Computing the Earth Mover's Distance under Transformations This project aims at extending the Earth Mover's Distance (EMD) between distributions to be invariant to some given set of distribution transformations. This problem is motivated by examples from content-based image retrieval. A monotonically convergent iteration is given, although the iteration may converge to only a locally optimal transformation. Specific cases are identified in which a globally optimal transformation can be computed directly, without the aid of our iteration. A gentle introduction to the EMD is also included.