Earth Movers Distance-Based Simultaneous Comparison of Hyperspectral Endmembers and Proportions

A new approach for simultaneously comparing sets of hyperspectral endmembers and proportion values using the Earth Movers Distance (EMD) is presented. First, the EMD is defined and calculated per-pixel based on the proportion values and corresponding endmembers. Next, these per-pixel EMD distances are aggregated to obtain a final measure of dissimilarity. In particular, the proposed EMD approach can be used to simultaneously compare endmembers and proportion values with differing numbers of endmembers. The proposed method has a number of uses, including: computing the similarity between two sets of endmembers and proportion values that were obtained using any algorithm or underlying mixing model, clustering sets of hyperspectral endmember and proportion values, or evaluating spectral unmixing results by comparing estimated values to ground truth information. Experiments on both simulated and measured hyperspectral data sets demonstrate that the EMD is effective at simultaneous endmember and proportion comparison.