Fast and Robust Earth Mover's Distances

Abstract

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.