Report Number: CS-TN-98-86
Institution: Stanford University, Department of Computer Science
Title: The Earth Mover's Distance as a Metric for Image Retrieval
Author: Rubner, Yossi
Author: Tomasi, Carlo
Author: Guibas, Leonidas J.
Date: September 1998
Abstract: We introduce a metric between two distributions that we call the Earth Mover's Distance (EMD). The EMD is based on the minimal cost that must be paid to transform one distribution into the other, in a precise sense. We show that the EMD has attractive properties for content-based image retrieval. The most important one, as we show, is that it matches perceptual similarity better than other distances used for image retrieval. The EMD is based on a solution to the transportation problem from linear optimization, for which efficient algorithms are available, and also allows naturally for partial matching. It is more robust than histogram matching techniques, in that it can operate on variable-length representations of the distributions that avoid quantization and other binning problems typical of histograms. When used to compare distributions with the same overall mass, the EMD is a true metric. In this paper we focus on applications to color and texture, and we compare the retrieval performance of the EMD with that of other distances.