) of the feature vectors that are used to represent objects. We provide an overview of the work in computational geometry on this problem and highlight the results we found are most useful in practice, including the use of approximate nearest neighbor algorithms. We also present a variant of the optimized kd tree we call the VAM kd tree, and provide algorithms to create an optimized Rtree we call the VAMSplit Rtree. We found that the VAMSplit Rtree provided better overall performance than all competing structures we tested for main memory and secondary memory applications. We observed large improvements in performance relative to the R*tree and SStree in secondary memory applications, and modest improvements relative to optimized kd tree variants.Nearest Neighbor Search
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 104 (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...
Using the Triangle Inequality to Accelerate kMeans
, 2003
"... The kmeans algorithm is by far the most widely used method for discovering clusters in data. We show how to accelerate it dramatically, while still always computing exactly the same result as the standard algorithm. The accelerated algorithm avoids unnecessary distance calculations by applying the ..."
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Cited by 104 (1 self)
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The kmeans algorithm is by far the most widely used method for discovering clusters in data. We show how to accelerate it dramatically, while still always computing exactly the same result as the standard algorithm. The accelerated algorithm avoids unnecessary distance calculations by applying the triangle inequality in two different ways, and by keeping track of lower and upper bounds for distances between points and centers. Experiments show that the new algorithm is effective for datasets with up to 1000 dimensions, and becomes more and more effective as the number k of clusters increases. For k>=20 it is many times faster than the best previously known accelerated kmeans method.
Algorithms for Fast Vector Quantization
 Proc. of DCC '93: Data Compression Conference
, 1993
"... Nearest neighbor searching is an important geometric subproblem in vector quantization. ..."
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Cited by 65 (12 self)
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Nearest neighbor searching is an important geometric subproblem in vector quantization.
Fast block matching algorithm based on the winnerupdate strategy
 IEEE Transactions on Image Processing
, 2001
"... Abstract — Block matching is a widelyused method for stereo vision, visual tracking, and video compression. Many fast algorithms for block matching have been proposed in the past, but most of them do not guarantee that the match found is the globally optimal match in a search range. This paper pres ..."
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Cited by 32 (4 self)
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Abstract — Block matching is a widelyused method for stereo vision, visual tracking, and video compression. Many fast algorithms for block matching have been proposed in the past, but most of them do not guarantee that the match found is the globally optimal match in a search range. This paper presents a new fast algorithm based on the winnerupdate strategy which utilizes an ascending lower bound list of the matching error to determine the temporary winner. Two lower bound lists derived by using partial distance and by using Minkowski’s inequality are described in this paper. The basic idea of the winnerupdate strategy is to avoid, at each search position, the costly computation of matching error when there exists a lower bound larger than the global minimum matching error. The proposed algorithm can significantly speed up the computation of the block matching because 1) computational cost of the lower bound we use is less than that of the matching error itself; 2) an element in the ascending lower bound list will be calculated only when its preceding element has already been smaller than the minimum matching error computed so far; 3) for many search positions, only the first several lower bounds in the list need to be calculated. Our experiments have shown that, when applying to motion vector estimation for several widelyused test videos, 92 % to 98 % of operations can be saved while still guaranteeing the global optimality. Moreover, the proposed algorithm can be easily modified either to meet the limited time requirement or to provide an ordered list of best candidate matches. Our source codes of the proposed algorithm are available at
Real time pattern matching using projection kernels
, 2002
"... A novel approach to pattern matching is presented, which reduces time complexity by two orders of magnitude compared to traditional approaches. The suggested approach uses an efficient projection scheme which bounds the distance between a pattern and an image window using very few operations. The pr ..."
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Cited by 20 (8 self)
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A novel approach to pattern matching is presented, which reduces time complexity by two orders of magnitude compared to traditional approaches. The suggested approach uses an efficient projection scheme which bounds the distance between a pattern and an image window using very few operations. The projection framework is combined with a rejection scheme which allows rapid rejection of image windows that are distant from the pattern. Experiments show that the approach is effective even under very noisy conditions. The approach described here can also be used in classification schemes where the projection values serve as input features that are informative and fast to extract. 1.
Normalized Partial Distortion Search Algorithm for Block. . .
, 2000
"... Many fast blockmatching algorithms reduce computations by limiting the number of checking points. They can achieve high computation reduction, but often result in relatively higher matching error compared with the fullsearch algorithm. In this letter, a novel fast blockmatching algorithm named no ..."
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Cited by 18 (0 self)
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Many fast blockmatching algorithms reduce computations by limiting the number of checking points. They can achieve high computation reduction, but often result in relatively higher matching error compared with the fullsearch algorithm. In this letter, a novel fast blockmatching algorithm named normalized partial distortion search is proposed. The proposed algorithm reduces computations by using a halfwaystop technique in the calculation of block distortion measure. In order to increase the probability of early rejection of nonpossible candidate motion vectors, the proposed algorithm normalized the accumulated partial distortion and the current minimum distortion before comparison. Experimental results show that the proposed algorithm can maintain its mean square error performance very close to the full search algorithm while achieving an average computation reduction of 1213 times, with respect to the fullsearch algorithm. I. INTRODUCTION M OTION compensation is a vital comp...
Analysis of Approximate Nearest Neighbor Searching with Clustered Point Sets.” ALENEX 99
, 1999
"... Nearest neighbor searching is the following problem: we are given a set S of n data points in a metric space, X, and are asked to preprocess these points so that, given any query point q ∈ X, the data point nearest to q can be reported quickly. Nearest neighbor searching has applications in many are ..."
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Cited by 18 (5 self)
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Nearest neighbor searching is the following problem: we are given a set S of n data points in a metric space, X, and are asked to preprocess these points so that, given any query point q ∈ X, the data point nearest to q can be reported quickly. Nearest neighbor searching has applications in many areas, including