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Finding color and shape patterns in images

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The Earth Mover's Distance : lower bounds and invariance under translation

Abstract: "The Earth Mover's Distance (EMD) between two finite distributions of weight is proportional to the minimum amount of work required to transform one distribution into the other. Current content-based retrieval work in the Stanford Vision Laboratory uses the EMD as a common framework for measuring image similarity with respect to color, texture, and shape content. In this report, we present some fast to compute lower bounds on the EMD which may allow a system to avoid exact, more expensive EMD computations during query processing. The effectiveness of the lower bounds is tested in a color-based retrieval system. In addition to the lower bound work, we also show how to compute the EMD under translation. In this problem, the points in one distribution are free to translate, and the goal is to find a translation that minimizes the EMD to the other distribution."

Finding color and shape patterns in images [electronic resource]

"This thesis is devoted to the Earth Mover's Distance (EMD), an edit distance between distributions, and its use within content-based image retrieval (CBIR). The major CBIR problem discussed is the pattern problem: Given an image and a query pattern, determine if the image contains a region which is visually similar to the pattern; if so, find at least one such image region. An important problem that arises in applying the EMD to CBIR is the EMD under transformation (EMD%5FG) problem: find a transformation of one distribution which minimizes its EMD to another, where the set of allowable transformations G is given. The problem of estimating the size/scale at which a pattern occurs in an image is phrased and efficiently solved as an EMD%5FG problem. For a large class of transformation sets, we also present a monotonically convergent iteration to find at least a locally optimal transformation. Our pattern problem solution is the SEDL (Scale Estimation for Directed Location) image retrieval system. Three important contributions of SEDL are (1) a general framework for finding both color and shape patterns, (2) the previously mentioned scale estimation algorithm using the EMD, and (3) a directed (as opposed to exhaustive) search strategy."--Abstract.

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