Localized earth mover's distance for robust histogram comparison

Abstract

The Earth Mover's Distance (EMD) is a useful cross-bin distance metric for comparing two histograms. The EMD is based on the minimal cost that must be paid to transform one histogram into the other. But outlier noise in the histogram causes the EMD to be greatly exaggerated. In this paper, we propose the localized Earth Mover's Distance (LEMD). The LEMD separates noises from meaningful transportation of data by specifying local relations among bins, and gives a predefined penalty to those noises, according to the applications. An extended version of the tree-based transportation simplex algorithm is proposed for LEMD. The localized property of LEMD is formulated similarly to the original EMD with the thresholded ground distance, such as EMD-hat [7] and FastEMD [8]. However, we show that LEMD is more stable than EMD-hat for noise-added or shape-deformed data, and is faster than FastEMD that is the state of the art among EMD variants. © 2011 Springer-Verlag Berlin Heidelberg.