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.