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 easy-to-compute 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 color-distribution and texture spaces by means of Multi-Dimensional 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

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...

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

... 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 Multi-Dimensional Scaling techniques to embed a group of images as points in a two- or three-dimensional 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 mug-shot retrieval.

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 multi-dimensional scaling (MDS) techniques to embed a group of images as points in a two- or three-dimensional 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 2-d MDS embeddings can be used to organize and re ne the results of a nearest-neighbor 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

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

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 on-board 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

DRAFT We propose EMD-L1: 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 EMD-L1 significantly simplifies the original linear programming formulation of EMD. Exploiting the L1 metric structure, the number of unknown variables in EMD-L1 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 EMD-L1 formulation is equivalent to the original EMD with a L1 ground distance. To perform the EMD-L1 computation, we propose an efficient tree-based algorithm, Tree-EMD. Tree-EMD exploits the fact that a basic feasible solution of the simplex algorithm-based solver forms a spanning tree when we interpret EMD-L1 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 super-cubic complexity of the original EMD. The accuracy of the proposed methods is evaluated by

We present a new algorithm for a robust family of Earth Mover’s Distances- EMDs with thresholded ground distances. The algorithm transforms the flow-network 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.

For the sake of classification, spectra are traditionally represented by points in a high-dimensional feature space, spanned by spectral bands. An alternative approach is to represent spectra by dissimilarities to other spectra. This relational representation enables one to treat spectra as connected entities and to emphasize characteristics such as shape, which are difficult to handle in the traditional approach. Several classification methods for relational representations were developed and found to outperform the nearest-neighbor rule. Existing studies focus only on the performance measured by the classification error. However, for real-time spectral imaging applications, classification speed is of crucial importance. Therefore, in this paper, we focus on the computational aspects of the on-line classification of spectra. We show, that classifiers built in dissimilarity spaces may also be applied significantly faster than the nearest-neighbor rule. r 2003 Elsevier Ltd. All rights reserved. 1.