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 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

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.

: In this report, we focus on robust image retrieval. We first describe why robustness is of importance in this kind of search. Then we propose a very general architecture based on three steps. As an assumption, we assume that any image of the database is characterized by a set of features (each feature resulting in a statistical distribution of a particular measure over the image). The first step of the process consists in computing, for any characteristic, a similarity/dissimilarity measure between the distribution related to the image request and those of the images in the database. This results in a set of scalar values that have to be summarize in a 1D value in order to easily sort the image with respect to the request. This is what the second step is about. Even when powerful tools (i.e. robust: : : ) are used, given the m best matches, it can happen that part of the answers is not satisfactory. Therefore the third step intends to increase the robustness of the overall process u...

The role of indexing in query optimization is well-understood in the database community. Indexes enable efficient access to a subset of a database. There have been many studies on indexing within the context of relational database management systems (RDBMS). The most popular indexing techniques are based on B-trees [1]. However, these index structures do not apply for images in Multimedia Database Systems (MMDBS). Some novel index structures to retrieve images have been proposed. In this report 1 , we discuss some issues concerning these advanced indexing techniques, and report the results. 1 This research has been supported by a grant from the Canadian Institute for Telecommunication Research (CITR), a Federal Network of Centre of Excellence funded by the Government of Canada. Contents 1 Introduction 4 2 Image representations 5 2.1 Texture features : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.2 Color features : : : : : : : : : : : : : : : : : :...

In medical imaging applications such as ultrasound, it is often required to segment the image to determine its meaningful parts. Segmentation may be simple differentiation between the background and the object, or more complexly, distinguishing different objects or parts of objects within each image. There are many methods available for segmenting an image. The number of these methods applicable to segmenting 2D ultrasound images is significantly reduced because of the presence of noise. It was found experimentally that textures detectable in ultrasound images are more appropriate features for segmentation than simple edges. Detection of edges is profoundly affected by the presence of noise. A segmentation algorithm based on texture discrimination is presented in this thesis. This algorithm uses a constrained optimization approach to produce a segmentation. Because this algorithm can not deal with varying texture region sizes effectively a multiresolution algorithm is developed. This...

The compass operator has proven to be a useful tool for the detection of color edges in real images. Its fundamental contribution is the comparison of oriented distributions of image features over a local area at each pixel.