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97
Similarity estimation techniques from rounding algorithms
 In Proc. of 34th STOC
, 2002
"... A locality sensitive hashing scheme is a distribution on a family F of hash functions operating on a collection of objects, such that for two objects x, y, Prh∈F[h(x) = h(y)] = sim(x,y), where sim(x,y) ∈ [0, 1] is some similarity function defined on the collection of objects. Such a scheme leads ..."
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Cited by 448 (6 self)
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A locality sensitive hashing scheme is a distribution on a family F of hash functions operating on a collection of objects, such that for two objects x, y, Prh∈F[h(x) = h(y)] = sim(x,y), where sim(x,y) ∈ [0, 1] is some similarity function defined on the collection of objects. Such a scheme leads to a compact representation of objects so that similarity of objects can be estimated from their compact sketches, and also leads to efficient algorithms for approximate nearest neighbor search and clustering. Minwise independent permutations provide an elegant construction of such a locality sensitive hashing scheme for a collection of subsets with the set similarity measure sim(A, B) = A∩B A∪B . We show that rounding algorithms for LPs and SDPs used in the context of approximation algorithms can be viewed as locality sensitive hashing schemes for several interesting collections of objects. Based on this insight, we construct new locality sensitive hashing schemes for: 1. A collection of vectors with the distance between ⃗u and ⃗v measured by θ(⃗u,⃗v)/π, where θ(⃗u,⃗v) is the angle between ⃗u and ⃗v. This yields a sketching scheme for estimating the cosine similarity measure between two vectors, as well as a simple alternative to minwise independent permutations for estimating set similarity. 2. A collection of distributions on n points in a metric space, with distance between distributions measured by the Earth Mover Distance (EMD), (a popular distance measure in graphics and vision). Our hash functions map distributions to points in the metric space such that, for distributions P and Q,
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 96 (5 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
Optimal mass transport for registration and warping
 International Journal on Computer Vision
, 2004
"... Image registration is the process of establishing a common geometric reference frame between two or more image data sets possibly taken at different times. In this paper we present a method for computing elastic registration and warping maps based on the Monge–Kantorovich theory of optimal mass tran ..."
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Cited by 58 (9 self)
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Image registration is the process of establishing a common geometric reference frame between two or more image data sets possibly taken at different times. In this paper we present a method for computing elastic registration and warping maps based on the Monge–Kantorovich theory of optimal mass transport. This mass transport method has a number of important characteristics. First, it is parameter free. Moreover, it utilizes all of the grayscale data in both images, places the two images on equal footing and is symmetrical: the optimal mapping from image to ¡ image being the inverse of the optimal mapping ¡ from to £ ¢ The method does not require that landmarks be specified, and the minimizer of the distance functional involved is unique; there are no other local minimizers. Finally, optimal transport naturally takes into account changes in density that result from changes in area or volume. Although the optimal transport method is certainly not appropriate for all registration and warping problems, this mass preservation property makes the MongeKantorovich approach quite useful for an interesting class of warping problems, as we show in this paper. Our method for finding the registration mapping is based on a partial differential equation approach to the minimization of ¤¦ ¥ the Kantorovich–Wasserstein or “Earth Mover’s Distance ” under a mass preservation constraint. We show how this approach leads to practical algorithms, and demonstrate our method with a number of examples, including those from the medical field. We also extended this method to take into account changes in intensity, and show that it is well suited for applications such as image morphing. A. Image Registration I.
Visualization & UserModeling for Browsing Personal Photo Libraries
 International Journal of Computer Vision
, 2004
"... We present a usercentric system for visualization and layout for contentbased image retrieval. Image features (visual and/or semantic) are used to display retrievals as thumbnails in a 2D spatial layout or "configuration" which conveys all pairwise mutual similarities. A graphical opti ..."
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Cited by 35 (0 self)
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We present a usercentric system for visualization and layout for contentbased image retrieval. Image features (visual and/or semantic) are used to display retrievals as thumbnails in a 2D spatial layout or "configuration" which conveys all pairwise mutual similarities. A graphical optimization technique is used to provide maximally uncluttered and informative layouts. Moreover, a novel subspace feature weighting technique can be used to modify 2D layouts in a variety of contextdependent ways. An efficient computational technique for subspace weighting and reestimation leads to a simple usermodeling framework whereby the system can learn to display query results based on layout examples (or relevance feedback) as provided by the user. The resulting retrieval, browsing and visualization engine can adapt to the users' (timevarying) notions of content, context and preferences in presentation style and interactive navigation. Monte Carlo simulations with machinegenerated layouts as well as pilot user studies have demonstrated the ability of this framework to model or "mimic" users, by automatically generating layouts according to their preferences.
RETIN: A contentbased image indexing and retrieval system
, 2001
"... This paper presents RETIN, a new system for automatic image indexing and interactive contentbased image retrieval. The most original aspect of our work rests on the distance computation and its adjustment by relevance feedback. First of all, during an offline stage, the indexes are computed from a ..."
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Cited by 19 (10 self)
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This paper presents RETIN, a new system for automatic image indexing and interactive contentbased image retrieval. The most original aspect of our work rests on the distance computation and its adjustment by relevance feedback. First of all, during an offline stage, the indexes are computed from attribute vectors associated to image pixels. The feature spaces are partitioned through an unsupervised classification and then, thanks to these partitions, statistical distributions are processed for each image. During the online use of the system, the user makes an iconic request, i.e. he brings an example of the type of image he is looking for. The query may be global or partial, since the user can reduce his/her request to a region of interest. The comparison between the query distribution and that of every image in the collection, is carried out by using a weighted dissimilarity function which manages the use of several attributes. The results of the search are then refined by means of relevance feedback which tunes the weights of the dissimilarity metric via user interaction. Experiments are then performed on large databases and statistical quality assessment shows the good properties of RETIN for digital image retrieval. The evaluation also shows that relevance feedback brings flexibility and robustness to the search.
Differential Earth Mover’s Distance with Its Applications to Visual Tracking
"... The Earth Mover’s Distance (EMD) is a similarity measure that captures perceptual difference between two distributions. Its computational complexity, however, prevents a direct use in many applications. This paper proposes a novel Differential EMD (DEMD) algorithm based on the sensitivity analysis o ..."
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Cited by 17 (0 self)
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The Earth Mover’s Distance (EMD) is a similarity measure that captures perceptual difference between two distributions. Its computational complexity, however, prevents a direct use in many applications. This paper proposes a novel Differential EMD (DEMD) algorithm based on the sensitivity analysis of the simplex method, and offers a speedup at orders of magnitude compared with its brute force counterparts. The DEMD algorithm is discussed and empirically verified in the visual tracking context. The deformations of the distributions for objects at different time instances are accommodated well by the EMD, and the differential algorithm makes the use of EMD in realtime tracking possible. To further reduce the computation, signatures, i.e., variablesize descriptions of distributions, are employed as an object representation. The new algorithm models and estimates local background scenes as well as foreground objects to handle scale changes in a principled way. Extensive quantitative evaluation of the proposed algorithm has been carried out using benchmark sequences and the improvement over the standard Mean Shift tracker is demonstrated.
Mental Image Search by Boolean Composition of Region Categories
 Multimedia Tools and Applications
, 2004
"... Existing contentbased image retrieval paradigms almost never address the problem of starting the search, when the user has no starting example image but rather a mental image. ..."
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Cited by 17 (2 self)
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Existing contentbased image retrieval paradigms almost never address the problem of starting the search, when the user has no starting example image but rather a mental image.
The Analysis and Applications of AdaptiveBinning Color Histograms
"... Histograms are commonly used in contentbased image retrieval systems to represent the distributions of colors in images. It is a common understanding that histograms that adapt to images can represent their color distributions more efficiently than do histograms with fixed binnings. However, exi ..."
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Cited by 15 (1 self)
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Histograms are commonly used in contentbased image retrieval systems to represent the distributions of colors in images. It is a common understanding that histograms that adapt to images can represent their color distributions more efficiently than do histograms with fixed binnings. However, existing systems almost exclusively adopt fixedbinning histograms because, among existing wellknown dissimilarity measures, only the computationally expensive Earth Mover's Distance (EMD) can compare histograms with different binnings. This article addresses the issue by defining a new dissimilarity measure that is more reliable than the Euclidean distance and yet computationally less expensive than EMD. Moreover, a mathematically sound definition of mean histogram can be defined for histogram clustering applications. Extensive test results show that adaptive histograms produce the best overall performance, in terms of good accuracy, small number of bins, no empty bin, and efficient computation, compared to existing methods for histogram retrieval, classification, and clustering tasks.
An Image Morphing Technique Based on Optimal Mass Preserving Mapping
 IEEE Transactions on Image Processing
, 2007
"... Abstract—Image morphing, or image interpolation in the time domain, deals with the metamorphosis of one image into another. In this paper, a new class of image morphing algorithms is proposed based on the theory of optimal mass transport. The 2 mass moving energy functional is modified by adding an ..."
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Cited by 14 (0 self)
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Abstract—Image morphing, or image interpolation in the time domain, deals with the metamorphosis of one image into another. In this paper, a new class of image morphing algorithms is proposed based on the theory of optimal mass transport. The 2 mass moving energy functional is modified by adding an intensity penalizing term, in order to reduce the undesired double exposure effect. It is an intensitybased approach and, thus, is parameter free. The optimal warping function is computed using an iterative gradient descent approach. This proposed morphing method is also extended to doubly connected domains using a harmonic parameterization technique, along with finiteelement methods. Index Terms—Image interpolation, image morphing, image warping, mass preserving mapping, Monge–Kantorovich flow, optimal transport. I.