Fast contour matching using approximate earth mover's distance

Weighted graph matching is a good way to align a pair of shapes represented by a set of descriptive local features; the set of correspondences produced by the minimum cost matching between two shapes' features often reveals how similar the shapes are. However due to the complexity of computing the exact minimum cost matching, previous algorithms could only run efficiently when using a limited number of features per shape, and could not scale to perform retrievals from large databases. We present a contour matching algorithm that quickly computes the minimum weight matching between sets of descriptive local features using a recently introduced low-distortion embedding of the earth mover's distance (EMD) into a normed space. Given a novel embedded contour, the nearest neighbors in a database of embedded contours are retrieved in sublinear time via approximate nearest neighbors search with locality-sensitive hashing (LSH). We demonstrate our shape matching method on a database of 136,500 images of human figures. Our method achieves a speedup of four orders of magnitude over the exact method, at the cost of only a 4% reduction in accuracy.