Fast Contour Matching Using Approximate Earth Mover's Distance

Abstract

Weighted graph matching is a good way to align a pair of shapesrepresented by a set of descriptive local features; the set ofcorrespondences produced by the minimum cost of matching features fromone shape to the features of the other often reveals how similar thetwo shapes are. However, due to the complexity of computing the exactminimum cost matching, previous algorithms could only run efficientlywhen using a limited number of features per shape, and could not scaleto perform retrievals from large databases. We present a contourmatching algorithm that quickly computes the minimum weight matchingbetween sets of descriptive local features using a recently introducedlow-distortion embedding of the Earth Mover's Distance (EMD) into anormed space. Given a novel embedded contour, the nearest neighborsin a database of embedded contours are retrieved in sublinear time viaapproximate nearest neighbors search. We demonstrate our shapematching method on databases of 10,000 images of human figures and60,000 images of handwritten digits.