Results 1  10
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27
A metric for distributions with applications to image databases
, 1998
"... We introduce a new distance between two distributions that we call the Earth Mover’s Distance (EMD), which reflects the minimal amount of work that must be performed to transform one distributioninto the other by moving “distribution mass ” around. This is a special case of the transportation proble ..."
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Cited by 311 (4 self)
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We introduce a new distance between two distributions that we call the Earth Mover’s Distance (EMD), which reflects the minimal amount of work that must be performed to transform one distributioninto the other by moving “distribution mass ” around. This is a special case of the transportation problem from linear optimization, for which efficient algorithms are available. The EMD also allows for partial matching. When used to compare distributions that have the same overall mass, the EMD is a true metric, and has easytocompute lower bounds. In this paper we focus on applications to image databases, especially color and texture. We use the EMD to exhibit the structure of colordistribution and texture spaces by means of MultiDimensional Scaling displays. We also propose a novel approach to the problem of navigating through a collection of color images, which leads to a new paradigm for image database search. 1
Shape Distributions
 ACM Transactions on Graphics
, 2002
"... this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The pr ..."
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Cited by 192 (0 self)
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this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is simpler than traditional shape matching methods that require pose registration, feature correspondence, or model fitting
Matching 3D Models with Shape Distributions
"... Measuring the similarity between 3D shapes is a fundamental problem, with applications in computer vision, molecular biology, computer graphics, and a variety of other fields. A challenging aspect of this problem is to find a suitable shape signature that can be constructed and compared quickly, whi ..."
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Cited by 172 (7 self)
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Measuring the similarity between 3D shapes is a fundamental problem, with applications in computer vision, molecular biology, computer graphics, and a variety of other fields. A challenging aspect of this problem is to find a suitable shape signature that can be constructed and compared quickly, while still discriminating between similar and dissimilar shapes. In this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is a simpler problem than the comparison of 3D surfaces by traditional shape matching methods that require pose registration, feature correspondence, or model fitting. We find that the dissimilarities be...
Perceptual Metrics For Image Database Navigation
, 1999
"... ... This metric, which we call the "Earth Mover's Distance" (EMD), represents the least amount of work that is needed to rearrange the mass is one distribution in order to obtain the other. We show that the EMD matches perceptual dissimilarity better than other dissimilarity measures, and argue that ..."
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Cited by 75 (3 self)
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... This metric, which we call the "Earth Mover's Distance" (EMD), represents the least amount of work that is needed to rearrange the mass is one distribution in order to obtain the other. We show that the EMD matches perceptual dissimilarity better than other dissimilarity measures, and argue that it has many desirable properties for image retrieval. Using this metric, we employ MultiDimensional Scaling techniques to embed a group of images as points in a two or threedimensional Euclidean space so that their distances reflect image dissimilarities as well as possible. Such geometric embeddings exhibit the structure in the image set at hand, allowing the user to understand better the result of a database query and to refine the query in a perceptually intuitiveway. By iterating this process, the user can quickly zoom in to the portion of the image space of interest. We also apply these techniques to other modalities such as mugshot retrieval.
The earth mover’s distance, multidimensional scaling, and colorbased image retrieval
 in Proceedings of the ARPA Image Understanding Workshop
, 1997
"... In this paper we present a novel approach tothe problem of navigating through a database of color images. We consider the images as points in a metric space in which we wish to move around so as to locate image neighborhoods of interest, based on color information. The data base images are mapped to ..."
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Cited by 65 (2 self)
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In this paper we present a novel approach tothe problem of navigating through a database of color images. We consider the images as points in a metric space in which we wish to move around so as to locate image neighborhoods of interest, based on color information. The data base images are mapped to distributions in color space, these distributions are appropriately compressed, and then the distances between all pairs I;J of images are computed based on the work needed to rearrange the mass in the compressed distribution representing I to that of J. We also propose the use of multidimensional scaling (MDS) techniques to embed a group of images as points in a two or threedimensional Euclidean space so that their distances are preserved as much as possible. Such geometric embeddings allow the user to perceive the dominant axes of variation in the displayed image group. In particular, displays of 2d MDS embeddings can be used to organize and re ne the results of a nearestneighbor query in a perceptually intuitive way. By iterating this process, the user is able to quickly navigate to the portion of the image space of interest. 1
A survey of shape similarity assessment algorithms for product design and manufacturing applications
 Journal of Computing and Information Science in Engineering
, 2003
"... This document contains the draft version of the following paper: A. Cardone, S.K. Gupta, and M. Karnik. A survey of shape similarity assessment algorithms for product design and manufacturing applications. ASME Journal of ..."
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Cited by 45 (13 self)
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This document contains the draft version of the following paper: A. Cardone, S.K. Gupta, and M. Karnik. A survey of shape similarity assessment algorithms for product design and manufacturing applications. ASME Journal of
An efficient earth mover’s distance algorithm for robust histogram comparison
 PAMI
, 2007
"... DRAFT We propose EMDL1: a fast and exact algorithm for computing the Earth Mover’s Distance (EMD) between a pair of histograms. The efficiency of the new algorithm enables its application to problems that were previously prohibitive due to high time complexities. The proposed EMDL1 significantly s ..."
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Cited by 44 (4 self)
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DRAFT We propose EMDL1: a fast and exact algorithm for computing the Earth Mover’s Distance (EMD) between a pair of histograms. The efficiency of the new algorithm enables its application to problems that were previously prohibitive due to high time complexities. The proposed EMDL1 significantly simplifies the original linear programming formulation of EMD. Exploiting the L1 metric structure, the number of unknown variables in EMDL1 is reduced to O(N) from O(N 2) of the original EMD for a histogram with N bins. In addition, the number of constraints is reduced by half and the objective function of the linear program is simplified. Formally without any approximation, we prove that the EMDL1 formulation is equivalent to the original EMD with a L1 ground distance. To perform the EMDL1 computation, we propose an efficient treebased algorithm, TreeEMD. TreeEMD exploits the fact that a basic feasible solution of the simplex algorithmbased solver forms a spanning tree when we interpret EMDL1 as a network flow optimization problem. We empirically show that this new algorithm has average time complexity of O(N 2), which significantly improves the best reported supercubic complexity of the original EMD. The accuracy of the proposed methods is evaluated by
Fast and Robust Earth Mover’s Distances
"... We present a new algorithm for a robust family of Earth Mover’s Distances EMDs with thresholded ground distances. The algorithm transforms the flownetwork of the EMD so that the number of edges is reduced by an order of magnitude. As a result, we compute the EMD by an order of magnitude faster tha ..."
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Cited by 32 (6 self)
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We present a new algorithm for a robust family of Earth Mover’s Distances EMDs with thresholded ground distances. The algorithm transforms the flownetwork of the EMD so that the number of edges is reduced by an order of magnitude. As a result, we compute the EMD by an order of magnitude faster than the original algorithm, which makes it possible to compute the EMD on large histograms and databases. In addition, we show that EMDs with thresholded ground distances have many desirable properties. First, they correspond to the way humans perceive distances. Second, they are robust to outlier noise and quantization effects. Third, they are metrics. Finally, experimental results on image retrieval show that thresholding the ground distance of the EMD improves both accuracy and speed. 1.
Topological mobile robot localization using fast vision techniques
 In IEEE International Conference on Robotics and Automation
, 2002
"... In this paper we present a system for topologically localizing a mobile robot using color histogram matching of omnidirectional images. The system is intended for use as a navigational tool for the Autonomous Vehicle for Exploration and Navigation of Urban Environments (AVENUE) mobile robot. Our met ..."
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Cited by 29 (2 self)
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In this paper we present a system for topologically localizing a mobile robot using color histogram matching of omnidirectional images. The system is intended for use as a navigational tool for the Autonomous Vehicle for Exploration and Navigation of Urban Environments (AVENUE) mobile robot. Our method makes use of omnidirectional images which are acquired from the robot’s onboard camera. The method is fast and rotation invariant. Our tests have indicated that normalized color histograms are best for an outdoor environment while normalization is not required for indoor work. The system quickly narrows down the robot’s location to one or two regions within the much larger test environment. Using this regional localization information, other vision systems that we have developed can further localize the robot. 1
Approximate earth mover’s distance in linear time
"... The earth mover’s distance (EMD) [16] is an important perceptually meaningful metric for comparing histograms, butitsuffersfromhigh(O(N 3 log N))computationalcomplexity. We present a novel linear time algorithm for approximating the EMD for low dimensional histograms using the sum of absolute values ..."
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Cited by 18 (0 self)
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The earth mover’s distance (EMD) [16] is an important perceptually meaningful metric for comparing histograms, butitsuffersfromhigh(O(N 3 log N))computationalcomplexity. We present a novel linear time algorithm for approximating the EMD for low dimensional histograms using the sum of absolute values of the weighted wavelet coefficients of the difference histogram. EMD computation is aspecialcaseoftheKantorovichRubinsteintransshipment problem, andweexploittheHölder continuityconstraintin its dual form to convert it into a simple optimization problem with an explicit solution in the wavelet domain. We prove that the resulting wavelet EMD metric is equivalent to EMD, i.e. the ratio of the two is bounded. We also provide estimates for the bounds. Theweightedwavelettransformcanbecomputedintime linear in the number of histogram bins, while the comparison is about as fast as for normal Euclidean distance or χ 2 statistic. WeexperimentallyshowthatwaveletEMDisa good approximation to EMD, has similar performance, but requires much less computation. 1.