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Searching in metric spaces
, 2001
"... The problem of searching the elements of a set that are close to a given query element under some similarity criterion has a vast number of applications in many branches of computer science, from pattern recognition to textual and multimedia information retrieval. We are interested in the rather gen ..."
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Cited by 436 (38 self)
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The problem of searching the elements of a set that are close to a given query element under some similarity criterion has a vast number of applications in many branches of computer science, from pattern recognition to textual and multimedia information retrieval. We are interested in the rather general case where the similarity criterion defines a metric space, instead of the more restricted case of a vector space. Many solutions have been proposed in different areas, in many cases without crossknowledge. Because of this, the same ideas have been reconceived several times, and very different presentations have been given for the same approaches. We present some basic results that explain the intrinsic difficulty of the search problem. This includes a quantitative definition of the elusive concept of “intrinsic dimensionality. ” We also present a unified
An Efficient kMeans Clustering Algorithm: Analysis and Implementation
, 2000
"... Kmeans clustering is a very popular clustering technique, which is used in numerous applications. Given a set of n data points in R d and an integer k, the problem is to determine a set of k points R d , called centers, so as to minimize the mean squared distance from each data point to its ..."
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Cited by 417 (4 self)
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Kmeans clustering is a very popular clustering technique, which is used in numerous applications. Given a set of n data points in R d and an integer k, the problem is to determine a set of k points R d , called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for kmeans clustering is Lloyd's algorithm. In this paper we present a simple and efficient implementation of Lloyd's kmeans clustering algorithm, which we call the filtering algorithm. This algorithm is very easy to implement. It differs from most other approaches in that it precomputes a kdtree data structure for the data points rather than the center points. We establish the practical efficiency of the filtering algorithm in two ways. First, we present a datasensitive analysis of the algorithm's running time. Second, we have implemented the algorithm and performed a number of empirical studies, both on synthetically generated data and on real...
Distance Browsing in Spatial Databases
, 1999
"... Two different techniques of browsing through a collection of spatial objects stored in an Rtree spatial data structure on the basis of their distances from an arbitrary spatial query object are compared. The conventional approach is one that makes use of a knearest neighbor algorithm where k is kn ..."
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Cited by 390 (21 self)
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Two different techniques of browsing through a collection of spatial objects stored in an Rtree spatial data structure on the basis of their distances from an arbitrary spatial query object are compared. The conventional approach is one that makes use of a knearest neighbor algorithm where k is known prior to the invocation of the algorithm. Thus if m#kneighbors are needed, the knearest neighbor algorithm needs to be reinvoked for m neighbors, thereby possibly performing some redundant computations. The second approach is incremental in the sense that having obtained the k nearest neighbors, the k +1 st neighbor can be obtained without having to calculate the k +1nearest neighbors from scratch. The incremental approach finds use when processing complex queries where one of the conditions involves spatial proximity (e.g., the nearest city to Chicago with population greater than a million), in which case a query engine can make use of a pipelined strategy. A general incremental nearest neighbor algorithm is presented that is applicable to a large class of hierarchical spatial data structures. This algorithm is adapted to the Rtree and its performance is compared to an existing knearest neighbor algorithm for Rtrees [45]. Experiments show that the incremental nearest neighbor algorithm significantly outperforms the knearest neighbor algorithm for distance browsing queries in a spatial database that uses the Rtree as a spatial index. Moreover, the incremental nearest neighbor algorithm also usually outperforms the knearest neighbor algorithm when applied to the knearest neighbor problem for the Rtree, although the improvement is not nearly as large as for distance browsing queries. In fact, we prove informally that, at any step in its execution, the incremental...
RapidlyExploring Random Trees: Progress and Prospects
 Algorithmic and Computational Robotics: New Directions
, 2000
"... this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints. ..."
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Cited by 333 (20 self)
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this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints.
Building rome in a day.
 In Proc. Int. Conf. on Computer Vision.
, 2009
"... We present a system that can reconstruct 3D geometry from large, unorganized collections of photographs such as those found by searching for a given city (e.g., Rome) on Internet photosharing sites. Our system is built on a set of new, distributed computer vision algorithms for image matching and ..."
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Cited by 285 (30 self)
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We present a system that can reconstruct 3D geometry from large, unorganized collections of photographs such as those found by searching for a given city (e.g., Rome) on Internet photosharing sites. Our system is built on a set of new, distributed computer vision algorithms for image matching and 3D reconstruction, designed to maximize parallelism at each stage of the pipeline and to scale gracefully with both the size of the problem and the amount of available computation. Our experimental results demonstrate that it is now possible to reconstruct cityscale image collections with more than a hundred thousand images in less than a day. intRoDuction Amateur photography was once largely a personal endeavor. Traditionally, a photographer would capture a moment on film and share it with a small number of friends and family members, perhaps storing a few hundred of them in a shoebox. The advent of digital photography, and the recent growth of photosharing Web sites such as Flickr.com, have brought about a seismic change in photography and the use of photo collections. Today, a photograph shared online can potentially be seen by millions of people. As a result, we now have access to a vast, evergrowing collection of photographs the world over capturing its cities and landmarks innumerable times. For instance, a search for the term "Rome" on Flickr returns nearly 3 million photographs. This collection represents an increasingly complete photographic record of the city, capturing every popular site, façade, interior, fountain, sculpture, painting, and café. Virtually anything that people find interesting in Rome has been captured from thousands of viewpoints and under myriad illumination and weather conditions. For example, the Trevi Fountain appears in over 50,000 of these photographs. How much of the city of Rome can be reconstructed in 3D from this photo collection? In principle, the photos of Rome on Flickr represent an ideal data set for 3D modeling research, as they capture the highlights of the city in exquisite detail and from a broad range of viewpoints. However, extracting high quality 3D models from such a collection is challenging for several reasons. First, the photos are unstructuredthey are taken in no particular order and we have no control over the distribution of camera viewpoints. Second, they are uncalibratedthe photos are taken by thousands of different photographers and we know very little about the camera settings. Third, the scale of the problem is
Modeling the World from Internet Photo Collections
 INT J COMPUT VIS
, 2007
"... There are billions of photographs on the Internet, comprising the largest and most diverse photo collection ever assembled. How can computer vision researchers exploit this imagery? This paper explores this question from the standpoint of 3D scene modeling and visualization. We present structurefro ..."
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Cited by 267 (6 self)
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There are billions of photographs on the Internet, comprising the largest and most diverse photo collection ever assembled. How can computer vision researchers exploit this imagery? This paper explores this question from the standpoint of 3D scene modeling and visualization. We present structurefrommotion and imagebased rendering algorithms that operate on hundreds of images downloaded as a result of keywordbased image search queries like “Notre Dame ” or “Trevi Fountain.” This approach, which we call Photo Tourism, has enabled reconstructions of numerous wellknown world sites. This paper presents these algorithms and results as a first step towards 3D modeling of the world’s wellphotographed sites, cities, and landscapes from Internet imagery, and discusses key open problems and challenges for the research community.
Geometric Range Searching and Its Relatives
 CONTEMPORARY MATHEMATICS
"... ... process a set S of points in so that the points of S lying inside a query R region can be reported or counted quickly. Wesurvey the known techniques and data structures for range searching and describe their application to other related searching problems. ..."
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Cited by 266 (39 self)
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... process a set S of points in so that the points of S lying inside a query R region can be reported or counted quickly. Wesurvey the known techniques and data structures for range searching and describe their application to other related searching problems.
Cover trees for nearest neighbor
 In Proceedings of the 23rd international conference on Machine learning
, 2006
"... ABSTRACT. We present a tree data structure for fast nearest neighbor operations in generalpoint metric spaces. The data structure requires space regardless of the metric’s structure. If the point set has an expansion constant � in the sense of Karger and Ruhl [KR02], the data structure can be const ..."
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Cited by 218 (0 self)
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ABSTRACT. We present a tree data structure for fast nearest neighbor operations in generalpoint metric spaces. The data structure requires space regardless of the metric’s structure. If the point set has an expansion constant � in the sense of Karger and Ruhl [KR02], the data structure can be constructed in � time. Nearest neighbor queries obeying the expansion bound require � time. In addition, the nearest neighbor of points can be queried in time. We experimentally test the algorithm showing speedups over the brute force search varying between 1 and 2000 on natural machine learning datasets. 1.