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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 776 (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.
A Quantitative Analysis and Performance Study for SimilaritySearch Methods in HighDimensional Spaces
, 1998
"... For similarity search in highdimensional vector spaces (or `HDVSs'), researchers have proposed a number of new methods (or adaptations of existing methods) based, in the main, on dataspace partitioning. However, the performance of these methods generally degrades as dimensionality increases. Altho ..."
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Cited by 487 (12 self)
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For similarity search in highdimensional vector spaces (or `HDVSs'), researchers have proposed a number of new methods (or adaptations of existing methods) based, in the main, on dataspace partitioning. However, the performance of these methods generally degrades as dimensionality increases. Although this phenomenonknown as the `dimensional curse'is well known, little or no quantitative analysis of the phenomenon is available. In this paper, we provide a detailed analysis of partitioning and clustering techniques for similarity search in HDVSs. We show formally that these methods exhibit linear complexity at high dimensionality, and that existing methods are outperformed on average by a simple sequential scan if the number of dimensions exceeds around 10. Consequently, we come up with an alternative organization based on approximations to make the unavoidable sequential scan as fast as possible. We describe a simple vector approximation scheme, called VAfile, and report on an ...
Photon Mapping on Programmable Graphics Hardware
 GRAPHICS HARDWARE
, 2003
"... We present a modified photon mapping algorithm capable of running entirely on GPUs. Our implementation uses breadthfirst photon tracing to distribute photons using the GPU. The photons are stored in a gridbased photon map that is constructed directly on the graphics hardware using one of two met ..."
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Cited by 125 (4 self)
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We present a modified photon mapping algorithm capable of running entirely on GPUs. Our implementation uses breadthfirst photon tracing to distribute photons using the GPU. The photons are stored in a gridbased photon map that is constructed directly on the graphics hardware using one of two methods: the first method is a multipass technique that uses fragment programs to directly sort the photons into a compact grid. The second method uses a single rendering pass combining a vertex program and the stencil buffer to route photons to their respective grid cells, producing an approximate photon map. We also present an efficient method for locating the nearest photons in the grid, which makes it possible to compute an estimate of the radiance at any surface location in the scene. Finally, we describe a breadthfirst stochastic ray tracer that uses the photon map to simulate full global illumination directly on the graphics hardware. Our implementation demonstrates that current graphics hardware is capable of fully simulating global illumination with progressive, interactive feedback to the user.
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 111 (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 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...
Accounting for Boundary Effects in Nearest Neighbor Searching
, 1995
"... Given n data points in ddimensional space, nearest neighbor searching involves determining the nearest of these data points to a given query point. Most averagecase analyses of nearest neighbor searching algorithms are made under the simplifying assumption that d is fixed and that n is so large rel ..."
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Cited by 33 (4 self)
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Given n data points in ddimensional space, nearest neighbor searching involves determining the nearest of these data points to a given query point. Most averagecase analyses of nearest neighbor searching algorithms are made under the simplifying assumption that d is fixed and that n is so large relative to d that boundary effects can be ignored. This means that for any query point the statistical distribution of the data points surrounding it is independent of the location of the query point. However, in many applications of nearest neighbor searching (such as data compression by vector quantization) this assumption is not met, since the number of data points n grows roughly as 2^d. Largely for this reason, the actual performances of many nearest neighbor algorithms tend to be much better than their theoretical analyses would suggest. We present evidence of why this is the case. We provide an accurate analysis of the number of cells visited in nearest neighbor searching by the buck...
An Efficient Cost Model for Optimization of Nearest Neighbor Search in Low and Medium Dimensional Spaces
 IEEE TKDE
, 2004
"... Existing models for nearest neighbor search in multidimensional spaces are not appropriate for query optimization because they either lead to erroneous estimation, or involve complex equations that are expensive to evaluate in realtime. This paper proposes an alternative method that captures the p ..."
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Cited by 21 (2 self)
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Existing models for nearest neighbor search in multidimensional spaces are not appropriate for query optimization because they either lead to erroneous estimation, or involve complex equations that are expensive to evaluate in realtime. This paper proposes an alternative method that captures the performance of nearest neighbor queries using approximation. For uniform data, our model involves closed formulae that are very efficient to compute and accurate for up to 10 dimensions. Further, the proposed equations can be applied on nonuniform data with the aid of histograms. We demonstrate the effectiveness of the model by using it to solve several optimization problems related to nearest neighbor search. To appear in IEEE TKDE
An ApproximationBased Data Structure for Similarity Search
, 1997
"... Many similarity measures for multimedia retrieval, decision support, and data mining are based on underlying vector spaces of high dimensionality. Datapartitioning index methods for such spaces (e.g. gridfiles, quadtrees, Rtrees, Xtrees, etc.) generally work well for lowdimensional spaces, but ..."
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Cited by 17 (0 self)
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Many similarity measures for multimedia retrieval, decision support, and data mining are based on underlying vector spaces of high dimensionality. Datapartitioning index methods for such spaces (e.g. gridfiles, quadtrees, Rtrees, Xtrees, etc.) generally work well for lowdimensional spaces, but perform poorly as dimensionality increasesa phenomenon which has become known as the `dimensional curse'. In this paper, we first provide an analysis of the nearestneighbor search problem in highdimensional vector spaces. Under the assumptions of uniformity and independence, we establish bounds on the average performance of three important classes of datapartitioning techniques. We then introduce the vectorapproximation file (VAFile), a method which overcomes the difficulties of high dimensionality by following not the datapartitioning approach of conventional index methods, but rather a filterbased approach. A VAFile contains a compact, geometric approximation for each vector. By...
The SS+tree: An Improved Index Structure for Similarity Searches in a HighDimensional Feature Space
 Proc. of SPIE/IS&T Conf. on Storage and Retrieval for Image and Video Databases V
, 1997
"... In this paper, we describe the SS + tree, a tree structure for supporting similarity searches in a highdimensional Euclidean space. Compared to the SStree, the tree uses a tighter bounding sphere for each node which is an approximation to the smallest enclosing sphere and it also makes a better ..."
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Cited by 14 (2 self)
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In this paper, we describe the SS + tree, a tree structure for supporting similarity searches in a highdimensional Euclidean space. Compared to the SStree, the tree uses a tighter bounding sphere for each node which is an approximation to the smallest enclosing sphere and it also makes a better use of the clustering property of the available data by using a variant of the kmeans clustering algorithm as the split heuristic for its nodes. A local reorganization rule is also introduced during the tree building to reduce the overlapping between the nodes' bounding spheres. Keywords: highdimensional indexing and retrieval, similarity search, multimedia databases, enclosing spheres, enclosing boxes (MBR) 1. INTRODUCTION Representing images by a vector of features is a useful approach to handling the retrieval of images from image databases. 10,17,19 Under such a scheme, similarity searches can be performed by using the Euclidean distance between two vectors as a measure of dissim...
3D Modeling of Optically Challenging Objects
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS (TVCG
, 2008
"... We present a system for constructing 3D models of realworld objects with optically challenging surfaces. The system utilizes a new range imaging concept called multipeak range imaging, which stores multiple candidates of range measurements for each point on the object surface. The multiple measure ..."
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Cited by 11 (0 self)
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We present a system for constructing 3D models of realworld objects with optically challenging surfaces. The system utilizes a new range imaging concept called multipeak range imaging, which stores multiple candidates of range measurements for each point on the object surface. The multiple measurements include the erroneous range data caused by various surface properties that are not ideal for structuredlight range sensing. False measurements generated by spurious reflections are eliminated by applying a series of constraint tests. The constraint tests based on local surface and local sensor visibility are applied first to individual range images. The constraint tests based on global consistency of coordinates and visibility are then applied to all range images acquired from different viewpoints. We show the effectiveness of our method by constructing 3D models of five different optically challenging objects. To evaluate the performance of the constraint tests and to examine the effects of the parameters used in the constraint tests, we acquired the groundtruth data by painting those objects to suppress the surfacerelated properties that cause difficulties in range sensing. Experimental results indicate that our method significantly improves upon the traditional methods for constructing reliable 3D models of optically challenging objects.